|\^/| Maple 2019 (X86 64 WINDOWS)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2019
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
| Type ? for help.
#BEGIN OUTFILE1
# before write maple top matter
# before write_ats library and user def block
#BEGIN ATS LIBRARY BLOCK
# Begin Function number 2
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s\n",str);
> fi;# end if 1;
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
# End Function number 2
# Begin Function number 3
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s",str);
> fi;# end if 1;
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
# End Function number 3
# Begin Function number 4
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> print(label,str);
> fi;# end if 1;
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
# End Function number 4
# Begin Function number 5
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 5
# Begin Function number 6
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> if vallen = 5 then # if number 1
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 6
# Begin Function number 7
> logitem_time := proc(fd,secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> fprintf(fd,"| ");
> if (secs_in >= 0) then # if number 0
> years_int := int_trunc(secs_in / glob_sec_in_year);
> sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
> days_int := int_trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := sec_temp mod int_trunc(glob_sec_in_day) ;
> hours_int := int_trunc(sec_temp / glob_sec_in_hour);
> sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
> minutes_int := int_trunc(sec_temp / glob_sec_in_minute);
> sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
> if (years_int > 0) then # if number 1
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 2
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 3
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 4
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 4
> else
> fprintf(fd," 0.0 Seconds");
> fi;# end if 3
> fprintf(fd," | \n");
> end;
logitem_time := proc(fd, secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
fprintf(fd, "");
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then
fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then
fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then
fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int,
minutes_int, sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, " 0.0 Seconds")
end if;
fprintf(fd, " | \n")
end proc
# End Function number 7
# Begin Function number 8
> omniout_timestr := proc(secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> if (secs_in >= 0) then # if number 3
> years_int := int_trunc(secs_in / glob_sec_in_year);
> sec_temp := (int_trunc(secs_in) mod int_trunc(glob_sec_in_year));
> days_int := int_trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_day)) ;
> hours_int := int_trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_hour));
> minutes_int := int_trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod int_trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 4
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 5
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 6
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 7
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 7
> else
> printf(" 0.0 Seconds\n");
> fi;# end if 6
> end;
omniout_timestr := proc(secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then
printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then
printf(" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then
printf(" = %d Hours %d Minutes %d Seconds\n", hours_int,
minutes_int, sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" 0.0 Seconds\n")
end if
end proc
# End Function number 8
# Begin Function number 9
> zero_ats_ar := proc(arr_a)
> global ATS_MAX_TERMS;
> local iii;
> iii := 1;
> while (iii <= ATS_MAX_TERMS) do # do number 1
> arr_a [iii] := glob__0;
> iii := iii + 1;
> od;# end do number 1
> end;
zero_ats_ar := proc(arr_a)
local iii;
global ATS_MAX_TERMS;
iii := 1;
while iii <= ATS_MAX_TERMS do arr_a[iii] := glob__0; iii := iii + 1
end do
end proc
# End Function number 9
# Begin Function number 10
> ats := proc(mmm_ats,arr_a,arr_b,jjj_ats)
> global ATS_MAX_TERMS;
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := glob__0;
> if (jjj_ats <= mmm_ats) then # if number 6
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> if ((lll_ats <= ATS_MAX_TERMS and (iii_ats <= ATS_MAX_TERMS) )) then # if number 7
> ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]);
> fi;# end if 7;
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 6;
> ret_ats;
> end;
ats := proc(mmm_ats, arr_a, arr_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
global ATS_MAX_TERMS;
ret_ats := glob__0;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
if lll_ats <= ATS_MAX_TERMS and iii_ats <= ATS_MAX_TERMS then
ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats])
end if;
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
# End Function number 10
# Begin Function number 11
> att := proc(mmm_att,arr_aa,arr_bb,jjj_att)
> global ATS_MAX_TERMS;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := glob__0;
> if (jjj_att < mmm_att) then # if number 6
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while ((iii_att < mmm_att) and (iii_att <= ATS_MAX_TERMS) ) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if ((lll_att <= ATS_MAX_TERMS and (iii_att <= ATS_MAX_TERMS) )) then # if number 7
> ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att);
> fi;# end if 7;
> iii_att := iii_att + 1;
> od;# end do number 1;
> ret_att := ret_att / c(mmm_att) ;
> fi;# end if 6;
> ret_att;
> end;
att := proc(mmm_att, arr_aa, arr_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global ATS_MAX_TERMS;
ret_att := glob__0;
if jjj_att < mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att < mmm_att and iii_att <= ATS_MAX_TERMS do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= ATS_MAX_TERMS and iii_att <= ATS_MAX_TERMS then
ret_att := ret_att
+ c(arr_aa[iii_att])*c(arr_bb[lll_att])*c(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/c(mmm_att)
end if;
ret_att
end proc
# End Function number 11
# Begin Function number 12
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
# End Function number 12
# Begin Function number 13
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
# End Function number 13
# Begin Function number 14
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
# End Function number 14
# Begin Function number 15
> logitem_good_digits := proc(file,rel_error)
> global glob_small_float,glob_prec;
> local good_digits;
> fprintf(file,"");
> fprintf(file,"%d",glob_min_good_digits);
> fprintf(file," | ");
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float, glob_prec;
fprintf(file, "");
fprintf(file, "%d", glob_min_good_digits);
fprintf(file, " | ")
end proc
# End Function number 15
# Begin Function number 16
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
# End Function number 16
# Begin Function number 17
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
# End Function number 17
# Begin Function number 18
> logitem_h_reason := proc(file)
> global glob_h_reason;
> fprintf(file,"");
> if (glob_h_reason = 1) then # if number 6
> fprintf(file,"Max H");
> elif
> (glob_h_reason = 2) then # if number 7
> fprintf(file,"Display Interval");
> elif
> (glob_h_reason = 3) then # if number 8
> fprintf(file,"Optimal");
> elif
> (glob_h_reason = 4) then # if number 9
> fprintf(file,"Pole Accuracy");
> elif
> (glob_h_reason = 5) then # if number 10
> fprintf(file,"Min H (Pole)");
> elif
> (glob_h_reason = 6) then # if number 11
> fprintf(file,"Pole");
> elif
> (glob_h_reason = 7) then # if number 12
> fprintf(file,"Opt Iter");
> else
> fprintf(file,"Impossible");
> fi;# end if 12
> fprintf(file," | ");
> end;
logitem_h_reason := proc(file)
global glob_h_reason;
fprintf(file, "");
if glob_h_reason = 1 then fprintf(file, "Max H")
elif glob_h_reason = 2 then fprintf(file, "Display Interval")
elif glob_h_reason = 3 then fprintf(file, "Optimal")
elif glob_h_reason = 4 then fprintf(file, "Pole Accuracy")
elif glob_h_reason = 5 then fprintf(file, "Min H (Pole)")
elif glob_h_reason = 6 then fprintf(file, "Pole")
elif glob_h_reason = 7 then fprintf(file, "Opt Iter")
else fprintf(file, "Impossible")
end if;
fprintf(file, " | ")
end proc
# End Function number 18
# Begin Function number 19
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
# End Function number 19
# Begin Function number 20
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file) fprintf(file, "\n") end proc
# End Function number 20
# Begin Function number 21
> chk_data := proc()
> global glob_max_iter,ALWAYS, ATS_MAX_TERMS;
> local errflag;
> errflag := false;
> if (glob_max_iter < 2) then # if number 12
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 12;
> if (errflag) then # if number 12
> quit;
> fi;# end if 12
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, ATS_MAX_TERMS;
errflag := false;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
# End Function number 21
# Begin Function number 22
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := c(clock_sec2);
> sub1 := c(t_end2-t_start2);
> sub2 := c(t2-t_start2);
> if (sub1 = glob__0) then # if number 12
> sec_left := glob__0;
> else
> if (sub2 > glob__0) then # if number 13
> rrr := (sub1/sub2);
> sec_left := rrr * c(ms2) - c(ms2);
> else
> sec_left := glob__0;
> fi;# end if 13
> fi;# end if 12;
> sec_left;
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := c(clock_sec2);
sub1 := c(t_end2 - t_start2);
sub2 := c(t2 - t_start2);
if sub1 = glob__0 then sec_left := glob__0
else
if glob__0 < sub2 then
rrr := sub1/sub2; sec_left := rrr*c(ms2) - c(ms2)
else sec_left := glob__0
end if
end if;
sec_left
end proc
# End Function number 22
# Begin Function number 23
> comp_percent := proc(t_end2,t_start2, t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub2 > glob_small_float) then # if number 12
> rrr := (glob__100*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 12;
> rrr;
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < sub2 then rrr := glob__100*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
# End Function number 23
# Begin Function number 24
> comp_rad_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 12
> ret := float_abs(term1 * glob_h / term2);
> else
> ret := glob_larger_float;
> fi;# end if 12;
> ret;
> #BOTTOM TWO TERM RADIUS ANALYSIS
> end;
comp_rad_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := float_abs(term1*glob_h/term2)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 24
# Begin Function number 25
> comp_ord_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM ORDER ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 12
> ret := glob__1 + float_abs(term2) * c(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(c(last_no));
> else
> ret := glob_larger_float;
> fi;# end if 12;
> ret;
> #BOTTOM TWO TERM ORDER ANALYSIS
> end;
comp_ord_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then
ret := glob__1 + float_abs(term2)*c(last_no)*
ln(float_abs(term1*glob_h/term2))/ln(c(last_no))
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 25
# Begin Function number 26
> c := proc(in_val)
> #To Force Conversion when needed
> local ret;
> ret := evalf(in_val);
> ret;
> #End Conversion
> end;
c := proc(in_val) local ret; ret := evalf(in_val); ret end proc
# End Function number 26
# Begin Function number 27
> comp_rad_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret,temp;
> temp := float_abs(term2*term2*c(last_no)+glob__m2*term2*term2-term1*term3*c(last_no)+term1*term3);
> if (float_abs(temp) > glob__0) then # if number 12
> ret := float_abs((term2*glob_h*term1)/(temp));
> else
> ret := glob_larger_float;
> fi;# end if 12;
> ret;
> #BOTTOM THREE TERM RADIUS ANALYSIS
> end;
comp_rad_from_three_terms := proc(term1, term2, term3, last_no)
local ret, temp;
global glob_h, glob_larger_float;
temp := float_abs(term2*term2*c(last_no) + glob__m2*term2*term2
- term1*term3*c(last_no) + term1*term3);
if glob__0 < float_abs(temp) then
ret := float_abs(term2*glob_h*term1/temp)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 27
# Begin Function number 28
> comp_ord_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM ORDER ANALYSIS
> local ret;
> ret := float_abs((glob__4*term1*term3*c(last_no)-glob__3*term1*term3-glob__4*term2*term2*c(last_no)+glob__4*term2*term2+term2*term2*c(last_no*last_no)-term1*term3*c(last_no*last_no))/(term2*term2*c(last_no)-glob__2*term2*term2-term1*term3*c(last_no)+term1*term3));
> ret;
> #TOP THREE TERM ORDER ANALYSIS
> end;
comp_ord_from_three_terms := proc(term1, term2, term3, last_no)
local ret;
ret := float_abs((glob__4*term1*term3*c(last_no) - glob__3*term1*term3
- glob__4*term2*term2*c(last_no) + glob__4*term2*term2
+ term2*term2*c(last_no*last_no) - term1*term3*c(last_no*last_no))
/(term2*term2*c(last_no) - glob__2*term2*term2
- term1*term3*c(last_no) + term1*term3));
ret
end proc
# End Function number 28
# Begin Function number 29
> comp_rad_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> #TOP SIX TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float,glob_six_term_ord_save;
> local ret,rm0,rm1,rm2,rm3,rm4,nr1,nr2,dr1,dr2,ds2,rad_c,ord_no,ds1,rcs;
> if ((term5 <> glob__0) and (term4 <> glob__0) and (term3 <> glob__0) and (term2 <> glob__0) and (term1 <> glob__0)) then # if number 12
> rm0 := term6/term5;
> rm1 := term5/term4;
> rm2 := term4/term3;
> rm3 := term3/term2;
> rm4 := term2/term1;
> nr1 := c(last_no-1)*rm0 - glob__2*c(last_no-2)*rm1 + c(last_no-3)*rm2;
> nr2 := c(last_no-2)*rm1 - glob__2*c(last_no-3)*rm2 + c(last_no-4)*rm3;
> dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
> dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
> ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
> ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
> if ((float_abs(nr1 * dr2 - nr2 * dr1) = glob__0) or (float_abs(dr1) = glob__0)) then # if number 13
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> else
> if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0) then # if number 14
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) -c(last_no)/glob__2;
> if (float_abs(rcs) <> glob__0) then # if number 15
> if (rcs > glob__0) then # if number 16
> rad_c := sqrt(rcs) * float_abs(glob_h);
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 16
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 15
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 14
> fi;# end if 13
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 12;
> glob_six_term_ord_save := ord_no;
> rad_c;
> #BOTTOM SIX TERM RADIUS ANALYSIS
> end;
comp_rad_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
local ret, rm0, rm1, rm2, rm3, rm4, nr1, nr2, dr1, dr2, ds2, rad_c, ord_no,
ds1, rcs;
global glob_h, glob_larger_float, glob_six_term_ord_save;
if term5 <> glob__0 and term4 <> glob__0 and term3 <> glob__0 and
term2 <> glob__0 and term1 <> glob__0 then
rm0 := term6/term5;
rm1 := term5/term4;
rm2 := term4/term3;
rm3 := term3/term2;
rm4 := term2/term1;
nr1 := c(last_no - 1)*rm0 - glob__2*c(last_no - 2)*rm1
+ c(last_no - 3)*rm2;
nr2 := c(last_no - 2)*rm1 - glob__2*c(last_no - 3)*rm2
+ c(last_no - 4)*rm3;
dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
if
float_abs(nr1*dr2 - nr2*dr1) = glob__0 or float_abs(dr1) = glob__0
then rad_c := glob_larger_float; ord_no := glob_larger_float
else
if glob__0 < float_abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no :=
(rcs*nr1 - ds1)/(glob__2*dr1) - c(last_no)/glob__2;
if float_abs(rcs) <> glob__0 then
if glob__0 < rcs then
rad_c := sqrt(rcs)*float_abs(glob_h)
else
rad_c := glob_larger_float;
ord_no := glob_larger_float
end if
else
rad_c := glob_larger_float; ord_no := glob_larger_float
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if;
glob_six_term_ord_save := ord_no;
rad_c
end proc
# End Function number 29
# Begin Function number 30
> comp_ord_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> global glob_six_term_ord_save;
> #TOP SIX TERM ORDER ANALYSIS
> #TOP SAVED FROM SIX TERM RADIUS ANALYSIS
> glob_six_term_ord_save;
> #BOTTOM SIX TERM ORDER ANALYSIS
> end;
comp_ord_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
global glob_six_term_ord_save;
glob_six_term_ord_save
end proc
# End Function number 30
# Begin Function number 31
> factorial_2 := proc(nnn)
> ret := nnn!;
> ret;;
> end;
Warning, `ret` is implicitly declared local to procedure `factorial_2`
factorial_2 := proc(nnn) local ret; ret := nnn!; ret end proc
# End Function number 31
# Begin Function number 32
> factorial_1 := proc(nnn)
> global ATS_MAX_TERMS,array_fact_1;
> local ret;
> if (nnn <= ATS_MAX_TERMS) then # if number 12
> if (array_fact_1[nnn] = 0) then # if number 13
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 13;
> else
> ret := factorial_2(nnn);
> fi;# end if 12;
> ret;
> end;
factorial_1 := proc(nnn)
local ret;
global ATS_MAX_TERMS, array_fact_1;
if nnn <= ATS_MAX_TERMS then
if array_fact_1[nnn] = 0 then
ret := factorial_2(nnn); array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := factorial_2(nnn)
end if;
ret
end proc
# End Function number 32
# Begin Function number 33
> factorial_3 := proc(mmm,nnn)
> global ATS_MAX_TERMS,array_fact_2;
> local ret;
> if ((nnn <= ATS_MAX_TERMS) and (mmm <= ATS_MAX_TERMS)) then # if number 12
> if (array_fact_2[mmm,nnn] = 0) then # if number 13
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 13;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 12;
> ret;
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global ATS_MAX_TERMS, array_fact_2;
if nnn <= ATS_MAX_TERMS and mmm <= ATS_MAX_TERMS then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := factorial_2(mmm)/factorial_2(nnn)
end if;
ret
end proc
# End Function number 33
# Begin Function number 34
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
# End Function number 34
# Begin Function number 35
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
# End Function number 35
# Begin Function number 36
> float_abs := proc(x)
> abs(x);
> end;
float_abs := proc(x) abs(x) end proc
# End Function number 36
# Begin Function number 37
> expt := proc(x,y)
> x^y;
> end;
expt := proc(x, y) x^y end proc
# End Function number 37
# Begin Function number 38
> neg := proc(x)
> -x;
> end;
neg := proc(x) -x end proc
# End Function number 38
# Begin Function number 39
> int_trunc := proc(x)
> trunc(x);
> end;
int_trunc := proc(x) trunc(x) end proc
# End Function number 39
# Begin Function number 40
> estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer)
> local desired_abs_gbl_error,range,estimated_steps,step_error;
> global glob_desired_digits_correct,ALWAYS,ATS_MAX_TERMS;
> omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
> desired_abs_gbl_error := expt(glob__10,c( -glob_desired_digits_correct)) * c(float_abs(c(estimated_answer)));
> omniout_float(ALWAYS,"estimated_h",32,estimated_h,32,"");
> omniout_float(ALWAYS,"estimated_answer",32,estimated_answer,32,"");
> omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,"");
> range := (x_end - x_start);
> omniout_float(ALWAYS,"range",32,range,32,"");
> estimated_steps := range / estimated_h;
> omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,"");
> step_error := (c(float_abs(desired_abs_gbl_error) /sqrt(c( estimated_steps))/c(ATS_MAX_TERMS)));
> omniout_float(ALWAYS,"step_error",32,step_error,32,"");
> (step_error);;
> end;
estimated_needed_step_error := proc(
x_start, x_end, estimated_h, estimated_answer)
local desired_abs_gbl_error, range, estimated_steps, step_error;
global glob_desired_digits_correct, ALWAYS, ATS_MAX_TERMS;
omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, "");
desired_abs_gbl_error :=
expt(glob__10, c(-glob_desired_digits_correct))*
c(float_abs(c(estimated_answer)));
omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, "");
omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, "")
;
omniout_float(ALWAYS, "desired_abs_gbl_error", 32,
desired_abs_gbl_error, 32, "");
range := x_end - x_start;
omniout_float(ALWAYS, "range", 32, range, 32, "");
estimated_steps := range/estimated_h;
omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, "");
step_error := c(float_abs(desired_abs_gbl_error)/(
sqrt(c(estimated_steps))*c(ATS_MAX_TERMS)));
omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
step_error
end proc
# End Function number 40
#END ATS LIBRARY BLOCK
#BEGIN USER FUNCTION BLOCK
#BEGIN BLOCK 3
#BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return(c(1.0)/c(x)/c(x));
> end;
exact_soln_y := proc(x) return c(1.0)/(c(x)*c(x)) end proc
#END USER DEF BLOCK
#END BLOCK 3
#END USER FUNCTION BLOCK
# before write_aux functions
# Begin Function number 2
> display_poles := proc()
> local rad_given;
> global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ;
> if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1
> rad_given := sqrt((array_x[1] - array_given_rad_poles[1,1]) * (array_x[1] - array_given_rad_poles[1,1]) + array_given_rad_poles[1,2] * array_given_rad_poles[1,2]);
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," ");
> omniout_float(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," ");
> if (rad_given < glob_least_given_sing) then # if number 2
> glob_least_given_sing := rad_given;
> fi;# end if 2;
> elif
> (glob_type_given_pole = 3) then # if number 2
> omniout_str(ALWAYS,"NO POLE (given) for Equation 1");
> elif
> (glob_type_given_pole = 5) then # if number 3
> omniout_str(ALWAYS,"SOME POLE (given) for Equation 1");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 1");
> fi;# end if 3;
> if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," ");
> if (array_rad_test_poles[1,1]< glob_least_ratio_sing) then # if number 4
> glob_least_ratio_sing := array_rad_test_poles[1,1];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," ");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," ");
> if (array_rad_test_poles[1,2]< glob_least_3_sing) then # if number 4
> glob_least_3_sing := array_rad_test_poles[1,2];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," ");
> if (array_rad_test_poles[1,3]< glob_least_6_sing) then # if number 4
> glob_least_6_sing := array_rad_test_poles[1,3];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1");
> fi;# end if 3
> ;
> end;
display_poles := proc()
local rad_given;
global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float,
glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord,
glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
glob_least_3_sing, glob_least_6_sing, glob_least_given_sing,
glob_least_ratio_sing, array_x;
if glob_type_given_pole = 1 or glob_type_given_pole = 2 then
rad_given := sqrt((array_x[1] - array_given_rad_poles[1, 1])*
(array_x[1] - array_given_rad_poles[1, 1])
+ array_given_rad_poles[1, 2]*array_given_rad_poles[1, 2]);
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 1 ", 4,
rad_given, 4, " ");
omniout_float(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles[1, 1], 4, " ");
if rad_given < glob_least_given_sing then
glob_least_given_sing := rad_given
end if
elif glob_type_given_pole = 3 then
omniout_str(ALWAYS, "NO POLE (given) for Equation 1")
elif glob_type_given_pole = 5 then
omniout_str(ALWAYS, "SOME POLE (given) for Equation 1")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 1")
end if;
if array_rad_test_poles[1, 1] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (ratio test) for eq 1 ", 4,
array_rad_test_poles[1, 1], 4, " ");
if array_rad_test_poles[1, 1] < glob_least_ratio_sing then
glob_least_ratio_sing := array_rad_test_poles[1, 1]
end if;
omniout_float(ALWAYS,
"Order of pole (ratio test) ", 4,
array_ord_test_poles[1, 1], 4, " ")
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 2] and
array_rad_test_poles[1, 2] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 1 ", 4,
array_rad_test_poles[1, 2], 4, " ");
if array_rad_test_poles[1, 2] < glob_least_3_sing then
glob_least_3_sing := array_rad_test_poles[1, 2]
end if;
omniout_float(ALWAYS,
"Order of pole (three term test) ", 4,
array_ord_test_poles[1, 2], 4, " ")
else
omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 3] and
array_rad_test_poles[1, 3] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 1 ", 4,
array_rad_test_poles[1, 3], 4, " ");
if array_rad_test_poles[1, 3] < glob_least_6_sing then
glob_least_6_sing := array_rad_test_poles[1, 3]
end if;
omniout_float(ALWAYS,
"Order of pole (six term test) ", 4,
array_ord_test_poles[1, 3], 4, " ")
else
omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 1")
end if
end proc
# End Function number 2
# Begin Function number 3
> my_check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 3
> ret := glob__1;
> else
> ret := glob__m1;
> fi;# end if 3;
> ret;;
> end;
my_check_sign := proc(x0, xf)
local ret;
if x0 < xf then ret := glob__1 else ret := glob__m1 end if; ret
end proc
# End Function number 3
# Begin Function number 4
> est_size_answer := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local min_size;
> min_size := glob_estimated_size_answer;
> if (float_abs(array_y[1]) < min_size) then # if number 3
> min_size := float_abs(array_y[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> if (min_size < glob__1) then # if number 3
> min_size := glob__1;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> min_size;
> end;
est_size_answer := proc()
local min_size;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_y_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
min_size := glob_estimated_size_answer;
if float_abs(array_y[1]) < min_size then
min_size := float_abs(array_y[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if min_size < glob__1 then
min_size := glob__1;
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
min_size
end proc
# End Function number 4
# Begin Function number 5
> test_suggested_h := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> max_estimated_step_error := glob__small;
> no_terms := ATS_MAX_TERMS;
> hn_div_ho := glob__0_5;
> hn_div_ho_2 := glob__0_25;
> hn_div_ho_3 := glob__0_125;
> omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,"");
> omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,"");
> omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,"");
> est_tmp := float_abs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3);
> if (est_tmp >= max_estimated_step_error) then # if number 3
> max_estimated_step_error := est_tmp;
> fi;# end if 3;
> omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,"");
> max_estimated_step_error;
> end;
test_suggested_h := proc()
local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3,
no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_y_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
max_estimated_step_error := glob__small;
no_terms := ATS_MAX_TERMS;
hn_div_ho := glob__0_5;
hn_div_ho_2 := glob__0_25;
hn_div_ho_3 := glob__0_125;
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, "");
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, "");
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, "");
est_tmp := float_abs(array_y[no_terms - 3]
+ array_y[no_terms - 2]*hn_div_ho
+ array_y[no_terms - 1]*hn_div_ho_2
+ array_y[no_terms]*hn_div_ho_3);
if max_estimated_step_error <= est_tmp then
max_estimated_step_error := est_tmp
end if;
omniout_float(ALWAYS, "max_estimated_step_error", 32,
max_estimated_step_error, 32, "");
max_estimated_step_error
end proc
# End Function number 5
# Begin Function number 6
> track_estimated_error := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> no_terms := ATS_MAX_TERMS;
> hn_div_ho := glob__0_5;
> hn_div_ho_2 := glob__0_25;
> hn_div_ho_3 := glob__0_125;
> est_tmp := c(float_abs(array_y[no_terms-3])) + c(float_abs(array_y[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y[no_terms])) * c(hn_div_ho_3);
> if (glob_prec * c(float_abs(array_y[1])) > c(est_tmp)) then # if number 3
> est_tmp := c(glob_prec) * c(float_abs(array_y[1]));
> fi;# end if 3;
> if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 3
> array_max_est_error[1] := c(est_tmp);
> fi;# end if 3
> ;
> end;
track_estimated_error := proc()
local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_y_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
no_terms := ATS_MAX_TERMS;
hn_div_ho := glob__0_5;
hn_div_ho_2 := glob__0_25;
hn_div_ho_3 := glob__0_125;
est_tmp := c(float_abs(array_y[no_terms - 3]))
+ c(float_abs(array_y[no_terms - 2]))*c(hn_div_ho)
+ c(float_abs(array_y[no_terms - 1]))*c(hn_div_ho_2)
+ c(float_abs(array_y[no_terms]))*c(hn_div_ho_3);
if c(est_tmp) < glob_prec*c(float_abs(array_y[1])) then
est_tmp := c(glob_prec)*c(float_abs(array_y[1]))
end if;
if c(array_max_est_error[1]) <= c(est_tmp) then
array_max_est_error[1] := c(est_tmp)
end if
end proc
# End Function number 6
# Begin Function number 7
> reached_interval := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local ret;
> if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 3
> ret := true;
> else
> ret := false;
> fi;# end if 3;
> return(ret);
> end;
reached_interval := proc()
local ret;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_y_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
if glob_check_sign*glob_next_display - glob_h/glob__10 <=
glob_check_sign*array_x[1] then ret := true
else ret := false
end if;
return ret
end proc
# End Function number 7
# Begin Function number 8
> display_alot := proc(iter)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err;
> #TOP DISPLAY ALOT
> if (reached_interval()) then # if number 3
> if (iter >= 0) then # if number 4
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> closed_form_val_y := evalf(exact_soln_y(ind_var));
> omniout_float(ALWAYS,"y[1] (closed_form) ",33,closed_form_val_y,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> abserr := float_abs(numeric_val - closed_form_val_y);
> omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> if (c(float_abs(closed_form_val_y)) > c(glob_prec)) then # if number 5
> relerr := abserr/float_abs(closed_form_val_y);
> if (c(relerr) > c(glob_prec)) then # if number 6
> glob_good_digits := round(-log10(relerr));
> else
> glob_good_digits := Digits;
> fi;# end if 6;
> else
> relerr := glob__m1 ;
> glob_good_digits := -16;
> fi;# end if 5;
> if (glob_good_digits < glob_min_good_digits) then # if number 5
> glob_min_good_digits := glob_good_digits;
> fi;# end if 5;
> if (glob_apfp_est_good_digits < glob_min_apfp_est_good_digits) then # if number 5
> glob_min_apfp_est_good_digits := glob_apfp_est_good_digits;
> fi;# end if 5;
> if (evalf(float_abs(numeric_val)) > glob_prec) then # if number 5
> est_rel_err := evalf(array_max_est_error[1]*100.0 * sqrt(glob_iter)*23*ATS_MAX_TERMS/float_abs(numeric_val));
> if (evalf(est_rel_err) > glob_prec) then # if number 6
> glob_est_digits := -int_trunc(log10(est_rel_err)) + 3;
> else
> glob_est_digits := Digits;
> fi;# end if 6;
> else
> relerr := glob__m1 ;
> glob_est_digits := -16;
> fi;# end if 5;
> array_est_digits[1] := glob_est_digits;
> if (glob_iter = 1) then # if number 5
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 5;
> array_est_rel_error[1] := est_rel_err;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr * c(100.0),20,"%");
> omniout_int(INFO,"Desired digits ",32,glob_desired_digits_correct,4," ");
> omniout_int(INFO,"Estimated correct digits ",32,glob_est_digits,4," ");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> fi;# end if 4;
> #BOTTOM DISPLAY ALOT
> fi;# end if 3;
> end;
display_alot := proc(iter)
local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no,
est_rel_err;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_y_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
if reached_interval() then
if 0 <= iter then
ind_var := array_x[1];
omniout_float(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
closed_form_val_y := evalf(exact_soln_y(ind_var));
omniout_float(ALWAYS, "y[1] (closed_form) ", 33,
closed_form_val_y, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
abserr := float_abs(numeric_val - closed_form_val_y);
omniout_float(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
if c(glob_prec) < c(float_abs(closed_form_val_y)) then
relerr := abserr/float_abs(closed_form_val_y);
if c(glob_prec) < c(relerr) then
glob_good_digits := round(-log10(relerr))
else glob_good_digits := Digits
end if
else relerr := glob__m1; glob_good_digits := -16
end if;
if glob_good_digits < glob_min_good_digits then
glob_min_good_digits := glob_good_digits
end if;
if glob_apfp_est_good_digits < glob_min_apfp_est_good_digits
then glob_min_apfp_est_good_digits := glob_apfp_est_good_digits
end if;
if glob_prec < evalf(float_abs(numeric_val)) then
est_rel_err := evalf(array_max_est_error[1]*100.0*
sqrt(glob_iter)*23*ATS_MAX_TERMS/float_abs(numeric_val))
;
if glob_prec < evalf(est_rel_err) then
glob_est_digits := -int_trunc(log10(est_rel_err)) + 3
else glob_est_digits := Digits
end if
else relerr := glob__m1; glob_est_digits := -16
end if;
array_est_digits[1] := glob_est_digits;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
array_est_rel_error[1] := est_rel_err;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr*c(100.0), 20, "%");
omniout_int(INFO, "Desired digits ", 32,
glob_desired_digits_correct, 4, " ");
omniout_int(INFO, "Estimated correct digits ", 32,
glob_est_digits, 4, " ");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end if
end proc
# End Function number 8
# Begin Function number 9
> prog_report := proc(x_start,x_end)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := (clock_sec1) - (glob_orig_start_sec);
> glob_clock_sec := (clock_sec1) - (glob_clock_start_sec);
> left_sec := (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1);
> expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h) ,( clock_sec1) - (glob_orig_start_sec));
> opt_clock_sec := ( clock_sec1) - (glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec));
> glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
> percent_done := comp_percent((x_end),(x_start),(array_x[1]) + (glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr((total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr((glob_clock_sec));
> if (c(percent_done) < glob__100) then # if number 3
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr((expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr((glob_optimal_expect_sec));
> omniout_str_noeol(INFO,"Expected Total Time ");
> omniout_timestr((glob_total_exp_sec));
> fi;# end if 3;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr((left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_y_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec := clock_sec1 - glob_orig_start_sec;
glob_clock_sec := clock_sec1 - glob_clock_start_sec;
left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1;
expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h,
clock_sec1 - glob_orig_start_sec);
opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec;
glob_optimal_expect_sec :=
comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec)
;
glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h);
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(total_clock_sec);
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(glob_clock_sec);
if c(percent_done) < glob__100 then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(expect_sec);
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(glob_optimal_expect_sec);
omniout_str_noeol(INFO, "Expected Total Time ");
omniout_timestr(glob_total_exp_sec)
end if;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(left_sec);
omniout_float(INFO, "Percent Done ", 33,
percent_done, 4, "%")
end proc
# End Function number 9
# Begin Function number 10
> check_for_pole := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad, last_no;
> #TOP CHECK FOR POLE
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,1] := glob_larger_float;
> array_ord_test_poles[1,1] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 3
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 3;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 3
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 4
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 5
> found_sing := 0;
> fi;# end if 5;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 5
> if (rad_c < array_rad_test_poles[1,1]) then # if number 6
> array_rad_test_poles[1,1] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,1] := rad_c;
> array_ord_test_poles[1,1] := tmp_ord;
> fi;# end if 6;
> fi;# end if 5;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,2] := glob_larger_float;
> array_ord_test_poles[1,2] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 5
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 5;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 6
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 7
> found_sing := 0;
> fi;# end if 7;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 7
> if (rad_c < array_rad_test_poles[1,2]) then # if number 8
> array_rad_test_poles[1,2] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,2] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 9
> glob_min_pole_est := rad_c;
> fi;# end if 9;
> array_ord_test_poles[1,2] := tmp_ord;
> fi;# end if 8;
> fi;# end if 7;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,3] := glob_larger_float;
> array_ord_test_poles[1,3] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 7
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 7;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 8
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 9
> found_sing := 0;
> fi;# end if 9;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 9
> if (rad_c < array_rad_test_poles[1,3]) then # if number 10
> array_rad_test_poles[1,3] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,3] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 11
> glob_min_pole_est := rad_c;
> fi;# end if 11;
> array_ord_test_poles[1,3] := tmp_ord;
> fi;# end if 10;
> fi;# end if 9;
> #BOTTOM general radius test1
> #START ADJUST ALL SERIES
> if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 9
> h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius;
> omniout_str(ALWAYS,"SETTING H FOR POLE");
> glob_h_reason := 6;
> if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> h_new := glob_min_h;
> glob_h_reason := 5;
> fi;# end if 10;
> term := 1;
> ratio := c(1.0);
> while (term <= ATS_MAX_TERMS) do # do number 1
> array_y[term] := array_y[term]* ratio;
> array_y_higher[1,term] := array_y_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / float_abs(glob_h);
> term := term + 1;
> od;# end do number 1;
> glob_h := h_new;
> fi;# end if 9;
> #BOTTOM ADJUST ALL SERIES
> ;
> if (reached_interval()) then # if number 9
> display_poles();
> fi;# end if 9
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2,
term3, part1, part2, part3, part4, part5, part6, part7, part8, part9,
part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4,
found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio,
prev_tmp_rad, last_no;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_y_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 1] := glob_larger_float;
array_ord_test_poles[1, 1] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do
tmp_rad := comp_rad_from_ratio(array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 1] then
array_rad_test_poles[1, 1] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_ratio(array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
array_rad_test_poles[1, 1] := rad_c;
array_ord_test_poles[1, 1] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 2] := glob_larger_float;
array_ord_test_poles[1, 2] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do
tmp_rad := comp_rad_from_three_terms(
array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 2] then
array_rad_test_poles[1, 2] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_three_terms(
array_y_higher[1, last_no - 2],
array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
last_no);
array_rad_test_poles[1, 2] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 2] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 3] := glob_larger_float;
array_ord_test_poles[1, 3] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do
tmp_rad := comp_rad_from_six_terms(array_y_higher[1, last_no - 5],
array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3],
array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 3] then
array_rad_test_poles[1, 3] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_six_terms(
array_y_higher[1, last_no - 5],
array_y_higher[1, last_no - 4],
array_y_higher[1, last_no - 3],
array_y_higher[1, last_no - 2],
array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
last_no);
array_rad_test_poles[1, 3] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 3] := tmp_ord
end if
end if;
if
float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h)
then
h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius;
omniout_str(ALWAYS, "SETTING H FOR POLE");
glob_h_reason := 6;
if glob_check_sign*h_new < glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
h_new := glob_min_h;
glob_h_reason := 5
end if;
term := 1;
ratio := c(1.0);
while term <= ATS_MAX_TERMS do
array_y[term] := array_y[term]*ratio;
array_y_higher[1, term] := array_y_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/float_abs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
if reached_interval() then display_poles() end if
end proc
# End Function number 10
# Begin Function number 11
> atomall := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> # before write maple main top matter
> # before generate constants assign
> # before generate globals assign
> #END OUTFILE1
> #BEGIN OUTFILE2
> #END OUTFILE2
> #BEGIN ATOMHDR1
> #emit pre neg ID_CONST $eq_no = 1
> array_tmp1[1] := neg(array_const_2D0[1]);
> #emit pre div CONST - LINEAR $eq_no = 1 i = 1
> array_tmp2[1] := array_tmp1[1] / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 1
> array_tmp3[1] := array_tmp2[1] / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 1
> array_tmp4[1] := array_tmp3[1] / array_x[1];
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp5[1] := array_const_0D0[1] + array_tmp4[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y_set_initial[1,2]) then # if number 1
> if (1 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp5[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
> if (2 <= ATS_MAX_TERMS) then # if number 3
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(1);
> array_y_higher[2,1] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre div CONST - LINEAR $eq_no = 1 i = 2
> array_tmp2[2] := neg(array_tmp2[1])* array_x[2] / array_x[1];
> #emit pre div CONST - LINEAR $eq_no = 1 i = 3
> #emit pre div CONST - LINEAR $eq_no = 1 i = 4
> #emit pre div CONST - LINEAR $eq_no = 1 i = 5
> #emit pre div FULL - LINEAR $eq_no = 1 i = 2
> array_tmp3[2] := (array_tmp2[2] - array_tmp3[1] * array_x[2]) / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 2
> array_tmp4[2] := (array_tmp3[2] - array_tmp4[1] * array_x[2]) / array_x[1];
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp5[2] := array_tmp4[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y_set_initial[1,3]) then # if number 1
> if (2 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp5[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2));
> if (3 <= ATS_MAX_TERMS) then # if number 3
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y_higher[2,2] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> array_tmp2[3] := neg(array_tmp2[2])* array_x[2] / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 3
> array_tmp3[3] := (array_tmp2[3] - array_tmp3[2] * array_x[2]) / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 3
> array_tmp4[3] := (array_tmp3[3] - array_tmp4[2] * array_x[2]) / array_x[1];
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp5[3] := array_tmp4[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y_set_initial[1,4]) then # if number 1
> if (3 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp5[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3));
> if (4 <= ATS_MAX_TERMS) then # if number 3
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y_higher[2,3] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> array_tmp2[4] := neg(array_tmp2[3])* array_x[2] / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 4
> array_tmp3[4] := (array_tmp2[4] - array_tmp3[3] * array_x[2]) / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 4
> array_tmp4[4] := (array_tmp3[4] - array_tmp4[3] * array_x[2]) / array_x[1];
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp5[4] := array_tmp4[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y_set_initial[1,5]) then # if number 1
> if (4 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp5[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4));
> if (5 <= ATS_MAX_TERMS) then # if number 3
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y_higher[2,4] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> array_tmp2[5] := neg(array_tmp2[4])* array_x[2] / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 5
> array_tmp3[5] := (array_tmp2[5] - array_tmp3[4] * array_x[2]) / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 5
> array_tmp4[5] := (array_tmp3[5] - array_tmp4[4] * array_x[2]) / array_x[1];
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp5[5] := array_tmp4[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y_set_initial[1,6]) then # if number 1
> if (5 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp5[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5));
> if (6 <= ATS_MAX_TERMS) then # if number 3
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y_higher[2,5] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= ATS_MAX_TERMS) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit div CONST LINEAR (NOP) $eq_no = 1 i = 1
> array_tmp2[kkk] := array_tmp1[1] * array_x[kkk];
> #emit div FULL LINEAR $eq_no = 1 i = 1
> array_tmp3[kkk] := neg(ats(kkk,array_x,array_tmp3,2)) / array_x[1];
> #emit div FULL LINEAR $eq_no = 1 i = 1
> array_tmp4[kkk] := neg(ats(kkk,array_x,array_tmp4,2)) / array_x[1];
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp5[kkk] := array_tmp4[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1
> if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2
> temporary := c(array_tmp5[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
> array_y[kkk + order_d] := c(temporary);
> array_y_higher[1,kkk + order_d] := c(temporary);
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := c(temporary) / c(glob_h) * c(adj2);
> else
> temporary := c(temporary);
> fi;# end if 4;
> array_y_higher[adj3,term] := c(temporary);
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 1
> fi;# end if 2
> fi;# end if 1;
> kkk := kkk + 1;
> od;# end do number 1;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_y_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
array_tmp1[1] := neg(array_const_2D0[1]);
array_tmp2[1] := array_tmp1[1]/array_x[1];
array_tmp3[1] := array_tmp2[1]/array_x[1];
array_tmp4[1] := array_tmp3[1]/array_x[1];
array_tmp5[1] := array_const_0D0[1] + array_tmp4[1];
if not array_y_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
if 2 <= ATS_MAX_TERMS then
array_y[2] := temporary; array_y_higher[1, 2] := temporary
end if;
temporary := c(temporary)*c(1)/c(glob_h);
array_y_higher[2, 1] := c(temporary)
end if
end if;
kkk := 2;
array_tmp2[2] := neg(array_tmp2[1])*array_x[2]/array_x[1];
array_tmp3[2] := (-array_x[2]*array_tmp3[1] + array_tmp2[2])/array_x[1]
;
array_tmp4[2] := (-array_x[2]*array_tmp4[1] + array_tmp3[2])/array_x[1]
;
array_tmp5[2] := array_tmp4[2];
if not array_y_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
if 3 <= ATS_MAX_TERMS then
array_y[3] := temporary; array_y_higher[1, 3] := temporary
end if;
temporary := c(temporary)*c(2)/c(glob_h);
array_y_higher[2, 2] := c(temporary)
end if
end if;
kkk := 3;
array_tmp2[3] := neg(array_tmp2[2])*array_x[2]/array_x[1];
array_tmp3[3] := (-array_x[2]*array_tmp3[2] + array_tmp2[3])/array_x[1]
;
array_tmp4[3] := (-array_x[2]*array_tmp4[2] + array_tmp3[3])/array_x[1]
;
array_tmp5[3] := array_tmp4[3];
if not array_y_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[3])*expt(glob_h, c(1))*c(factorial_3(2, 3));
if 4 <= ATS_MAX_TERMS then
array_y[4] := temporary; array_y_higher[1, 4] := temporary
end if;
temporary := c(temporary)*c(3)/c(glob_h);
array_y_higher[2, 3] := c(temporary)
end if
end if;
kkk := 4;
array_tmp2[4] := neg(array_tmp2[3])*array_x[2]/array_x[1];
array_tmp3[4] := (-array_x[2]*array_tmp3[3] + array_tmp2[4])/array_x[1]
;
array_tmp4[4] := (-array_x[2]*array_tmp4[3] + array_tmp3[4])/array_x[1]
;
array_tmp5[4] := array_tmp4[4];
if not array_y_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[4])*expt(glob_h, c(1))*c(factorial_3(3, 4));
if 5 <= ATS_MAX_TERMS then
array_y[5] := temporary; array_y_higher[1, 5] := temporary
end if;
temporary := c(temporary)*c(4)/c(glob_h);
array_y_higher[2, 4] := c(temporary)
end if
end if;
kkk := 5;
array_tmp2[5] := neg(array_tmp2[4])*array_x[2]/array_x[1];
array_tmp3[5] := (-array_x[2]*array_tmp3[4] + array_tmp2[5])/array_x[1]
;
array_tmp4[5] := (-array_x[2]*array_tmp4[4] + array_tmp3[5])/array_x[1]
;
array_tmp5[5] := array_tmp4[5];
if not array_y_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[5])*expt(glob_h, c(1))*c(factorial_3(4, 5));
if 6 <= ATS_MAX_TERMS then
array_y[6] := temporary; array_y_higher[1, 6] := temporary
end if;
temporary := c(temporary)*c(5)/c(glob_h);
array_y_higher[2, 5] := c(temporary)
end if
end if;
kkk := 6;
while kkk <= ATS_MAX_TERMS do
array_tmp2[kkk] := array_tmp1[1]*array_x[kkk];
array_tmp3[kkk] := neg(ats(kkk, array_x, array_tmp3, 2))/array_x[1]
;
array_tmp4[kkk] := neg(ats(kkk, array_x, array_tmp4, 2))/array_x[1]
;
array_tmp5[kkk] := array_tmp4[kkk];
order_d := 1;
if kkk + order_d <= ATS_MAX_TERMS then
if not array_y_set_initial[1, kkk + order_d] then
temporary := c(array_tmp5[kkk])*expt(glob_h, c(order_d))*
c(factorial_3(kkk - 1, kkk + order_d - 1));
array_y[kkk + order_d] := c(temporary);
array_y_higher[1, kkk + order_d] := c(temporary);
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while
1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1
do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := c(temporary)*c(adj2)/c(glob_h)
else temporary := c(temporary)
end if;
array_y_higher[adj3, term] := c(temporary)
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
# End Function number 12
#END OUTFILE5
# Begin Function number 12
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it;
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> ATS_MAX_TERMS := 20;
> # before first input block
> #BEGIN FIRST INPUT BLOCK
> #BEGIN BLOCK 1
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=20;
> #END BLOCK 1
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> # before generate arrays
> array_y_init:= Array(0..(20),[]);
> array_norms:= Array(0..(20),[]);
> array_fact_1:= Array(0..(20),[]);
> array_1st_rel_error:= Array(0..(2),[]);
> array_last_rel_error:= Array(0..(2),[]);
> array_est_rel_error:= Array(0..(2),[]);
> array_max_est_error:= Array(0..(2),[]);
> array_type_pole:= Array(0..(2),[]);
> array_type_real_pole:= Array(0..(2),[]);
> array_type_complex_pole:= Array(0..(2),[]);
> array_est_digits:= Array(0..(2),[]);
> array_y:= Array(0..(20),[]);
> array_x:= Array(0..(20),[]);
> array_tmp0:= Array(0..(20),[]);
> array_tmp1:= Array(0..(20),[]);
> array_tmp2:= Array(0..(20),[]);
> array_tmp3:= Array(0..(20),[]);
> array_tmp4:= Array(0..(20),[]);
> array_tmp5:= Array(0..(20),[]);
> array_m1:= Array(0..(20),[]);
> array_y_higher := Array(0..(2) ,(0..20+ 1),[]);
> array_y_higher_work := Array(0..(2) ,(0..20+ 1),[]);
> array_y_higher_work2 := Array(0..(2) ,(0..20+ 1),[]);
> array_y_set_initial := Array(0..(2) ,(0..20+ 1),[]);
> array_given_rad_poles := Array(0..(2) ,(0..3+ 1),[]);
> array_given_ord_poles := Array(0..(2) ,(0..3+ 1),[]);
> array_rad_test_poles := Array(0..(2) ,(0..4+ 1),[]);
> array_ord_test_poles := Array(0..(2) ,(0..4+ 1),[]);
> array_fact_2 := Array(0..(20) ,(0..20+ 1),[]);
> # before generate constants
> # before generate globals definition
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> # before generate const definition
> # before arrays initialized
> term := 1;
> while (term <= 20) do # do number 1
> array_y_init[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_norms[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_fact_1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_1st_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_last_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_est_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_max_est_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_real_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_complex_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_est_digits[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_y[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_x[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp0[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp3[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp4[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp5[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_m1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 20) do # do number 2
> array_y_higher[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 20) do # do number 2
> array_y_higher_work[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 20) do # do number 2
> array_y_higher_work2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 20) do # do number 2
> array_y_set_initial[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_rad_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_ord_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_rad_test_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_ord_test_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=20) do # do number 1
> term := 1;
> while (term <= 20) do # do number 2
> array_fact_2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> # before symbols initialized
> #BEGIN SYMBOLS INITIALIZATED
> zero_ats_ar(array_y);
> zero_ats_ar(array_x);
> zero_ats_ar(array_tmp0);
> zero_ats_ar(array_tmp1);
> zero_ats_ar(array_tmp2);
> zero_ats_ar(array_tmp3);
> zero_ats_ar(array_tmp4);
> zero_ats_ar(array_tmp5);
> zero_ats_ar(array_m1);
> zero_ats_ar(array_const_1);
> array_const_1[1] := c(1);
> zero_ats_ar(array_const_0D0);
> array_const_0D0[1] := c(0.0);
> zero_ats_ar(array_const_2D0);
> array_const_2D0[1] := c(2.0);
> zero_ats_ar(array_m1);
> array_m1[1] := glob__m1;
> #END SYMBOLS INITIALIZATED
> # before generate factorials init
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= ATS_MAX_TERMS) do # do number 1
> jjjf := 0;
> while (jjjf <= ATS_MAX_TERMS) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Table
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> glob_yes_pole := 4;
> glob_no_pole := 3;
> glob_not_given := 0;
> glob_no_sing_tests := 4;
> glob_ratio_test := 1;
> glob_three_term_test := 2;
> glob_six_term_test := 3;
> glob_log_10 := log(c(10.0));
> MAX_UNCHANGED := 10;
> glob__small := c(0.1e-50);
> glob_small_float := c(0.1e-50);
> glob_smallish_float := c(0.1e-60);
> glob_large_float := c(1.0e100);
> glob_larger_float := c(1.1e100);
> glob__m2 := c(-2);
> glob__m1 := c(-1);
> glob__0 := c(0);
> glob__1 := c(1);
> glob__2 := c(2);
> glob__3 := c(3);
> glob__4 := c(4);
> glob__5 := c(5);
> glob__8 := c(8);
> glob__10 := c(10);
> glob__100 := c(100);
> glob__pi := c(0.0);
> glob__0_5 := c(0.5);
> glob__0_8 := c(0.8);
> glob__m0_8 := c(-0.8);
> glob__0_25 := c(0.25);
> glob__0_125 := c(0.125);
> glob_prec := c(1.0e-16);
> glob_check_sign := c(1.0);
> glob_desired_digits_correct := c(8.0);
> glob_max_estimated_step_error := c(0.0);
> glob_ratio_of_radius := c(0.1);
> glob_percent_done := c(0.0);
> glob_total_exp_sec := c(0.1);
> glob_optimal_expect_sec := c(0.1);
> glob_estimated_size_answer := c(100.0);
> glob_almost_1 := c(0.9990);
> glob_clock_sec := c(0.0);
> glob_clock_start_sec := c(0.0);
> glob_disp_incr := c(0.1);
> glob_h := c(0.1);
> glob_diff_rc_fm := c(0.1);
> glob_diff_rc_fmm1 := c(0.1);
> glob_diff_rc_fmm2 := c(0.1);
> glob_diff_ord_fm := c(0.1);
> glob_diff_ord_fmm1 := c(0.1);
> glob_diff_ord_fmm2 := c(0.1);
> glob_six_term_ord_save := c(0.1);
> glob_guess_error_rc := c(0.1);
> glob_guess_error_ord := c(0.1);
> glob_least_given_sing := c(9.9e200);
> glob_least_ratio_sing := c(9.9e200);
> glob_least_3_sing := c(9.9e100);
> glob_least_6_sing := c(9.9e100);
> glob_last_good_h := c(0.1);
> glob_max_h := c(0.1);
> glob_min_h := c(0.000001);
> glob_display_interval := c(0.1);
> glob_abserr := c(0.1e-10);
> glob_relerr := c(0.1e-10);
> glob_min_pole_est := c(0.1e+10);
> glob_max_rel_trunc_err := c(0.1e-10);
> glob_max_trunc_err := c(0.1e-10);
> glob_max_hours := c(0.0);
> glob_optimal_clock_start_sec := c(0.0);
> glob_optimal_start := c(0.0);
> glob_upper_ratio_limit := c(1.0001);
> glob_lower_ratio_limit := c(0.9999);
> glob_max_sec := c(10000.0);
> glob_orig_start_sec := c(0.0);
> glob_normmax := c(0.0);
> glob_max_minutes := c(0.0);
> glob_next_display := c(0.0);
> glob_est_digits := 1;
> glob_subiter_method := 3;
> glob_html_log := true;
> glob_min_good_digits := 99999;
> glob_good_digits := 0;
> glob_min_apfp_est_good_digits := 99999;
> glob_apfp_est_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> glob_h_reason := 0;
> glob_sec_in_minute := 60 ;
> glob_min_in_hour := 60;
> glob_hours_in_day := 24;
> glob_days_in_year := 365;
> glob_sec_in_hour := 3600;
> glob_sec_in_day := 86400;
> glob_sec_in_year := 31536000;
> glob_not_yet_finished := true;
> glob_initial_pass := true;
> glob_not_yet_start_msg := true;
> glob_reached_optimal_h := false;
> glob_optimal_done := false;
> glob_type_given_pole := 0;
> glob_optimize := false;
> glob_look_poles := false;
> glob_dump_closed_form := false;
> glob_max_iter := 1000;
> glob_no_eqs := 0;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_start := 0;
> glob_iter := 0;
> # before generate set diff initial
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> # before generate init omniout const
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> ATS_MAX_TERMS := 20;
> glob_iolevel := INFO;
> # set default block
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> glob_display_flag := true;
> glob_no_eqs := 1;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := (0.0);
> glob_max_minutes := (15.0);
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############R:\Temp/sing3_backpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = neg ( 2.0 ) / x / x / x ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=20;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := c(-0.7);");
> omniout_str(ALWAYS,"x_end := c(-2.0);");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_type_given_pole := 1;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_rad_poles[1,1] := c(0.0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_rad_poles[1,2] := c(0.0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_ord_poles[1,1] := c(2.0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_ord_poles[1,2] := c(0.0);");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=12;");
> omniout_str(ALWAYS,"glob_max_minutes:=(3.0);");
> omniout_str(ALWAYS,"glob_subiter_method:=2;");
> omniout_str(ALWAYS,"glob_max_iter:=1000000;");
> omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);");
> omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);");
> omniout_str(ALWAYS,"glob_look_poles:=true;");
> omniout_str(ALWAYS,"glob_h:=c(0.001);");
> omniout_str(ALWAYS,"glob_display_interval:=c(0.01);");
> omniout_str(ALWAYS,"glob_h_reason:=1;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"return(c(1.0)/c(x)/c(x));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := glob__0;
> glob_smallish_float := glob__0;
> glob_large_float := c(1.0e100);
> glob_larger_float := c( 1.1e100);
> glob_almost_1 := c( 0.99);
> # before second block
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #BEGIN BLOCK 2
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := c(-0.7);
> x_end := c(-2.0);
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_type_given_pole := 1;
> array_given_rad_poles[1,1] := c(0.0);
> array_given_rad_poles[1,2] := c(0.0);
> array_given_ord_poles[1,1] := c(2.0);
> array_given_ord_poles[1,2] := c(0.0);
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=12;
> glob_max_minutes:=(3.0);
> glob_subiter_method:=2;
> glob_max_iter:=1000000;
> glob_upper_ratio_limit:=c(1.000001);
> glob_lower_ratio_limit:=c(0.999999);
> glob_look_poles:=true;
> glob_h:=c(0.001);
> glob_display_interval:=c(0.01);
> glob_h_reason:=1;
> #END OVERRIDE BLOCK
> #END BLOCK 2
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_sec := (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours);
> # after second input block
> glob_check_sign := c(my_check_sign(x_start,x_end));
> glob__pi := arccos(glob__m1);
> glob_prec = expt(10.0,c(-Digits));
> if (glob_optimize) then # if number 9
> #BEGIN OPTIMIZE CODE
> omniout_str(ALWAYS,"START of Optimize");
> #Start Series -- INITIALIZE FOR OPTIMIZE
> found_h := false;
> glob_min_pole_est := glob_larger_float;
> last_min_pole_est := glob_larger_float;
> glob_least_given_sing := glob_larger_float;
> glob_least_ratio_sing := glob_larger_float;
> glob_least_3_sing := glob_larger_float;
> glob_least_6_sing := glob_larger_float;
> glob_min_h := float_abs(glob_min_h) * glob_check_sign;
> glob_max_h := float_abs(glob_max_h) * glob_check_sign;
> glob_h := float_abs(glob_min_h) * glob_check_sign;
> glob_display_interval := c((float_abs(c(glob_display_interval))) * (glob_check_sign));
> display_max := c(x_end) - c(x_start)/glob__10;
> if ((glob_display_interval) > (display_max)) then # if number 10
> glob_display_interval := c(display_max);
> fi;# end if 10;
> chk_data();
> min_value := glob_larger_float;
> est_answer := est_size_answer();
> opt_iter := 1;
> est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
> omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
> estimated_step_error := glob_small_float;
> while ((opt_iter <= 100) and ( not found_h)) do # do number 1
> omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,"");
> array_x[1] := c(x_start);
> array_x[2] := c(glob_h);
> glob_next_display := c(x_start);
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1));
> term_no := term_no + 1;
> od;# end do number 2;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> if (term_no < ATS_MAX_TERMS) then # if number 10
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 10;
> term_no := term_no + 1;
> od;# end do number 3;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> atomall();
> if (glob_check_sign * glob_min_h >= glob_check_sign * glob_h) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> glob_h := glob_check_sign * float_abs(glob_min_h);
> glob_h_reason := 1;
> found_h := true;
> fi;# end if 10;
> if (glob_check_sign * glob_display_interval <= glob_check_sign * glob_h) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR DISPLAY INTERVAL");
> glob_h_reason := 2;
> glob_h := glob_display_interval;
> found_h := true;
> fi;# end if 10;
> if (glob_look_poles) then # if number 10
> check_for_pole();
> fi;# end if 10;
> if ( not found_h) then # if number 10
> est_answer := est_size_answer();
> est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
> omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
> estimated_step_error := test_suggested_h();
> omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,"");
> if (estimated_step_error < est_needed_step_err) then # if number 11
> omniout_str(ALWAYS,"Double H and LOOP");
> glob_h := glob_h*glob__2;
> else
> omniout_str(ALWAYS,"Found H for OPTIMAL");
> found_h := true;
> glob_h_reason := 3;
> glob_h := glob_h/glob__2;
> fi;# end if 11;
> fi;# end if 10;
> opt_iter := opt_iter + 1;
> od;# end do number 1;
> if (( not found_h) and (opt_iter = 1)) then # if number 10
> omniout_str(ALWAYS,"Beginning glob_h too large.");
> found_h := false;
> fi;# end if 10;
> if (glob_check_sign * glob_max_h <= glob_check_sign * glob_h) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR MAX H");
> glob_h := glob_check_sign * float_abs(glob_max_h);
> glob_h_reason := 1;
> found_h := true;
> fi;# end if 10;
> else
> found_h := true;
> glob_h := glob_h * glob_check_sign;
> fi;# end if 9;
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 9
> html_log_file := fopen("entry.html",WRITE,TEXT);
> fi;# end if 9;
> #BEGIN SOLUTION CODE
> if (found_h) then # if number 9
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := c(x_start);
> array_x[2] := c(glob_h);
> glob_next_display := c(x_start);
> glob_min_pole_est := glob_larger_float;
> glob_least_given_sing := glob_larger_float;
> glob_least_ratio_sing := glob_larger_float;
> glob_least_3_sing := glob_larger_float;
> glob_least_6_sing := glob_larger_float;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 1
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1));
> term_no := term_no + 1;
> od;# end do number 1;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 1
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 2
> it := term_no + r_order - 1;
> if (term_no < ATS_MAX_TERMS) then # if number 10
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 10;
> term_no := term_no + 1;
> od;# end do number 2;
> r_order := r_order + 1;
> od;# end do number 1
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> glob_clock_sec := elapsed_time_seconds();
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_iter < glob_max_iter) and (glob_check_sign * array_x[1] < glob_check_sign * x_end ) and (((glob_clock_sec) - (glob_orig_start_sec)) < (glob_max_sec))) do # do number 1
> #left paren 0001C
> if (reached_interval()) then # if number 10
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> fi;# end if 10;
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> track_estimated_error();
> atomall();
> track_estimated_error();
> display_alot(current_iter);
> if (glob_look_poles) then # if number 10
> check_for_pole();
> fi;# end if 10;
> if (reached_interval()) then # if number 10
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 10;
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y;
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := ATS_MAX_TERMS;
> while (term_no >= 1) do # do number 2
> array_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 3
> array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 3;
> term_no := term_no - 1;
> od;# end do number 2;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> ;
> od;# end do number 1;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 10
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 10;
> if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec )) then # if number 10
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 10;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 1 ) = neg ( 2.0 ) / x / x / x ; ");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 10
> logstart(html_log_file);
> logitem_str(html_log_file,"2020-05-26T00:33:07-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"sing3_back")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = neg ( 2.0 ) / x / x / x ; ")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_h_reason(html_log_file)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_float(html_log_file,glob_desired_digits_correct)
> ;
> if (array_est_digits[1] <> -16) then # if number 11
> logitem_integer(html_log_file,array_est_digits[1])
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_min_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_min_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> logitem_integer(html_log_file,ATS_MAX_TERMS)
> ;
> if (glob_type_given_pole = 0) then # if number 11
> logitem_str(html_log_file,"Not Given")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 4) then # if number 12
> logitem_str(html_log_file,"No Solution")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 5) then # if number 13
> logitem_str(html_log_file,"Some Pole")
> ;
> logitem_str(html_log_file,"????")
> ;
> elif
> (glob_type_given_pole = 3) then # if number 14
> logitem_str(html_log_file,"No Pole")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 1) then # if number 15
> logitem_str(html_log_file,"Real Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> elif
> (glob_type_given_pole = 2) then # if number 16
> logitem_str(html_log_file,"Complex Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> fi;# end if 16;
> if (glob_least_ratio_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_ratio_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_3_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_3_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_6_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_6_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_time(html_log_file,(glob_clock_sec))
> ;
> if (c(glob_percent_done) < glob__100) then # if number 16
> logitem_time(html_log_file,(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 16;
> log_revs(html_log_file," 310 | ")
> ;
> logitem_str(html_log_file,"sing3_back diffeq.mxt")
> ;
> logitem_str(html_log_file,"sing3_back maple results")
> ;
> logitem_str(html_log_file,"OK")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 15;
> if (glob_html_log) then # if number 15
> fclose(html_log_file);
> fi;# end if 15
> ;
> ;;
> fi;# end if 14
> #END OUTFILEMAIN
> end;
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max,
term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order,
sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it,
last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err,
estimated_step_error, min_value, est_answer, found_h, repeat_it;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_y_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2,
array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
ATS_MAX_TERMS := 20;
Digits := 32;
max_terms := 20;
glob_html_log := true;
array_y_init := Array(0 .. 20, []);
array_norms := Array(0 .. 20, []);
array_fact_1 := Array(0 .. 20, []);
array_1st_rel_error := Array(0 .. 2, []);
array_last_rel_error := Array(0 .. 2, []);
array_est_rel_error := Array(0 .. 2, []);
array_max_est_error := Array(0 .. 2, []);
array_type_pole := Array(0 .. 2, []);
array_type_real_pole := Array(0 .. 2, []);
array_type_complex_pole := Array(0 .. 2, []);
array_est_digits := Array(0 .. 2, []);
array_y := Array(0 .. 20, []);
array_x := Array(0 .. 20, []);
array_tmp0 := Array(0 .. 20, []);
array_tmp1 := Array(0 .. 20, []);
array_tmp2 := Array(0 .. 20, []);
array_tmp3 := Array(0 .. 20, []);
array_tmp4 := Array(0 .. 20, []);
array_tmp5 := Array(0 .. 20, []);
array_m1 := Array(0 .. 20, []);
array_y_higher := Array(0 .. 2, 0 .. 21, []);
array_y_higher_work := Array(0 .. 2, 0 .. 21, []);
array_y_higher_work2 := Array(0 .. 2, 0 .. 21, []);
array_y_set_initial := Array(0 .. 2, 0 .. 21, []);
array_given_rad_poles := Array(0 .. 2, 0 .. 4, []);
array_given_ord_poles := Array(0 .. 2, 0 .. 4, []);
array_rad_test_poles := Array(0 .. 2, 0 .. 5, []);
array_ord_test_poles := Array(0 .. 2, 0 .. 5, []);
array_fact_2 := Array(0 .. 20, 0 .. 21, []);
term := 1;
while term <= 20 do array_y_init[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 20 do array_norms[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 20 do array_fact_1[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_1st_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do
array_last_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_est_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_max_est_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_type_pole[term] := 0; term := term + 1 end do;
term := 1;
while term <= 2 do array_type_real_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 2 do array_type_complex_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 2 do array_est_digits[term] := 0; term := term + 1 end do
;
term := 1;
while term <= 20 do array_y[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_x[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_tmp0[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_tmp1[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_tmp2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_tmp3[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_tmp4[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_tmp5[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_m1[term] := c(0.); term := term + 1 end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 20 do
array_y_higher[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 20 do
array_y_higher_work[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 20 do
array_y_higher_work2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 20 do
array_y_set_initial[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_rad_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_ord_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 4 do
array_rad_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 4 do
array_ord_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 20 do
term := 1;
while term <= 20 do
array_fact_2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
zero_ats_ar(array_y);
zero_ats_ar(array_x);
zero_ats_ar(array_tmp0);
zero_ats_ar(array_tmp1);
zero_ats_ar(array_tmp2);
zero_ats_ar(array_tmp3);
zero_ats_ar(array_tmp4);
zero_ats_ar(array_tmp5);
zero_ats_ar(array_m1);
zero_ats_ar(array_const_1);
array_const_1[1] := c(1);
zero_ats_ar(array_const_0D0);
array_const_0D0[1] := c(0.);
zero_ats_ar(array_const_2D0);
array_const_2D0[1] := c(2.0);
zero_ats_ar(array_m1);
array_m1[1] := glob__m1;
iiif := 0;
while iiif <= ATS_MAX_TERMS do
jjjf := 0;
while jjjf <= ATS_MAX_TERMS do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
glob_yes_pole := 4;
glob_no_pole := 3;
glob_not_given := 0;
glob_no_sing_tests := 4;
glob_ratio_test := 1;
glob_three_term_test := 2;
glob_six_term_test := 3;
glob_log_10 := log(c(10.0));
MAX_UNCHANGED := 10;
glob__small := c(0.1*10^(-50));
glob_small_float := c(0.1*10^(-50));
glob_smallish_float := c(0.1*10^(-60));
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob__m2 := c(-2);
glob__m1 := c(-1);
glob__0 := c(0);
glob__1 := c(1);
glob__2 := c(2);
glob__3 := c(3);
glob__4 := c(4);
glob__5 := c(5);
glob__8 := c(8);
glob__10 := c(10);
glob__100 := c(100);
glob__pi := c(0.);
glob__0_5 := c(0.5);
glob__0_8 := c(0.8);
glob__m0_8 := c(-0.8);
glob__0_25 := c(0.25);
glob__0_125 := c(0.125);
glob_prec := c(0.10*10^(-15));
glob_check_sign := c(1.0);
glob_desired_digits_correct := c(8.0);
glob_max_estimated_step_error := c(0.);
glob_ratio_of_radius := c(0.1);
glob_percent_done := c(0.);
glob_total_exp_sec := c(0.1);
glob_optimal_expect_sec := c(0.1);
glob_estimated_size_answer := c(100.0);
glob_almost_1 := c(0.9990);
glob_clock_sec := c(0.);
glob_clock_start_sec := c(0.);
glob_disp_incr := c(0.1);
glob_h := c(0.1);
glob_diff_rc_fm := c(0.1);
glob_diff_rc_fmm1 := c(0.1);
glob_diff_rc_fmm2 := c(0.1);
glob_diff_ord_fm := c(0.1);
glob_diff_ord_fmm1 := c(0.1);
glob_diff_ord_fmm2 := c(0.1);
glob_six_term_ord_save := c(0.1);
glob_guess_error_rc := c(0.1);
glob_guess_error_ord := c(0.1);
glob_least_given_sing := c(0.99*10^201);
glob_least_ratio_sing := c(0.99*10^201);
glob_least_3_sing := c(0.99*10^101);
glob_least_6_sing := c(0.99*10^101);
glob_last_good_h := c(0.1);
glob_max_h := c(0.1);
glob_min_h := c(0.1*10^(-5));
glob_display_interval := c(0.1);
glob_abserr := c(0.1*10^(-10));
glob_relerr := c(0.1*10^(-10));
glob_min_pole_est := c(0.1*10^10);
glob_max_rel_trunc_err := c(0.1*10^(-10));
glob_max_trunc_err := c(0.1*10^(-10));
glob_max_hours := c(0.);
glob_optimal_clock_start_sec := c(0.);
glob_optimal_start := c(0.);
glob_upper_ratio_limit := c(1.0001);
glob_lower_ratio_limit := c(0.9999);
glob_max_sec := c(10000.0);
glob_orig_start_sec := c(0.);
glob_normmax := c(0.);
glob_max_minutes := c(0.);
glob_next_display := c(0.);
glob_est_digits := 1;
glob_subiter_method := 3;
glob_html_log := true;
glob_min_good_digits := 99999;
glob_good_digits := 0;
glob_min_apfp_est_good_digits := 99999;
glob_apfp_est_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
glob_h_reason := 0;
glob_sec_in_minute := 60;
glob_min_in_hour := 60;
glob_hours_in_day := 24;
glob_days_in_year := 365;
glob_sec_in_hour := 3600;
glob_sec_in_day := 86400;
glob_sec_in_year := 31536000;
glob_not_yet_finished := true;
glob_initial_pass := true;
glob_not_yet_start_msg := true;
glob_reached_optimal_h := false;
glob_optimal_done := false;
glob_type_given_pole := 0;
glob_optimize := false;
glob_look_poles := false;
glob_dump_closed_form := false;
glob_max_iter := 1000;
glob_no_eqs := 0;
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_start := 0;
glob_iter := 0;
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
ATS_MAX_TERMS := 20;
glob_iolevel := INFO;
glob_orig_start_sec := elapsed_time_seconds();
glob_display_flag := true;
glob_no_eqs := 1;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############R:Temp/sing3_backpostode.ode#################");
omniout_str(ALWAYS,
"diff ( y , x , 1 ) = neg ( 2.0 ) / x / x / x ; ")
;
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=20;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := c(-0.7);");
omniout_str(ALWAYS, "x_end := c(-2.0);");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_type_given_pole := 1;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_rad_poles[1,1] := c(0.0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_rad_poles[1,2] := c(0.0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_ord_poles[1,1] := c(2.0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_ord_poles[1,2] := c(0.0);");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=12;");
omniout_str(ALWAYS, "glob_max_minutes:=(3.0);");
omniout_str(ALWAYS, "glob_subiter_method:=2;");
omniout_str(ALWAYS, "glob_max_iter:=1000000;");
omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);");
omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);");
omniout_str(ALWAYS, "glob_look_poles:=true;");
omniout_str(ALWAYS, "glob_h:=c(0.001);");
omniout_str(ALWAYS, "glob_display_interval:=c(0.01);");
omniout_str(ALWAYS, "glob_h_reason:=1;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "return(c(1.0)/c(x)/c(x));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := glob__0;
glob_smallish_float := glob__0;
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob_almost_1 := c(0.99);
x_start := c(-0.7);
x_end := c(-2.0);
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_type_given_pole := 1;
array_given_rad_poles[1, 1] := c(0.);
array_given_rad_poles[1, 2] := c(0.);
array_given_ord_poles[1, 1] := c(2.0);
array_given_ord_poles[1, 2] := c(0.);
glob_desired_digits_correct := 12;
glob_max_minutes := 3.0;
glob_subiter_method := 2;
glob_max_iter := 1000000;
glob_upper_ratio_limit := c(1.000001);
glob_lower_ratio_limit := c(0.999999);
glob_look_poles := true;
glob_h := c(0.001);
glob_display_interval := c(0.01);
glob_h_reason := 1;
glob_last_good_h := glob_h;
glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours;
glob_check_sign := c(my_check_sign(x_start, x_end));
glob__pi := arccos(glob__m1);
glob_prec = expt(10.0, c(-Digits));
if glob_optimize then
omniout_str(ALWAYS, "START of Optimize");
found_h := false;
glob_min_pole_est := glob_larger_float;
last_min_pole_est := glob_larger_float;
glob_least_given_sing := glob_larger_float;
glob_least_ratio_sing := glob_larger_float;
glob_least_3_sing := glob_larger_float;
glob_least_6_sing := glob_larger_float;
glob_min_h := float_abs(glob_min_h)*glob_check_sign;
glob_max_h := float_abs(glob_max_h)*glob_check_sign;
glob_h := float_abs(glob_min_h)*glob_check_sign;
glob_display_interval :=
c(float_abs(c(glob_display_interval))*glob_check_sign);
display_max := c(x_end) - c(x_start)/glob__10;
if display_max < glob_display_interval then
glob_display_interval := c(display_max)
end if;
chk_data();
min_value := glob_larger_float;
est_answer := est_size_answer();
opt_iter := 1;
est_needed_step_err :=
estimated_needed_step_error(x_start, x_end, glob_h, est_answer)
;
omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, "");
estimated_step_error := glob_small_float;
while opt_iter <= 100 and not found_h do
omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, "");
array_x[1] := c(x_start);
array_x[2] := c(glob_h);
glob_next_display := c(x_start);
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, c(term_no - 1))/
c(factorial_1(term_no - 1));
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
if term_no < ATS_MAX_TERMS then
array_y_higher[r_order, term_no] :=
array_y_init[it]*expt(glob_h, c(term_no - 1))/
c(factorial_1(term_no - 1))
end if;
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
atomall();
if glob_check_sign*glob_h <= glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
glob_h := float_abs(glob_min_h)*glob_check_sign;
glob_h_reason := 1;
found_h := true
end if;
if
glob_check_sign*glob_display_interval <= glob_check_sign*glob_h
then
omniout_str(ALWAYS, "SETTING H FOR DISPLAY INTERVAL");
glob_h_reason := 2;
glob_h := glob_display_interval;
found_h := true
end if;
if glob_look_poles then check_for_pole() end if;
if not found_h then
est_answer := est_size_answer();
est_needed_step_err := estimated_needed_step_error(x_start,
x_end, glob_h, est_answer);
omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, "");
estimated_step_error := test_suggested_h();
omniout_float(ALWAYS, "estimated_step_error", 32,
estimated_step_error, 32, "");
if estimated_step_error < est_needed_step_err then
omniout_str(ALWAYS, "Double H and LOOP");
glob_h := glob_h*glob__2
else
omniout_str(ALWAYS, "Found H for OPTIMAL");
found_h := true;
glob_h_reason := 3;
glob_h := glob_h/glob__2
end if
end if;
opt_iter := opt_iter + 1
end do;
if not found_h and opt_iter = 1 then
omniout_str(ALWAYS, "Beginning glob_h too large.");
found_h := false
end if;
if glob_check_sign*glob_max_h <= glob_check_sign*glob_h then
omniout_str(ALWAYS, "SETTING H FOR MAX H");
glob_h := float_abs(glob_max_h)*glob_check_sign;
glob_h_reason := 1;
found_h := true
end if
else found_h := true; glob_h := glob_check_sign*glob_h
end if;
if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT)
end if;
if found_h then
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := c(x_start);
array_x[2] := c(glob_h);
glob_next_display := c(x_start);
glob_min_pole_est := glob_larger_float;
glob_least_given_sing := glob_larger_float;
glob_least_ratio_sing := glob_larger_float;
glob_least_3_sing := glob_larger_float;
glob_least_6_sing := glob_larger_float;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1));
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
if term_no < ATS_MAX_TERMS then
array_y_higher[r_order, term_no] := array_y_init[it]*
expt(glob_h, c(term_no - 1))/
c(factorial_1(term_no - 1))
end if;
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
glob_clock_sec := elapsed_time_seconds();
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_iter < glob_max_iter and
glob_check_sign*array_x[1] < glob_check_sign*x_end and
glob_clock_sec - glob_orig_start_sec < glob_max_sec do
if reached_interval() then
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop")
end if;
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
track_estimated_error();
atomall();
track_estimated_error();
display_alot(current_iter);
if glob_look_poles then check_for_pole() end if;
if reached_interval() then
glob_next_display :=
glob_next_display + glob_display_interval
end if;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
term_no := ATS_MAX_TERMS;
while 1 <= term_no do
array_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then
omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if glob_max_sec <= elapsed_time_seconds() - glob_orig_start_sec
then
omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff ( y , x , 1 ) = neg ( 2.0 ) /\
x / x / x ; ");
omniout_int(INFO, "Iterations ", 32, glob_iter,
4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2020-05-26T00:33:07-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"sing3_back");
logitem_str(html_log_file, "diff ( y , x , 1 ) = ne\
g ( 2.0 ) / x / x / x ; ");
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_h_reason(html_log_file);
logitem_integer(html_log_file, Digits);
logitem_float(html_log_file, glob_desired_digits_correct);
if array_est_digits[1] <> -16 then
logitem_integer(html_log_file, array_est_digits[1])
else logitem_str(html_log_file, "Unknown")
end if;
if glob_min_good_digits <> -16 then
logitem_integer(html_log_file, glob_min_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
if glob_good_digits <> -16 then
logitem_integer(html_log_file, glob_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
logitem_integer(html_log_file, ATS_MAX_TERMS);
if glob_type_given_pole = 0 then
logitem_str(html_log_file, "Not Given");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 4 then
logitem_str(html_log_file, "No Solution");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 5 then
logitem_str(html_log_file, "Some Pole");
logitem_str(html_log_file, "????")
elif glob_type_given_pole = 3 then
logitem_str(html_log_file, "No Pole");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 1 then
logitem_str(html_log_file, "Real Sing");
logitem_float(html_log_file, glob_least_given_sing)
elif glob_type_given_pole = 2 then
logitem_str(html_log_file, "Complex Sing");
logitem_float(html_log_file, glob_least_given_sing)
end if;
if glob_least_ratio_sing < glob_large_float then
logitem_float(html_log_file, glob_least_ratio_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_3_sing < glob_large_float then
logitem_float(html_log_file, glob_least_3_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_6_sing < glob_large_float then
logitem_float(html_log_file, glob_least_6_sing)
else logitem_str(html_log_file, "NONE")
end if;
logitem_integer(html_log_file, glob_iter);
logitem_time(html_log_file, glob_clock_sec);
if c(glob_percent_done) < glob__100 then
logitem_time(html_log_file, glob_total_exp_sec); 0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 310 | ");
logitem_str(html_log_file, "sing3_back diffeq.mxt");
logitem_str(html_log_file, "sing3_back maple results");
logitem_str(html_log_file, "OK");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end if
end proc
# End Function number 12
> main();
##############ECHO OF PROBLEM#################
##############R:Temp/sing3_backpostode.ode#################
diff ( y , x , 1 ) = neg ( 2.0 ) / x / x / x ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=20;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := c(-0.7);
x_end := c(-2.0);
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_type_given_pole := 1;
array_given_rad_poles[1,1] := c(0.0);
array_given_rad_poles[1,2] := c(0.0);
array_given_ord_poles[1,1] := c(2.0);
array_given_ord_poles[1,2] := c(0.0);
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=12;
glob_max_minutes:=(3.0);
glob_subiter_method:=2;
glob_max_iter:=1000000;
glob_upper_ratio_limit:=c(1.000001);
glob_lower_ratio_limit:=c(0.999999);
glob_look_poles:=true;
glob_h:=c(0.001);
glob_display_interval:=c(0.01);
glob_h_reason:=1;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return(c(1.0)/c(x)/c(x));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
TOP MAIN SOLVE Loop
x[1] = -0.701
y[1] (closed_form) = 2.0349978937771799406187614595819
y[1] (numeric) = 2.0349978937771799060173142902233
absolute error = 3.46014471693586e-17
relative error = 1.7003185740469985398600000000000e-15 %
Desired digits = 12
Estimated correct digits = 14
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 0.701
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.701
Order of pole (three term test) = 4.078e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.702
y[1] (closed_form) = 2.0292043084065876088668111460134
y[1] (numeric) = 2.0292043084065875400567025390989
absolute error = 6.88101086069145e-17
relative error = 3.3909896761921893258000000000000e-15 %
Desired digits = 12
Estimated correct digits = 14
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 0.702
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.702
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4.3MB, alloc=40.3MB, time=0.11
TOP MAIN SOLVE Loop
x[1] = -0.703
y[1] (closed_form) = 2.0234354291403029892211594689696
y[1] (numeric) = 2.0234354291403028865901661294189
absolute error = 1.026309933395507e-16
relative error = 5.0721160587346011896300000000000e-15 %
Desired digits = 12
Estimated correct digits = 14
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 0.703
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.703
Order of pole (three term test) = 4.442e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.704
y[1] (closed_form) = 2.0176911157024793388429752066115
y[1] (numeric) = 2.0176911157024792027739356874634
absolute error = 1.360690395191481e-16
relative error = 6.7437993090322104729600000000002e-15 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 0.704
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.704
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.705
y[1] (closed_form) = 2.0119712288114279965796489110206
y[1] (numeric) = 2.0119712288114278274505333868673
absolute error = 1.691291155241533e-16
relative error = 8.4061398643392293932499999999999e-15 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 32
h = -0.001
Radius of convergence (given) for eq 1 = 0.705
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.705
Order of pole (three term test) = 1.451e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.706
y[1] (closed_form) = 2.0062756301711754367662046882649
y[1] (numeric) = 2.0062756301711752349501836457712
absolute error = 2.018160210424937e-16
relative error = 1.0059237026433638985320000000000e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 16
h = -0.001
Radius of convergence (given) for eq 1 = 0.706
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.706
Order of pole (three term test) = 1.009e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.707
y[1] (closed_form) = 2.0006041824631038573649242071106
y[1] (numeric) = 2.0006041824631036232304360709257
absolute error = 2.341344881361849e-16
relative error = 1.1703188976038388608010000000000e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 16
h = -0.001
Radius of convergence (given) for eq 1 = 0.707
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.707
Order of pole (three term test) = 5.266e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.708
y[1] (closed_form) = 1.994956749337674359219892112739
y[1] (numeric) = 1.9949567493376740931307098247772
absolute error = 2.660891822879618e-16
relative error = 1.3338092787039288371520000000000e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 16
h = -0.001
Radius of convergence (given) for eq 1 = 0.708
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.708
Order of pole (three term test) = 1.099e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.709
y[1] (closed_form) = 1.9893331954062317851679295616903
y[1] (numeric) = 1.9893331954062314874832261314251
absolute error = 2.976847034302652e-16
relative error = 1.4964044440502914100119999999999e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 16
h = -0.001
Radius of convergence (given) for eq 1 = 0.709
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.709
Order of pole (three term test) = 1.146e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.71
y[1] (closed_form) = 1.9837333862328902995437413211665
y[1] (numeric) = 1.9837333862328899706181543642642
absolute error = 3.289255869569023e-16
relative error = 1.6581138838497444942999999999999e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 16
h = -0.001
Radius of convergence (given) for eq 1 = 0.71
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.71
Order of pole (three term test) = 5.979e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.711
y[1] (closed_form) = 1.9781571883264988002476652799785
y[1] (numeric) = 1.9781571883264984404313605622786
absolute error = 3.598163047176999e-16
relative error = 1.8189469817719637114790000000000e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 16
h = -0.001
Radius of convergence (given) for eq 1 = 0.711
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.711
Order of pole (three term test) = 6.237e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.712
y[1] (closed_form) = 1.9726044691326852670117409418003
y[1] (numeric) = 1.9726044691326848766504749453432
absolute error = 3.903612659964571e-16
relative error = 1.9789130162930794810240000000000e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 16
h = -0.001
Radius of convergence (given) for eq 1 = 0.712
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.712
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.713
y[1] (closed_form) = 1.9670750970259791608064221067767
y[1] (numeric) = 1.9670750970259787402416036342748
absolute error = 4.205648184725019e-16
relative error = 2.1380211620204731840110000000001e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 16
h = -0.001
Radius of convergence (given) for eq 1 = 0.713
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.713
Order of pole (three term test) = 1.357e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.714
y[1] (closed_form) = 1.9615689413020110004786228216777
y[1] (numeric) = 1.9615689413020105500473736555278
absolute error = 4.504312491661499e-16
relative error = 2.2962804909990655442040000000000e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 16
h = -0.001
Radius of convergence (given) for eq 1 = 0.714
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.714
Order of pole (three term test) = 2.123e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.715
y[1] (closed_form) = 1.9560858721697882537043376204215
y[1] (numeric) = 1.9560858721697877737395522520673
absolute error = 4.799647853683542e-16
relative error = 2.4536999739993687589500000000000e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 16
h = -0.001
Radius of convergence (given) for eq 1 = 0.715
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.715
Order of pole (three term test) = 1.476e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.716
y[1] (closed_form) = 1.9506257607440466901782091695015
y[1] (numeric) = 1.9506257607440461810086136146655
absolute error = 5.091695955548360e-16
relative error = 2.6102884817876000441600000000001e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 16
h = -0.001
Radius of convergence (given) for eq 1 = 0.716
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.716
Order of pole (three term test) = 7.696e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.717
y[1] (closed_form) = 1.9451884790376763556504807533326
y[1] (numeric) = 1.9451884790376758176006904683599
absolute error = 5.380497902849727e-16
relative error = 2.7660547863781133037030000000000e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 16
h = -0.001
Radius of convergence (given) for eq 1 = 0.717
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.717
Order of pole (three term test) = 8.025e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.718
y[1] (closed_form) = 1.9397738999542213359610803764713
y[1] (numeric) = 1.9397738999542207693516572907511
absolute error = 5.666094230857202e-16
relative error = 2.9210075622684282038480000000000e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 16
h = -0.001
Radius of convergence (given) for eq 1 = 0.718
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.718
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.719
y[1] (closed_form) = 1.9343818972804524906134118434466
y[1] (numeric) = 1.9343818972804518957609205226069
absolute error = 5.948524913208397e-16
relative error = 3.0751553876571261215170000000000e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 16
h = -0.001
Radius of convergence (given) for eq 1 = 0.719
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.719
Order of pole (three term test) = 1.745e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.72
y[1] (closed_form) = 1.929012345679012345679012345679
y[1] (numeric) = 1.929012345679011722896075299988
absolute error = 6.227829370456910e-16
relative error = 3.2285067456448621440000000000000e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.72
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.72
Order of pole (three term test) = 9.096e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.721
y[1] (closed_form) = 1.9236651206811313459307749869671
y[1] (numeric) = 1.9236651206811306955261271391132
absolute error = 6.504046478478539e-16
relative error = 3.3810700254187621922990000000001e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.721
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.721
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.722
y[1] (closed_form) = 1.918340098679414676069090936994
y[1] (numeric) = 1.9183400986794139983476332631632
absolute error = 6.777214576738308e-16
relative error = 3.5328535234204521474720000000001e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.722
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.722
Order of pole (three term test) = 9.885e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.723
y[1] (closed_form) = 1.9130371569206988707341662697115
y[1] (numeric) = 1.9130371569206981659970186276322
absolute error = 7.047371476420793e-16
relative error = 3.6838654444979647040969999999999e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.723
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.723
Order of pole (three term test) = 1.030e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.724
y[1] (closed_form) = 1.9077561734989774426910045480907
y[1] (numeric) = 1.9077561734989767112355577054704
absolute error = 7.314554468426203e-16
relative error = 3.8341139030417733837280000000000e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.724
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.724
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.725
y[1] (closed_form) = 1.9024970273483947681331747919143
y[1] (numeric) = 1.9024970273483940102531416684524
absolute error = 7.578800331234619e-16
relative error = 3.9836069241051966118750000000002e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.725
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.725
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.726
y[1] (closed_form) = 1.897259598236307477479528568935
y[1] (numeric) = 1.8972595982363066934649947048626
absolute error = 7.840145338640724e-16
relative error = 4.1323524445093982430240000000001e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.726
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.726
Order of pole (three term test) = 1.167e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.727
y[1] (closed_form) = 1.8920437667564126093364791714362
y[1] (numeric) = 1.8920437667564117994739524353021
absolute error = 8.098625267361341e-16
relative error = 4.2803583139332221973890000000000e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.727
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.727
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.728
y[1] (closed_form) = 1.8868494143219417944692669967396
y[1] (numeric) = 1.8868494143219409590417265449344
absolute error = 8.354275404518052e-16
relative error = 4.4276322959880952711679999999998e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.728
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.728
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.729
y[1] (closed_form) = 1.8816764231589207456707329694171
y[1] (numeric) = 1.881676423158919884957677469707
absolute error = 8.607130554997101e-16
relative error = 4.5741820692782143525410000000000e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.729
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.729
Order of pole (three term test) = 1.320e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.73
y[1] (closed_form) = 1.8765246762994933383373991367986
y[1] (numeric) = 1.8765246762994924526148942679215
absolute error = 8.857225048688771e-16
relative error = 4.7200152284462460659000000000001e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.73
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.73
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.731
y[1] (closed_form) = 1.8713940575753095753619743955865
y[1] (numeric) = 1.8713940575753086649026996347509
absolute error = 9.104592747608356e-16
relative error = 4.8651392852047487205160000000000e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.731
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.731
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.732
y[1] (closed_form) = 1.8662844516109767386305951207859
y[1] (numeric) = 1.8662844516109758037038898307024
absolute error = 9.349267052900835e-16
relative error = 5.0095616693535370130400000000001e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.732
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.732
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.733
y[1] (closed_form) = 1.86119574381757303797397676111
y[1] (numeric) = 1.8611957438175720788458855879795
absolute error = 9.591280911731305e-16
relative error = 5.1532897297832011321449999999998e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.733
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.733
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.734
y[1] (closed_form) = 1.8561278203862230768659652978343
y[1] (numeric) = 1.856127820386222093799282891517
absolute error = 9.830666824063173e-16
relative error = 5.2963307354649788327879999999999e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.734
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.734
Order of pole (three term test) = 1.621e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.735
y[1] (closed_form) = 1.8510805682817344624924799851913
y[1] (numeric) = 1.8510805682817334557467950525807
absolute error = 1.0067456849326106e-15
relative error = 5.4386918764271956138500000000002e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.735
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.735
Order of pole (three term test) = 1.689e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.736
y[1] (closed_form) = 1.8460538752362948960302457466918
y[1] (numeric) = 1.8460538752362938658619844491258
absolute error = 1.0301682612975660e-15
relative error = 5.5803802647184631193600000000002e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.736
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.736
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.737
y[1] (closed_form) = 1.841047629743229087079711839225
y[1] (numeric) = 1.8410476297432280337421805445748
absolute error = 1.0533375312946502e-15
relative error = 5.7214029353578385448380000000000e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.737
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.737
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.738
y[1] (closed_form) = 1.8360617210508148441918023516279
y[1] (numeric) = 1.8360617210508137679352297515193
absolute error = 1.0762565726001086e-15
relative error = 5.8617668472721354833839999999998e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.738
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.738
Order of pole (three term test) = 1.908e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.739
y[1] (closed_form) = 1.8310960391561577013152762849258
y[1] (numeric) = 1.8310960391561566023868548873629
absolute error = 1.0989284213975629e-15
relative error = 6.0014788842205844851090000000002e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.739
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.739
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.74
y[1] (closed_form) = 1.8261504747991234477720964207451
y[1] (numeric) = 1.826150474799122326416023428228
absolute error = 1.1213560729925171e-15
relative error = 6.1405458557070236395999999999999e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.74
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.74
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.741
y[1] (closed_form) = 1.8212249194563279370438969842336
y[1] (numeric) = 1.8212249194563267935014145672863
absolute error = 1.1435424824169473e-15
relative error = 6.2789744978797984043130000000002e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.741
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.741
Order of pole (three term test) = 6.465e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.742
y[1] (closed_form) = 1.8163192653351835572249547736503
y[1] (numeric) = 1.8163192653351823917343897494978
absolute error = 1.1654905650241525e-15
relative error = 6.4167714744195749701000000000000e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.742
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.742
Order of pole (three term test) = 2.244e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.743
y[1] (closed_form) = 1.8114334053680017534675363962257
y[1] (numeric) = 1.8114334053680005662643393221952
absolute error = 1.1872031970740305e-15
relative error = 6.5539433774152146349450000000000e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.743
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.743
Order of pole (three term test) = 1.635e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.744
y[1] (closed_form) = 1.8065672332061510001156203029251
y[1] (numeric) = 1.8065672332061497914324039939742
absolute error = 1.2086832163089509e-15
relative error = 6.6904967282279144538240000000003e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.744
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.744
Order of pole (three term test) = 4.865e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.745
y[1] (closed_form) = 1.8017206432142696274942570154498
y[1] (numeric) = 1.8017206432142683975608344950645
absolute error = 1.2299334225203853e-15
relative error = 6.8264379783437685113249999999998e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.745
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.745
Order of pole (three term test) = 1.013e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.746
y[1] (closed_form) = 1.7968935304645329154956910493139
y[1] (numeric) = 1.7968935304645316645391129428588
absolute error = 1.2509565781064551e-15
relative error = 6.9617735102149196643160000000002e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.746
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.746
Order of pole (three term test) = 7.910e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.747
y[1] (closed_form) = 1.7920857907309738731812569331319
y[1] (numeric) = 1.7920857907309726014258483125738
absolute error = 1.2717554086205581e-15
relative error = 7.0965096380894900482290000000000e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.747
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.747
Order of pole (three term test) = 1.372e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.748
y[1] (closed_form) = 1.7872973204838571306013898023964
y[1] (numeric) = 1.7872973204838558382687864911731
absolute error = 1.2923326033112233e-15
relative error = 7.2306526088304268124320000000000e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.748
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.748
Order of pole (three term test) = 2.857e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.749
y[1] (closed_form) = 1.7825280168841053759262461207734
y[1] (numeric) = 1.7825280168841040632354304674243
absolute error = 1.3126908156533491e-15
relative error = 7.3642086027234449844910000000000e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.749
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.749
Order of pole (three term test) = 2.974e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.75
y[1] (closed_form) = 1.7777777777777777777777777777777
y[1] (numeric) = 1.7777777777777764449451139068049
absolute error = 1.3328326638709728e-15
relative error = 7.4971837342742220000000000000003e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.75
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.75
Order of pole (three term test) = 1.548e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.751
y[1] (closed_form) = 1.7730465016905998393619869468317
y[1] (numeric) = 1.7730465016905984866012554951147
absolute error = 1.3527607314517170e-15
relative error = 7.6295840529949983971699999999998e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.751
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.751
Order of pole (three term test) = 1.289e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.752
y[1] (closed_form) = 1.7683340878225441376188320507017
y[1] (numeric) = 1.7683340878225427651412643976457
absolute error = 1.3724775676530560e-15
relative error = 7.7614155441807378022399999999999e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.752
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.752
Order of pole (three term test) = 3.353e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.753
y[1] (closed_form) = 1.7636404360424614071381583008382
y[1] (numeric) = 1.7636404360424600151524703002932
absolute error = 1.3919856880005450e-15
relative error = 7.8926841296750101990500000000003e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.753
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.753
Order of pole (three term test) = 2.094e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.754
y[1] (closed_form) = 1.7589654468827614350343701848321
y[1] (numeric) = 1.7589654468827600237467954066847
absolute error = 1.4112875747781474e-15
relative error = 8.0233956686257324725840000000000e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.754
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.754
Order of pole (three term test) = 1.452e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.755
y[1] (closed_form) = 1.7543090215341432393316082627955
y[1] (numeric) = 1.7543090215341418089459307519987
absolute error = 1.4303856775107968e-15
relative error = 8.1535559582309194592000000000000e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.755
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.755
Order of pole (three term test) = 7.556e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.756
y[1] (closed_form) = 1.7496710618403740096861789983483
y[1] (numeric) = 1.7496710618403725604037655590198
absolute error = 1.4492824134393285e-15
relative error = 8.2831707344746005357600000000000e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.756
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.756
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.757
y[1] (closed_form) = 1.7450514702931162954651347441493
y[1] (numeric) = 1.7450514702931148274849667562415
absolute error = 1.4679801679879078e-15
relative error = 8.4122456728530257688219999999999e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.757
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.757
Order of pole (three term test) = 8.181e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.758
y[1] (closed_form) = 1.7404501500268029323104127651575
y[1] (numeric) = 1.7404501500268014458291175410714
absolute error = 1.4864812952240861e-15
relative error = 8.5407863890913180596040000000004e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.758
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.758
Order of pole (three term test) = 4.256e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.759
y[1] (closed_form) = 1.735867004813559204347999673657
y[1] (numeric) = 1.7358670048135576995598813620474
absolute error = 1.5047881183116096e-15
relative error = 8.6687984398507036997760000000000e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.759
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.759
Order of pole (three term test) = 8.855e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.76
y[1] (closed_form) = 1.7313019390581717451523545706371
y[1] (numeric) = 1.7313019390581702222494246145341
absolute error = 1.5229029299561030e-15
relative error = 8.7962873234264509280000000000001e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.76
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.76
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.761
y[1] (closed_form) = 1.7267548577931036864489459024971
y[1] (numeric) = 1.726754857793102145620953058745
absolute error = 1.5408279928437521e-15
relative error = 8.9232584804366655990409999999998e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.761
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.761
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.762
y[1] (closed_form) = 1.722225666673555569333360888944
y[1] (numeric) = 1.7222256666735540107678208158426
absolute error = 1.5585655400731014e-15
relative error = 9.0497172945020588930160000000000e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.762
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.762
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.763
y[1] (closed_form) = 1.7177142719725715385051419776731
y[1] (numeric) = 1.717714271972569962387366397587
absolute error = 1.5761177755800861e-15
relative error = 9.1756690929168314475090000000003e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.763
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.763
Order of pole (three term test) = 5.183e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.764
y[1] (closed_form) = 1.7132205805761903456593843370522
y[1] (numeric) = 1.7132205805761887521725097806407
absolute error = 1.5934868745564115e-15
relative error = 9.3011191473107916690399999999998e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.764
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.764
Order of pole (three term test) = 1.078e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.765
y[1] (closed_form) = 1.7087444999786406937502669913281
y[1] (numeric) = 1.7087444999786390830752831299357
absolute error = 1.6106749838613924e-15
relative error = 9.4260726743028336729000000000001e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.765
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.765
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.766
y[1] (closed_form) = 1.7042859382775804593391460845735
y[1] (numeric) = 1.704285938277578831654923657208
absolute error = 1.6276842224273655e-15
relative error = 9.5505348361459127131799999999999e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.766
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.766
Order of pole (three term test) = 1.166e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.767
y[1] (closed_form) = 1.6998448041693793356666536345232
y[1] (numeric) = 1.6998448041693776911499719757437
absolute error = 1.6445166816587795e-15
relative error = 9.6745107413636173327549999999998e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.767
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.767
Order of pole (three term test) = 6.064e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.768
y[1] (closed_form) = 1.6954210069444444444444444444444
y[1] (numeric) = 1.6954210069444427832700186193713
absolute error = 1.6611744258250731e-15
relative error = 9.7980054453784791613440000000003e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.768
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.768
Order of pole (three term test) = 1.261e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.769
y[1] (closed_form) = 1.6910144564825884696488270278222
y[1] (numeric) = 1.6910144564825867919893345803787
absolute error = 1.6776594924474435e-15
relative error = 9.9210239511321263560350000000004e-14 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.769
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.769
Order of pole (three term test) = 6.557e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.77
y[1] (closed_form) = 1.6866250632484398718164951931186
y[1] (numeric) = 1.6866250632484381778426025135101
absolute error = 1.6939738926796085e-15
relative error = 1.0043571209697398796500000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.77
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.77
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.771
y[1] (closed_form) = 1.6822527382868947464929236038564
y[1] (numeric) = 1.682252738286893036373311921193
absolute error = 1.7101196116826634e-15
relative error = 1.0165652120882541141594000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.771
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.771
Order of pole (three term test) = 2.126e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.772
y[1] (closed_form) = 1.6778973932186098955676662460737
y[1] (numeric) = 1.6778973932186081694690572519411
absolute error = 1.7260986089941326e-15
relative error = 1.0287271533827591234784000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.772
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.772
Order of pole (three term test) = 7.369e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.773
y[1] (closed_form) = 1.6735589402355366852487494330819
y[1] (numeric) = 1.6735589402355349433359305417708
absolute error = 1.7419128188913111e-15
relative error = 1.0408434247593062302719000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.773
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.773
Order of pole (three term test) = 7.661e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.774
y[1] (closed_form) = 1.6692372920964952693815141985324
y[1] (numeric) = 1.6692372920964935118173634495392
absolute error = 1.7575641507489932e-15
relative error = 1.0529145011741038502832000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.774
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.774
Order of pole (three term test) = 7.964e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.775
y[1] (closed_form) = 1.6649323621227887617065556711759
y[1] (numeric) = 1.6649323621227869886520662794939
absolute error = 1.7730544893916820e-15
relative error = 1.0649408526908790012500000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.775
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.775
Order of pole (three term test) = 8.278e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.776
y[1] (closed_form) = 1.6606440641938569454777340843872
y[1] (numeric) = 1.6606440641938551570920386440165
absolute error = 1.7883856954403707e-15
relative error = 1.0769229445375006666432000000001e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.776
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.776
Order of pole (three term test) = 1.721e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.777
y[1] (closed_form) = 1.656372312742969113625484281855
y[1] (numeric) = 1.6563723127429673100658786278664
absolute error = 1.8035596056539886e-15
relative error = 1.0888612371618768834894000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.777
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.777
Order of pole (three term test) = 8.944e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.778
y[1] (closed_form) = 1.6521170227529556373537050376352
y[1] (numeric) = 1.6521170227529538187756717720387
absolute error = 1.8185780332655965e-15
relative error = 1.1007561862871333119060000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.778
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.778
Order of pole (three term test) = 9.295e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.779
y[1] (closed_form) = 1.6478781097519778657012298114332
y[1] (numeric) = 1.6478781097519760322584614980086
absolute error = 1.8334427683134246e-15
relative error = 1.1126082429660868976886000000001e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.779
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.779
Order of pole (three term test) = 9.661e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.78
y[1] (closed_form) = 1.6436554898093359631821170282709
y[1] (numeric) = 1.6436554898093341150265390614382
absolute error = 1.8481555779668327e-15
relative error = 1.1244178536350210146800000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.78
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.78
Order of pole (three term test) = 1.004e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.781
y[1] (closed_form) = 1.6394490795313142971435878687326
y[1] (numeric) = 1.6394490795313124344253810214523
absolute error = 1.8627182068472803e-15
relative error = 1.1361854601667739390683000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.781
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.781
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.782
y[1] (closed_form) = 1.6352587960570639909472073050281
y[1] (numeric) = 1.6352587960570621138148299606383
absolute error = 1.8771323773443898e-15
relative error = 1.1479114999231506280552000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.782
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.782
Order of pole (three term test) = 1.084e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.783
y[1] (closed_form) = 1.6310845570545222634886615157017
y[1] (numeric) = 1.6310845570545203720888715885207
absolute error = 1.8913997899271810e-15
relative error = 1.1595964058066654721090000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.783
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.783
Order of pole (three term test) = 1.127e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.784
y[1] (closed_form) = 1.6269262807163681799250312369846
y[1] (numeric) = 1.6269262807163662744029077864255
absolute error = 1.9055221234505591e-15
relative error = 1.1712406063116268541696000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.784
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.784
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.785
y[1] (closed_form) = 1.6227838857560144427765832285285
y[1] (numeric) = 1.6227838857560125232755477713944
absolute error = 1.9195010354571341e-15
relative error = 1.1828445255745724607725000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.785
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.785
Order of pole (three term test) = 1.216e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.786
y[1] (closed_form) = 1.6186572914036348568135760024345
y[1] (numeric) = 1.6186572914036329234754135279863
absolute error = 1.9333381624744482e-15
relative error = 1.1944085834240642001672000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.786
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.786
Order of pole (three term test) = 1.263e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.787
y[1] (closed_form) = 1.6145464174022271053281646320691
y[1] (numeric) = 1.6145464174022251582930443243831
absolute error = 1.9470351203076860e-15
relative error = 1.2059331954298511701340000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.787
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.787
Order of pole (three term test) = 1.313e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.788
y[1] (closed_form) = 1.6104511840037104795279445489448
y[1] (numeric) = 1.6104511840037085189344402210006
absolute error = 1.9605935043279442e-15
relative error = 1.2174187729514109833248000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.788
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.788
Order of pole (three term test) = 1.364e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.789
y[1] (closed_form) = 1.6063715119650582068717360538842
y[1] (numeric) = 1.6063715119650562328568462977532
absolute error = 1.9740148897561310e-15
relative error = 1.2288657231858764262509999999999e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.789
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.789
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.79
y[1] (closed_form) = 1.6023073225444640282006088767825
y[1] (numeric) = 1.6023073225444620408997769342148
absolute error = 1.9873008319425677e-15
relative error = 1.2402744492153565015700000000001e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.79
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.79
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.791
y[1] (closed_form) = 1.5982585374975426774985975281334
y[1] (numeric) = 1.5982585374975406770457308857682
absolute error = 2.0004528666423652e-15
relative error = 1.2516453500536617007012000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.791
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.791
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.792
y[1] (closed_form) = 1.5942250790735639220487705336191
y[1] (numeric) = 1.5942250790735619085762602469796
absolute error = 2.0134725102866395e-15
relative error = 1.2629788206924386393279999999999e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.792
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.792
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.793
y[1] (closed_form) = 1.5902068700117198246319863751076
y[1] (numeric) = 1.5902068700117177982707261254675
absolute error = 2.0263612602496401e-15
relative error = 1.2742752521467259272449000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.793
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.793
Order of pole (three term test) = 1.648e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.794
y[1] (closed_form) = 1.5862038335374248932484820029314
y[1] (numeric) = 1.586203833537422854127886891078
absolute error = 2.0391205951118534e-15
relative error = 1.2855350314999364100823999999999e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.794
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.794
Order of pole (three term test) = 1.712e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.795
y[1] (closed_form) = 1.5822158933586487876270717139353
y[1] (numeric) = 1.5822158933586467358750967947867
absolute error = 2.0517519749191486e-15
relative error = 1.2967585419482748939150000000001e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.795
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.795
Order of pole (three term test) = 1.778e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.796
y[1] (closed_form) = 1.578242973662281255523850407818
y[1] (numeric) = 1.5782429736622791912670089697867
absolute error = 2.0642568414380313e-15
relative error = 1.3079461628445996401808000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.796
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.796
Order of pole (three term test) = 1.846e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.797
y[1] (closed_form) = 1.574284999110528975502551128841
y[1] (numeric) = 1.5742849991105268988659327217762
absolute error = 2.0766366184070648e-15
relative error = 1.3190982697417332245432000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.797
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.797
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.798
y[1] (closed_form) = 1.5703418948373439865327479098749
y[1] (numeric) = 1.5703418948373418976400361253484
absolute error = 2.0888927117845265e-15
relative error = 1.3302152344352336133060000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.798
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.798
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.799
y[1] (closed_form) = 1.5664135864448833883405571106562
y[1] (numeric) = 1.5664135864448812873140471183009
absolute error = 2.1010265099923553e-15
relative error = 1.3412974250056296158753000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.799
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.799
Order of pole (three term test) = 2.067e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.8
y[1] (closed_form) = 1.5625
y[1] (numeric) = 1.5624999999999978869606158435472
absolute error = 2.1130393841564528e-15
relative error = 1.3523452058601297920000000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.8
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8
Order of pole (three term test) = 2.146e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.801
y[1] (closed_form) = 1.5586010620307636677623632132743
y[1] (numeric) = 1.5586010620307615428296748698765
absolute error = 2.1249326883433978e-15
relative error = 1.3633589377738123718778000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.801
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.801
Order of pole (three term test) = 4.455e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.802
y[1] (closed_form) = 1.5547166995230129165863396371913
y[1] (numeric) = 1.5547166995230107798785798435617
absolute error = 2.1367077597936296e-15
relative error = 1.3743389779303017332384000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.802
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.802
Order of pole (three term test) = 2.313e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.803
y[1] (closed_form) = 1.5508468399169366432540488733873
y[1] (numeric) = 1.5508468399169344948881297222282
absolute error = 2.1483659191511591e-15
relative error = 1.3852856799619397481119000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.803
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.803
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.804
y[1] (closed_form) = 1.54699141110368555233781342046
y[1] (numeric) = 1.5469914111036833924293427305967
absolute error = 2.1599084706898633e-15
relative error = 1.3961993939894586749327999999999e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.804
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.804
Order of pole (three term test) = 1.246e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.805
y[1] (closed_form) = 1.5431503414220130396203850160102
y[1] (numeric) = 1.5431503414220108682836824795932
absolute error = 2.1713367025364170e-15
relative error = 1.4070804666611616264250000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.805
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.805
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.806
y[1] (closed_form) = 1.5393235596549452308677474770486
y[1] (numeric) = 1.5393235596549430482158605871305
absolute error = 2.1826518868899181e-15
relative error = 1.4179292411916188348116000000001e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.806
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.806
Order of pole (three term test) = 2.685e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.807
y[1] (closed_form) = 1.5355109950264798871092316456532
y[1] (numeric) = 1.5355109950264776932539514073962
absolute error = 2.1938552802382570e-15
relative error = 1.4287460573998846329930000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.807
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.807
Order of pole (three term test) = 2.787e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.808
y[1] (closed_form) = 1.5317125771983138907950200960691
y[1] (numeric) = 1.5317125771983116858468965247858
absolute error = 2.2049481235712833e-15
relative error = 1.4395312517472423003711999999999e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.808
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.808
Order of pole (three term test) = 2.892e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.809
y[1] (closed_form) = 1.5279282362665990303767412652163
y[1] (numeric) = 1.5279282362665968144450986743941
absolute error = 2.2159316425908222e-15
relative error = 1.4502851573744839042782000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.809
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.809
Order of pole (three term test) = 1.201e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.81
y[1] (closed_form) = 1.5241579027587258039932937052279
y[1] (numeric) = 1.5241579027587235771862457876381
absolute error = 2.2268070479175898e-15
relative error = 1.4610081041387306677800000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.81
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.81
Order of pole (three term test) = 6.230e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.811
y[1] (closed_form) = 1.5204015076301349660418323270809
y[1] (numeric) = 1.5204015076301327284662970320247
absolute error = 2.2375755352950562e-15
relative error = 1.4717004186497996589202000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.811
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.811
Order of pole (three term test) = 6.465e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.812
y[1] (closed_form) = 1.5166589822611565434735130675337
y[1] (numeric) = 1.5166589822611542952352272772263
absolute error = 2.2482382857903074e-15
relative error = 1.4823624243061244423456000000001e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.812
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.812
Order of pole (three term test) = 6.708e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.813
y[1] (closed_form) = 1.5129302584538760516756459077506
y[1] (numeric) = 1.5129302584538737928791799157995
absolute error = 2.2587964659919511e-15
relative error = 1.4929944413302339266159000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.813
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.813
Order of pole (three term test) = 3.480e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.814
y[1] (closed_form) = 1.5092152684290276427868565460703
y[1] (numeric) = 1.5092152684290253735356283409551
absolute error = 2.2692512282051152e-15
relative error = 1.5035967868037965110592000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.814
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.814
Order of pole (three term test) = 1.805e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.815
y[1] (closed_form) = 1.5055139448229139222402047498964
y[1] (numeric) = 1.505513944822911642636494106311
absolute error = 2.2796037106435854e-15
relative error = 1.5141697747022355123150000000001e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.815
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.815
Order of pole (three term test) = 3.746e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.816
y[1] (closed_form) = 1.5018262206843521722414455978469
y[1] (numeric) = 1.5018262206843498823864079787208
absolute error = 2.2898550376191261e-15
relative error = 1.5247137159289208284416000000001e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.816
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.816
Order of pole (three term test) = 3.887e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.817
y[1] (closed_form) = 1.4981520294716467237662343499294
y[1] (numeric) = 1.4981520294716444237599146218997
absolute error = 2.3000063197280297e-15
relative error = 1.5352289183489428164233000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.817
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.817
Order of pole (three term test) = 4.032e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.818
y[1] (closed_form) = 1.4944913050495872215015453040094
y[1] (numeric) = 1.4944913050495849114428912690709
absolute error = 2.3100586540349385e-15
relative error = 1.5457156868224741888740000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.818
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.818
Order of pole (three term test) = 4.183e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.819
y[1] (closed_form) = 1.4908439816864725289633714542139
y[1] (numeric) = 1.4908439816864702089502472002309
absolute error = 2.3200131242539830e-15
relative error = 1.5561743232377258910630000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.819
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.819
Order of pole (three term test) = 8.678e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.82
y[1] (closed_form) = 1.4872099940511600237953599048185
y[1] (numeric) = 1.4872099940511576939245589775413
absolute error = 2.3298708009272772e-15
relative error = 1.5666051265435011892800000000001e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.82
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.82
Order of pole (three term test) = 9.002e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=55.2MB, alloc=44.3MB, time=0.47
x[1] = -0.821
y[1] (closed_form) = 1.483589277210140035991875865118
y[1] (numeric) = 1.4835892772101376963591342643039
absolute error = 2.3396327416008141e-15
relative error = 1.5770083927813543367781000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.821
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.821
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.822
y[1] (closed_form) = 1.479981766624635184494527027427
y[1] (numeric) = 1.4799817666246328351945360296253
absolute error = 2.3492999909978017e-15
relative error = 1.5873844151173586438628000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.822
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.822
Order of pole (three term test) = 4.842e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.823
y[1] (closed_form) = 1.4763873981477243702838650050419
y[1] (numeric) = 1.4763873981477220114102838155613
absolute error = 2.3588735811894806e-15
relative error = 1.5977334838734897053174000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.823
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.823
Order of pole (three term test) = 5.022e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.824
y[1] (closed_form) = 1.4728061080214911867282495993967
y[1] (numeric) = 1.4728061080214888183737178359357
absolute error = 2.3683545317634610e-15
relative error = 1.6080558865586276959360000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.824
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.824
Order of pole (three term test) = 5.208e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.825
y[1] (closed_form) = 1.4692378328741965105601469237833
y[1] (numeric) = 1.4692378328741941328162969341621
absolute error = 2.3777438499896212e-15
relative error = 1.6183519078991859292500000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.825
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.825
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.826
y[1] (closed_form) = 1.4656825097174750394268595114001
y[1] (numeric) = 1.4656825097174726523843285277985
absolute error = 2.3870425309836016e-15
relative error = 1.6286218298693677652416000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.826
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.826
Order of pole (three term test) = 5.601e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.827
y[1] (closed_form) = 1.4621400759435555445082749817599
y[1] (numeric) = 1.4621400759435531482567171138238
absolute error = 2.3962515578679361e-15
relative error = 1.6388659317210596689368999999999e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.827
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.827
Order of pole (three term test) = 1.162e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.828
y[1] (closed_form) = 1.4586104693225046092090830591146
y[1] (numeric) = 1.4586104693225022038371811282598
absolute error = 2.4053719019308548e-15
relative error = 1.6490844900133631572032000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.828
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.828
Order of pole (three term test) = 6.023e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.829
y[1] (closed_form) = 1.4550936279994936274174561762176
y[1] (numeric) = 1.4550936279994912130129333934211
absolute error = 2.4144045227827965e-15
relative error = 1.6592777786417718494565000000001e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.829
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.829
Order of pole (three term test) = 6.245e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.83
y[1] (closed_form) = 1.4515894904920888372768181158369
y[1] (numeric) = 1.4515894904920864139264496051717
absolute error = 2.4233503685106652e-15
relative error = 1.6694460688669972562799999999999e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.83
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.83
Order of pole (three term test) = 6.475e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.831
y[1] (closed_form) = 1.4480979956875641688424339051872
y[1] (numeric) = 1.4480979956875617366320580753215
absolute error = 2.4322103758298657e-15
relative error = 1.6795896293434478876577000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.831
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.831
Order of pole (three term test) = 6.713e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.832
y[1] (closed_form) = 1.4446190828402366863905325443787
y[1] (numeric) = 1.4446190828402342454050623102231
absolute error = 2.4409854702341556e-15
relative error = 1.6897087261473681260544000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.832
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.832
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.833
y[1] (closed_form) = 1.4411526915688244085149065628652
y[1] (numeric) = 1.4411526915688219588383404195217
absolute error = 2.4496765661433435e-15
relative error = 1.6998036228046384778715000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.833
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.833
Order of pole (three term test) = 1.443e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.834
y[1] (closed_form) = 1.4376987618538262914847977732922
y[1] (numeric) = 1.4376987618538238332002307244215
absolute error = 2.4582845670488707e-15
relative error = 1.7098745803182443086091999999999e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.834
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.834
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.835
y[1] (closed_form) = 1.4342572340349241636487504033848
y[1] (numeric) = 1.434257234034921696838384746079
absolute error = 2.4668103656573058e-15
relative error = 1.7199218571954150364050000000001e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.835
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.835
Order of pole (three term test) = 7.753e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.836
y[1] (closed_form) = 1.4308280488084064009523591492868
y[1] (numeric) = 1.4308280488084039256975151174983
absolute error = 2.4752548440317885e-15
relative error = 1.7299457094744408554960000000001e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.836
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.836
Order of pole (three term test) = 1.607e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.837
y[1] (closed_form) = 1.4274111472246131358938234492248
y[1] (numeric) = 1.4274111472246106522749497177748
absolute error = 2.4836188737314500e-15
relative error = 1.7399463907511681950500000000001e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.837
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.837
Order of pole (three term test) = 8.330e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.838
y[1] (closed_form) = 1.4240064706854027944702980730345
y[1] (numeric) = 1.4240064706854003025669821241897
absolute error = 2.4919033159488448e-15
relative error = 1.7499241522051805677311999999999e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.838
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.838
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.839
y[1] (closed_form) = 1.4206139609416397578705564971069
y[1] (numeric) = 1.4206139609416372577615348516843
absolute error = 2.5001090216454226e-15
relative error = 1.7598792426256675220146000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.839
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.839
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.84
y[1] (closed_form) = 1.4172335600907029478458049886621
y[1] (numeric) = 1.4172335600907004396089733035903
absolute error = 2.5082368316850718e-15
relative error = 1.7698119084369866620800000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.84
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.84
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.841
y[1] (closed_form) = 1.4138652105740151368409444054061
y[1] (numeric) = 1.413865210574012620553367439643
absolute error = 2.5162875769657631e-15
relative error = 1.7797223937239218911310999999999e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.841
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.841
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.842
y[1] (closed_form) = 1.4105088551745927860935110950627
y[1] (numeric) = 1.4105088551745902618314325457399
absolute error = 2.5242620785493228e-15
relative error = 1.7896109402566420895791999999999e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.842
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.842
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.843
y[1] (closed_form) = 1.407164437014616217007270818646
y[1] (numeric) = 1.40716443701461368484612302928
absolute error = 2.5321611477893660e-15
relative error = 1.7994777875153651585340000000001e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.843
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.843
Order of pole (three term test) = 1.032e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.844
y[1] (closed_form) = 1.4038318995530199231823184564588
y[1] (numeric) = 1.4038318995530173831967319990432
absolute error = 2.5399855864574156e-15
relative error = 1.8093231727147295988415999999999e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.844
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.844
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.845
y[1] (closed_form) = 1.4005111865831028325338748643254
y[1] (numeric) = 1.4005111865831002847976879970895
absolute error = 2.5477361868672359e-15
relative error = 1.8191473308278781134975000000001e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.845
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.845
Order of pole (three term test) = 1.108e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.846
y[1] (closed_form) = 1.3972022422301583309580895215421
y[1] (numeric) = 1.397202242230155775544357524132
absolute error = 2.5554137319974101e-15
relative error = 1.8289504946102583671316000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.846
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.846
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.847
y[1] (closed_form) = 1.3939050109491238610053679281972
y[1] (numeric) = 1.3939050109491212979863723160135
absolute error = 2.5630189956121837e-15
relative error = 1.8387328946231410960333000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.847
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.847
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.848
y[1] (closed_form) = 1.3906194375222499110003559985761
y[1] (numeric) = 1.3906194375222473404476136179694
absolute error = 2.5705527423806067e-15
relative error = 1.8484947592568638003967999999999e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.848
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.848
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.849
y[1] (closed_form) = 1.387345467056788212003035511882
y[1] (numeric) = 1.3873454670567856339873075178872
absolute error = 2.5780157279939948e-15
relative error = 1.8582363147537994458347999999999e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.849
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.849
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.85
y[1] (closed_form) = 1.3840830449826989619377162629758
y[1] (numeric) = 1.3840830449826963765290169812371
absolute error = 2.5854086992817387e-15
relative error = 1.8679577852310562107500000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.85
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.85
Order of pole (three term test) = 1.323e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.851
y[1] (closed_form) = 1.3808321170503768981263489003744
y[1] (numeric) = 1.3808321170503743053939545748887
absolute error = 2.5927323943254857e-15
relative error = 1.8776593927029110694256999999999e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.851
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.851
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.852
y[1] (closed_form) = 1.3775926293283960413498203619211
y[1] (numeric) = 1.3775926293283934413622777902038
absolute error = 2.5999875425717173e-15
relative error = 1.8873413571029798749392000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.852
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.852
Order of pole (three term test) = 1.419e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.853
y[1] (closed_form) = 1.3743645282012729364260200189937
y[1] (numeric) = 1.3743645282012703292511550762439
absolute error = 2.6071748649427498e-15
relative error = 1.8970038963061292392282000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.853
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.853
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.854
y[1] (closed_form) = 1.3711477603672482161367637622101
y[1] (numeric) = 1.3711477603672456018416898160319
absolute error = 2.6142950739461782e-15
relative error = 1.9066472261501309001112000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.854
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.854
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.855
y[1] (closed_form) = 1.3679422728360863171574159570467
y[1] (numeric) = 1.3679422728360836958085421742561
absolute error = 2.6213488737827906e-15
relative error = 1.9162715604570644983649999999999e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.855
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.855
Order of pole (three term test) = 1.577e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.856
y[1] (closed_form) = 1.3647480129268931784435321862172
y[1] (numeric) = 1.3647480129268905501065717332437
absolute error = 2.6283369604529735e-15
relative error = 1.9258771110544699904959999999999e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.856
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.856
Order of pole (three term test) = 1.633e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.857
y[1] (closed_form) = 1.3615649282659517543083318242656
y[1] (numeric) = 1.3615649282659491190483099626327
absolute error = 2.6352600218616329e-15
relative error = 1.9354640877962544217720999999999e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.857
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.857
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.858
y[1] (closed_form) = 1.3583929667845751761835677919594
y[1] (numeric) = 1.358392966784572534064829870308
absolute error = 2.6421187379216514e-15
relative error = 1.9450326985833545812296000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.858
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.858
Order of pole (three term test) = 1.752e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.859
y[1] (closed_form) = 1.3552320767169773987946565909679
y[1] (numeric) = 1.3552320767169747498808759350617
absolute error = 2.6489137806559062e-15
relative error = 1.9545831493841607227622000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.859
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.859
Order of pole (three term test) = 1.814e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.86
y[1] (closed_form) = 1.3520822065981611681990265008113
y[1] (numeric) = 1.3520822065981585125532122029448
absolute error = 2.6556458142978665e-15
relative error = 1.9641156442547020633999999999999e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.86
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.86
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.861
y[1] (closed_form) = 1.3489433052618231508347935644613
y[1] (numeric) = 1.348943305261820488519298173667
absolute error = 2.6623154953907943e-15
relative error = 1.9736303853585990212703000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.861
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.861
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.862
y[1] (closed_form) = 1.3458153218382760644053380418926
y[1] (numeric) = 1.3458153218382733954818651563239
absolute error = 2.6689234728855687e-15
relative error = 1.9831275729867845091227999999999e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.862
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.862
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.863
y[1] (closed_form) = 1.3426982057523876530843791833441
y[1] (numeric) = 1.342698205752384977613990946191
absolute error = 2.6754703882371531e-15
relative error = 1.9926074055769962771339000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.863
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.863
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.864
y[1] (closed_form) = 1.3395919067215363511659807956104
y[1] (numeric) = 1.3395919067215336692091052958818
absolute error = 2.6819568754997286e-15
relative error = 2.0020700797330454009856000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.864
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.864
Order of pole (three term test) = 6.478e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.865
y[1] (closed_form) = 1.3364963747535834809048080457082
y[1] (numeric) = 1.336496374753580792521246625198
absolute error = 2.6883835614205102e-15
relative error = 2.0115157902438612443950000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.865
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.865
Order of pole (three term test) = 8.942e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.866
y[1] (closed_form) = 1.333411560144861831894137789417
y[1] (numeric) = 1.3334115601448591371430722571493
absolute error = 2.6947510655322677e-15
relative error = 2.0209447301023173552212000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.866
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.866
Order of pole (three term test) = 4.629e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.867
y[1] (closed_form) = 1.3303374134781804709128376230063
y[1] (numeric) = 1.330337413478177769852837378436
absolute error = 2.7010600002445703e-15
relative error = 2.0303570905238408042367000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.867
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.867
Order of pole (three term test) = 9.583e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.868
y[1] (closed_form) = 1.3272738856208456327380067531696
y[1] (numeric) = 1.3272738856208429254270358193958
absolute error = 2.7073109709337738e-15
relative error = 2.0397530609648075914911999999999e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.868
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.868
Order of pole (three term test) = 2.480e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.869
y[1] (closed_form) = 1.3242209277226975439674453527129
y[1] (numeric) = 1.3242209277226948304628693209451
absolute error = 2.7135045760317678e-15
relative error = 2.0491328291407258036157999999999e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.869
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.869
Order of pole (three term test) = 1.284e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.87
y[1] (closed_form) = 1.3211784912141630334258158277183
y[1] (numeric) = 1.3211784912141603137844087142134
absolute error = 2.7196414071135049e-15
relative error = 2.0584965810442118588100000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.87
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.87
Order of pole (three term test) = 2.657e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.871
y[1] (closed_form) = 1.318146527804323784240503742877
y[1] (numeric) = 1.3181465278043210585184547595513
absolute error = 2.7257220489833257e-15
relative error = 2.0678445009627591923737000000001e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.871
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.871
Order of pole (three term test) = 5.501e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.872
y[1] (closed_form) = 1.315124989479000084167999326656
y[1] (numeric) = 1.3151249894789973524209195665553
absolute error = 2.7317470797601007e-15
relative error = 2.0771767714963044106688000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.872
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.872
Order of pole (three term test) = 2.847e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.873
y[1] (closed_form) = 1.3121138284988499322293207580344
y[1] (numeric) = 1.3121138284988471945122497968296
absolute error = 2.7377170709612048e-15
relative error = 2.0864935735745920530192000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.873
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.873
Order of pole (three term test) = 8.840e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.874
y[1] (closed_form) = 1.3091129973974833611738030779865
y[1] (numeric) = 1.3091129973974806175412154926432
absolute error = 2.7436325875853433e-15
relative error = 2.0957950864743416986308000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.874
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.874
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.875
y[1] (closed_form) = 1.306122448979591836734693877551
y[1] (numeric) = 1.3061224489795890872405056833062
absolute error = 2.7494941881942448e-15
relative error = 2.1050814878362186750000000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.875
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.875
Order of pole (three term test) = 3.156e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.876
y[1] (closed_form) = 1.3031421363190925960676382894435
y[1] (numeric) = 1.3031421363190898407652132962043
absolute error = 2.7553024249932392e-15
relative error = 2.1143529536816119243392000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.876
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.876
Order of pole (three term test) = 6.532e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.877
y[1] (closed_form) = 1.3001720127572877891745077873803
y[1] (numeric) = 1.3001720127572850281166638766448
absolute error = 2.7610578439107355e-15
relative error = 2.1236096584292200843795000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.877
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.877
Order of pole (three term test) = 6.759e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.878
y[1] (closed_form) = 1.2972120319010382885103335910461
y[1] (numeric) = 1.2972120319010355217493489144284
absolute error = 2.7667609846766177e-15
relative error = 2.1328517749114497590468000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.878
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.878
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.879
y[1] (closed_form) = 1.2942621476209520333505470198967
y[1] (numeric) = 1.2942621476209492609381661203227
absolute error = 2.7724123808995740e-15
relative error = 2.1420794743906277549340000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.879
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.879
Order of pole (three term test) = 7.237e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.88
y[1] (closed_form) = 1.2913223140495867768595041322314
y[1] (numeric) = 1.291322314049583998846943988858
absolute error = 2.7780125601433734e-15
relative error = 2.1512929265750283609600000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.88
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.88
Order of pole (three term test) = 1.123e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.881
y[1] (closed_form) = 1.2883924855796671051495759256134
y[1] (numeric) = 1.2883924855796643215875319235054
absolute error = 2.7835620440021080e-15
relative error = 2.1604922996347201473880000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.881
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.881
Order of pole (three term test) = 3.874e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.882
y[1] (closed_form) = 1.2854726168623155989531111008273
y[1] (numeric) = 1.2854726168623128098917629264136
absolute error = 2.7890613481744137e-15
relative error = 2.1696777602172326031588000000001e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.882
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.882
Order of pole (three term test) = 1.202e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.883
y[1] (closed_form) = 1.282562662805298009847516125019
y[1] (numeric) = 1.2825626628052952153365335883324
absolute error = 2.7945109825366866e-15
relative error = 2.1788494734630466384674000000001e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.883
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.883
Order of pole (three term test) = 4.147e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.884
y[1] (closed_form) = 1.2796625785712823242767347105915
y[1] (numeric) = 1.2796625785712795243652834952842
absolute error = 2.7999114512153073e-15
relative error = 2.1880076030209091814288000000000e-13 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.884
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.884
Order of pole (three term test) = 4.290e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.885
y[1] (closed_form) = 1.276772319576111589900730952153
y[1] (numeric) = 1.2767723195761087846374782942636
absolute error = 2.8052632526578894e-15
relative error = 2.1971523110629754253149999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.885
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.885
Order of pole (three term test) = 1.775e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.886
y[1] (closed_form) = 1.2738918414870903800783698260883
y[1] (numeric) = 1.2738918414870875695114901225223
absolute error = 2.8105668797035660e-15
relative error = 2.2062837582997804957360000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.886
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.886
Order of pole (three term test) = 9.182e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.887
y[1] (closed_form) = 1.2710211002212847735485256790747
y[1] (numeric) = 1.271021100221281957725706026746
absolute error = 2.8158228196523287e-15
relative error = 2.2154021039950429989703000000002e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.887
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.887
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.888
y[1] (closed_form) = 1.2681600519438357276195114032952
y[1] (numeric) = 1.2681600519438329065879570698631
absolute error = 2.8210315543334321e-15
relative error = 2.2245075059803018818624000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.888
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.888
Order of pole (three term test) = 4.912e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.889
y[1] (closed_form) = 1.2653086530662857244081835102445
y[1] (numeric) = 1.2653086530662828982146233373679
absolute error = 2.8261935601728766e-15
relative error = 2.2336001206693880073886000000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.889
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.889
Order of pole (three term test) = 5.081e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.89
y[1] (closed_form) = 1.2624668602449185708875142027521
y[1] (numeric) = 1.2624668602449157395782059427653
absolute error = 2.8313093082599868e-15
relative error = 2.2426801030727355442800000000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.89
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.89
Order of pole (three term test) = 1.051e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.891
y[1] (closed_form) = 1.2596346303791122347052014092792
y[1] (numeric) = 1.2596346303791093983259369961859
absolute error = 2.8363792644130933e-15
relative error = 2.2517476068115309220973000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.891
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.891
Order of pole (three term test) = 5.435e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.892
y[1] (closed_form) = 1.2568119206097045989261798950311
y[1] (numeric) = 1.256811920609701757522290650696
absolute error = 2.8414038892443351e-15
relative error = 2.2608027841317046430063999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.892
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.892
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.893
y[1] (closed_form) = 1.253998688317372020028867049805
y[1] (numeric) = 1.2539986883173691736452288262116
absolute error = 2.8463836382235934e-15
relative error = 2.2698457859177663332366000000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.893
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.893
Order of pole (three term test) = 1.744e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.894
y[1] (closed_form) = 1.2511948911210205746487895940623
y[1] (numeric) = 1.2511948911210177233298278524919
absolute error = 2.8513189617415704e-15
relative error = 2.2788767617064857602144000000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.894
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.894
Order of pole (three term test) = 6.012e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.895
y[1] (closed_form) = 1.248400486876189881714053868481
y[1] (numeric) = 1.2484004868761870255037486964575
absolute error = 2.8562103051720235e-15
relative error = 2.2878958597004201240875000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.895
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.895
Order of pole (three term test) = 6.217e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.896
y[1] (closed_form) = 1.2456154336734693877551020408163
y[1] (numeric) = 1.2456154336734665266969931076461
absolute error = 2.8610581089331702e-15
relative error = 2.2969032267812919672832000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.896
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.896
Order of pole (three term test) = 1.929e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.897
y[1] (closed_form) = 1.2428396898369270042964968077662
y[1] (numeric) = 1.242839689836924138433688259493
absolute error = 2.8658628085482732e-15
relative error = 2.3058990085232175511788000000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.897
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.897
Order of pole (three term test) = 1.329e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.898
y[1] (closed_form) = 1.24007321392254998735125321799
y[1] (numeric) = 1.2400732139225471167264185125715
absolute error = 2.8706248347054185e-15
relative error = 2.3148833492057883000740000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.898
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.898
Order of pole (three term test) = 1.375e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.899
y[1] (closed_form) = 1.2373159647166979501386412538465
y[1] (numeric) = 1.2373159647166950747940279373488
absolute error = 2.8753446133164977e-15
relative error = 2.3238563918270067576377000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.899
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.899
Order of pole (three term test) = 1.421e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.9
y[1] (closed_form) = 1.2345679012345679012345679012346
y[1] (numeric) = 1.2345679012345650212120023258275
absolute error = 2.8800225655754071e-15
relative error = 2.3328182781160797509999999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.9
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9
Order of pole (three term test) = 1.470e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.901
y[1] (closed_form) = 1.2318289827186712014397617150016
y[1] (numeric) = 1.2318289827186683167806536995287
absolute error = 2.8846591080154729e-15
relative error = 2.3417691485460689156929000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.901
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.901
Order of pole (three term test) = 1.519e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.902
y[1] (closed_form) = 1.2290991686373223337151734750567
y[1] (numeric) = 1.229099168637319444460520908941
absolute error = 2.8892546525661157e-15
relative error = 2.3507091423464019979827999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.902
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.902
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.903
y[1] (closed_form) = 1.2263784186831393815864185948401
y[1] (numeric) = 1.2263784186831364877768119860764
absolute error = 2.8938096066087637e-15
relative error = 2.3596383975152453998533000000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.903
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.903
Order of pole (three term test) = 8.119e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.904
y[1] (closed_form) = 1.2236666927715561124598637324771
y[1] (numeric) = 1.2236666927715532141354907004509
absolute error = 2.8983243730320262e-15
relative error = 2.3685570508317403230592000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.904
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.904
Order of pole (three term test) = 2.518e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.905
y[1] (closed_form) = 1.220963951039345563322242910778
y[1] (numeric) = 1.2209639510393426605228926246406
absolute error = 2.9027993502861374e-15
relative error = 2.3774652378681036840350000000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.905
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.905
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.906
y[1] (closed_form) = 1.2182701538431550273136168491636
y[1] (numeric) = 1.2182701538431521200786844124814
absolute error = 2.9072349324366822e-15
relative error = 2.3863630930015964703191999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.906
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.906
Order of pole (three term test) = 8.969e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.907
y[1] (closed_form) = 1.2155852617580523406702007782176
y[1] (numeric) = 1.2155852617580494290386915606064
absolute error = 2.9116315092176112e-15
relative error = 2.3952507494263586360688000000002e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.907
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.907
Order of pole (three term test) = 9.270e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.908
y[1] (closed_form) = 1.2129092355760833705292165576665
y[1] (numeric) = 1.2129092355760804545397504741061
absolute error = 2.9159894660835604e-15
relative error = 2.4041283391651165416256000000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.908
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.908
Order of pole (three term test) = 9.582e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.909
y[1] (closed_form) = 1.2102420363048406050726084709681
y[1] (numeric) = 1.2102420363048376847634242094889
absolute error = 2.9203091842614792e-15
relative error = 2.4129959930807592948552000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.909
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.909
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.91
y[1] (closed_form) = 1.2075836251660427484603308779133
y[1] (numeric) = 1.2075836251660398238692900763322
absolute error = 2.9245910408015811e-15
relative error = 2.4218538408877893089100000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.91
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.91
Order of pole (three term test) = 1.024e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.911
y[1] (closed_form) = 1.2049339635941252239671004830581
y[1] (numeric) = 1.2049339635941222951316918554324
absolute error = 2.9288354086276257e-15
relative error = 2.4307020111636477485696999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.911
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.911
Order of pole (three term test) = 1.058e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.912
y[1] (closed_form) = 1.202293013234841489689135118498
y[1] (numeric) = 1.2022930132348385566464785319584
absolute error = 2.9330426565865396e-15
relative error = 2.4395406313599147930624000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.912
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.912
Order of pole (three term test) = 1.093e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.913
y[1] (closed_form) = 1.1996607359438750721296017486255
y[1] (numeric) = 1.1996607359438721349164522512367
absolute error = 2.9372131494973888e-15
relative error = 2.4483698278133888846272000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.913
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.913
Order of pole (three term test) = 1.130e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.914
y[1] (closed_form) = 1.1970370937854622239033943183832
y[1] (numeric) = 1.1970370937854592825561461186747
absolute error = 2.9413472481997085e-15
relative error = 2.4571897257570436820659999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.914
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.914
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.915
y[1] (closed_form) = 1.194422049031025112723580877303
y[1] (numeric) = 1.1944220490310221672782712761012
absolute error = 2.9454453096012018e-15
relative error = 2.4660004493308661770050000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.915
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.915
Order of pole (three term test) = 1.206e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.916
y[1] (closed_form) = 1.1918155641578154497435212905932
y[1] (numeric) = 1.1918155641578125002358345657776
absolute error = 2.9495076867248156e-15
relative error = 2.4748021215925768780736000000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.916
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.916
Order of pole (three term test) = 1.247e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.917
y[1] (closed_form) = 1.1892176018475684662303823691356
y[1] (numeric) = 1.1892176018475655126956536139339
absolute error = 2.9535347287552017e-15
relative error = 2.4835948645282328023112999999998e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.917
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.917
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.918
y[1] (closed_form) = 1.1866281249851671484376854106446
y[1] (numeric) = 1.1866281249851641909109043260725
absolute error = 2.9575267810845721e-15
relative error = 2.4923787990627149384003999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.918
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.918
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.919
y[1] (closed_form) = 1.1840470966573166414267293895882
y[1] (numeric) = 1.1840470966573136799425440316297
absolute error = 2.9614841853579585e-15
relative error = 2.5011540450701027887185000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.919
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.919
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.92
y[1] (closed_form) = 1.1814744801512287334593572778828
y[1] (numeric) = 1.1814744801512257680520777600002
absolute error = 2.9654072795178826e-15
relative error = 2.5099207213839358326400000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.92
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.92
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.921
y[1] (closed_form) = 1.1789102389533163334476876265118
y[1] (numeric) = 1.1789102389533133641512897780665
absolute error = 2.9692963978484453e-15
relative error = 2.5186789458073630897173000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.921
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.921
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.922
y[1] (closed_form) = 1.1763543367478978548002315065335
y[1] (numeric) = 1.1763543367478948816483604876884
absolute error = 2.9731518710188451e-15
relative error = 2.5274288351231839179883999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.922
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.922
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.923
y[1] (closed_form) = 1.1738067374159114198483676456606
y[1] (numeric) = 1.1738067374159084428743415193291
absolute error = 2.9769740261263315e-15
relative error = 2.5361705051037794684635000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.923
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.923
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.924
y[1] (closed_form) = 1.1712674050336387998725661063324
y[1] (numeric) = 1.1712674050336358191093793677296
absolute error = 2.9807631867386028e-15
relative error = 2.5449040705209373441727999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.924
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.924
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.925
y[1] (closed_form) = 1.1687363038714390065741417092769
y[1] (numeric) = 1.1687363038714360220544687736221
absolute error = 2.9845196729356548e-15
relative error = 2.5536296451555696382499999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.925
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.925
Order of pole (three term test) = 1.672e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.926
y[1] (closed_form) = 1.1662133983924914516557897830377
y[1] (numeric) = 1.1662133983924884634119884319483
absolute error = 2.9882438013510894e-15
relative error = 2.5623473418073267343543999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.926
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.926
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.927
y[1] (closed_form) = 1.1636986532515485919828144982888
y[1] (numeric) = 1.1636986532515456000469292853988
absolute error = 2.9919358852128900e-15
relative error = 2.5710572723041075508100000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.927
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.927
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.928
y[1] (closed_form) = 1.1611920332936979785969084423306
y[1] (numeric) = 1.1611920332936949830006740586598
absolute error = 2.9955962343836708e-15
relative error = 2.5797595475114671542271999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.928
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.928
Order of pole (three term test) = 1.842e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.929
y[1] (closed_form) = 1.158693503553133628645684272242
y[1] (numeric) = 1.1586935035531306294205288718343
absolute error = 2.9992251554004077e-15
relative error = 2.5884542773419232618157000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.929
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.929
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.93
y[1] (closed_form) = 1.1562030292519366400739969938722
y[1] (numeric) = 1.1562030292519336372510454802133
absolute error = 3.0028229515136589e-15
relative error = 2.5971415707641635826099999999998e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.93
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.93
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.931
y[1] (closed_form) = 1.1537205757988649696975290766429
y[1] (numeric) = 1.1537205757988619633076063503629
absolute error = 3.0063899227262800e-15
relative error = 2.6058215358121531790799999999998e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.931
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.931
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.932
y[1] (closed_form) = 1.151246108788152296045239367091
y[1] (numeric) = 1.1512461087881492861188735354472
absolute error = 3.0099263658316438e-15
relative error = 2.6144942795941457641311999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.932
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.932
Order of pole (three term test) = 2.096e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.933
y[1] (closed_form) = 1.1487795939983158891151984689065
y[1] (numeric) = 1.1487795939983128756826240175381
absolute error = 3.0134325744513684e-15
relative error = 2.6231599083015972271476000000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.933
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.933
Order of pole (three term test) = 4.329e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.934
y[1] (closed_form) = 1.1463209973909734099381445189808
y[1] (numeric) = 1.1463209973909703930293054464175
absolute error = 3.0169088390725633e-15
relative error = 2.6318185272179850301348000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.934
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.934
Order of pole (three term test) = 4.470e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.935
y[1] (closed_form) = 1.1438702851096685635848894735337
y[1] (numeric) = 1.1438702851096655432294423889364
absolute error = 3.0203554470845973e-15
relative error = 2.6404702407275320745925000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.935
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.935
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.936
y[1] (closed_form) = 1.1414274234787055299875812696326
y[1] (numeric) = 1.1414274234787025062148984542341
absolute error = 3.0237726828153985e-15
relative error = 2.6491151523238393642559999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.936
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.936
Order of pole (three term test) = 7.150e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.937
y[1] (closed_form) = 1.1389923790019920976708744841789
y[1] (numeric) = 1.1389923790019890705100469168903
absolute error = 3.0271608275672886e-15
relative error = 2.6577533646184248048533999999998e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.937
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.937
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.938
y[1] (closed_form) = 1.1365651183618914262073731252358
y[1] (numeric) = 1.1365651183618883956872134728741
absolute error = 3.0305201596523617e-15
relative error = 2.6663849793491725275748000000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.938
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.938
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.939
y[1] (closed_form) = 1.1341456084180823639223745379774
y[1] (numeric) = 1.1341456084180793300714201105658
absolute error = 3.0338509544274116e-15
relative error = 2.6750100973886917833636000000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.939
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.939
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=99.0MB, alloc=44.3MB, time=0.81
x[1] = -0.94
y[1] (closed_form) = 1.131733816206428248076052512449
y[1] (numeric) = 1.1317338162064252109225681840346
absolute error = 3.0371534843284144e-15
relative error = 2.6836288187525869638400000000002e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.94
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.94
Order of pole (three term test) = 5.417e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.941
y[1] (closed_form) = 1.1293297089378541154468588258811
y[1] (numeric) = 1.1293297089378510750188399213079
absolute error = 3.0404280189045732e-15
relative error = 2.6922412426076403817091999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.941
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.941
Order of pole (three term test) = 2.796e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.942
y[1] (closed_form) = 1.1269332539972322519281827975893
y[1] (numeric) = 1.1269332539972292082533579456599
absolute error = 3.0436748248519294e-15
relative error = 2.7008474672799074801015999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.942
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.942
Order of pole (three term test) = 2.887e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.943
y[1] (closed_form) = 1.1245444189422760104312740301086
y[1] (numeric) = 1.1245444189422729635371079835597
absolute error = 3.0468941660465489e-15
relative error = 2.7094475902627275627760999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.943
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.943
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.944
y[1] (closed_form) = 1.1221631715024418270611893134157
y[1] (numeric) = 1.1221631715024387769748857361293
absolute error = 3.0500863035772864e-15
relative error = 2.7180417082246486933504000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.944
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.944
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.945
y[1] (closed_form) = 1.119789479577839366199154558943
y[1] (numeric) = 1.1197894795778363129476587808073
absolute error = 3.0532514957781357e-15
relative error = 2.7266299170172696334924999999998e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.945
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.945
Order of pole (three term test) = 6.351e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.946
y[1] (closed_form) = 1.117423311238149725784319422158
y[1] (numeric) = 1.1174233112381466693943211619882
absolute error = 3.0563899982601698e-15
relative error = 2.7352123116829981167368000000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.946
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.946
Order of pole (three term test) = 3.278e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.947
y[1] (closed_form) = 1.1150646347215516347405077335307
y[1] (numeric) = 1.1150646347215485752384437904515
absolute error = 3.0595020639430792e-15
relative error = 2.7437889864627289142728000000002e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.947
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.947
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.948
y[1] (closed_form) = 1.1127134184336555751393117199879
y[1] (numeric) = 1.1127134184336525125513686336777
absolute error = 3.0625879430863102e-15
relative error = 2.7523600348034393219808000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.948
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.948
Order of pole (three term test) = 6.985e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.949
y[1] (closed_form) = 1.1103696309464457623298219744371
y[1] (numeric) = 1.1103696309464426966819386546256
absolute error = 3.0656478833198115e-15
relative error = 2.7609255493657055567114999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.949
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.949
Order of pole (three term test) = 1.081e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.95
y[1] (closed_form) = 1.1080332409972299168975069252078
y[1] (numeric) = 1.1080332409972268482153772508141
absolute error = 3.0686821296743937e-15
relative error = 2.7694856220311403142499999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.95
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.95
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.951
y[1] (closed_form) = 1.1057042174875967629403328833117
y[1] (numeric) = 1.105704217487593691249408271605
absolute error = 3.0716909246117067e-15
relative error = 2.7780403439097521511867000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.951
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.951
Order of pole (three term test) = 3.840e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.952
y[1] (closed_form) = 1.1033825294823811877692253371937
y[1] (numeric) = 1.1033825294823781130947172833537
absolute error = 3.0746745080538400e-15
relative error = 2.7865898053472274073600000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.952
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.952
Order of pole (three term test) = 3.963e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.953
y[1] (closed_form) = 1.1010681462086369987524897903456
y[1] (numeric) = 1.1010681462086339211193723777941
absolute error = 3.0776331174125515e-15
relative error = 2.7951340959321359852635000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.953
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.953
Order of pole (three term test) = 4.089e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.954
y[1] (closed_form) = 1.0987610370546172136299109124551
y[1] (numeric) = 1.0987610370546141330629232943251
absolute error = 3.0805669876181300e-15
relative error = 2.8036733045030620030800000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.954
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.954
Order of pole (three term test) = 1.266e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.955
y[1] (closed_form) = 1.0964611715687618212220059757134
y[1] (numeric) = 1.0964611715687587377456548278179
absolute error = 3.0834763511478955e-15
relative error = 2.8122075191556593933875000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.955
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.955
Order of pole (three term test) = 4.355e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.956
y[1] (closed_form) = 1.0941685194586929500533954237496
y[1] (numeric) = 1.0941685194586898636919573694063
absolute error = 3.0863614380543433e-15
relative error = 2.8207368272496342982288000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.956
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.956
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.957
y[1] (closed_form) = 1.0918830505902173829965420063788
y[1] (numeric) = 1.0918830505902142937740660134428
absolute error = 3.0892224759929360e-15
relative error = 2.8292613154156544426640000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.957
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.957
Order of pole (three term test) = 4.637e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.958
y[1] (closed_form) = 1.0896047349863363566232713420879
y[1] (numeric) = 1.0896047349863332645635810925396
absolute error = 3.0920596902495483e-15
relative error = 2.8377810695621864460012000000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.958
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.958
Order of pole (three term test) = 4.785e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.959
y[1] (closed_form) = 1.0873335428262625845265912854566
y[1] (numeric) = 1.0873335428262594896532875178869
absolute error = 3.0948733037675697e-15
relative error = 2.8462961748822622692657000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.959
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.959
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.96
y[1] (closed_form) = 1.0850694444444444444444444444445
y[1] (numeric) = 1.0850694444444413467809072697761
absolute error = 3.0976635371746684e-15
relative error = 2.8548067158601743974399999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.96
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.96
Order of pole (three term test) = 5.094e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.961
y[1] (closed_form) = 1.0828124103295972695802261128875
y[1] (numeric) = 1.0828124103295941691496173036642
absolute error = 3.1004306088092233e-15
relative error = 2.8633127762781027112393000000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.961
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.961
Order of pole (three term test) = 5.255e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.962
y[1] (closed_form) = 1.0805624111237416850722464028077
y[1] (numeric) = 1.080562411123738581897511656381
absolute error = 3.1031747347464267e-15
relative error = 2.8718144392226721109548000000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.962
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.962
Order of pole (three term test) = 5.422e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.963
y[1] (closed_form) = 1.078319417621248931115877282937
y[1] (numeric) = 1.0783194176212458252197484588752
absolute error = 3.1058961288240618e-15
relative error = 2.8803117870914413674042000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.963
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.963
Order of pole (three term test) = 5.593e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.964
y[1] (closed_form) = 1.0760834007678931147879685267127
y[1] (numeric) = 1.0760834007678900061929658587511
absolute error = 3.1085950026679616e-15
relative error = 2.8888049015993260430336000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.964
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.964
Order of pole (three term test) = 5.770e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.965
y[1] (closed_form) = 1.0738543316599103331633063974872
y[1] (numeric) = 1.0738543316599072218917406803359
absolute error = 3.1112715657171513e-15
relative error = 2.8972938637849542193424999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.965
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.965
Order of pole (three term test) = 1.191e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.966
y[1] (closed_form) = 1.0716321815430646108474895944516
y[1] (numeric) = 1.0716321815430614969214643457722
absolute error = 3.1139260252486794e-15
relative error = 2.9057787540169566741863999999998e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.966
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.966
Order of pole (three term test) = 6.140e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.967
y[1] (closed_form) = 1.0694169218117205955796720953835
y[1] (numeric) = 1.0694169218117174790210856932422
absolute error = 3.1165585864021413e-15
relative error = 2.9142596520001919060756999999998e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.967
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.967
Order of pole (three term test) = 6.334e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.968
y[1] (closed_form) = 1.0672085240079229560822348200259
y[1] (numeric) = 1.0672085240079198369127826161255
absolute error = 3.1191694522039004e-15
relative error = 2.9227366367819075684096000000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.968
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.968
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.969
y[1] (closed_form) = 1.0650069598204824268526594821297
y[1] (numeric) = 1.0650069598204793050938358911198
absolute error = 3.1217588235910099e-15
relative error = 2.9312097867578382467139000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.969
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.969
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.97
y[1] (closed_form) = 1.0628122010840684451057498140078
y[1] (numeric) = 1.0628122010840653207788503791695
absolute error = 3.1243268994348383e-15
relative error = 2.9396791796782393564700000000002e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.97
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.97
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.971
y[1] (closed_form) = 1.0606242197783083255819379937868
y[1] (numeric) = 1.0606242197783051987080614293808
absolute error = 3.1268738765644060e-15
relative error = 2.9481448926538611174460000000002e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.971
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.971
Order of pole (three term test) = 1.434e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.972
y[1] (closed_form) = 1.0584429880268929194397872952971
y[1] (numeric) = 1.0584429880268897900398375058648
absolute error = 3.1293999497894323e-15
relative error = 2.9566070021618590061232000000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.972
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.972
Order of pole (three term test) = 7.394e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.973
y[1] (closed_form) = 1.056268478096688703948014690582
y[1] (numeric) = 1.0562684780966855720427027674815
absolute error = 3.1319053119231005e-15
relative error = 2.9650655840516450132645000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.973
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.973
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.974
y[1] (closed_form) = 1.0541006623968562501844676159194
y[1] (numeric) = 1.0541006623968531157943138113766
absolute error = 3.1343901538045428e-15
relative error = 2.9735207135506784453328000000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.974
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.974
Order of pole (three term test) = 7.864e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.975
y[1] (closed_form) = 1.0519395134779750164365548980933
y[1] (numeric) = 1.051939513477971879581890577044
absolute error = 3.1368546643210493e-15
relative error = 2.9819724652701974908125000000002e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.975
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.975
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.976
y[1] (closed_form) = 1.0497850040311744154797097554421
y[1] (numeric) = 1.0497850040311712761806793254377
absolute error = 3.1392990304300044e-15
relative error = 2.9904209132108918713344000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.976
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.976
Order of pole (three term test) = 1.673e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.977
y[1] (closed_form) = 1.0476371068872711043876089673546
y[1] (numeric) = 1.0476371068872679626641717867998
absolute error = 3.1417234371805548e-15
relative error = 2.9988661307685177926891999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.977
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.977
Order of pole (three term test) = 1.725e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.978
y[1] (closed_form) = 1.0454957950159124460001421874281
y[1] (numeric) = 1.0454957950159093018720744524154
absolute error = 3.1441280677350127e-15
relative error = 3.0073081907394558873468000000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.978
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.978
Order of pole (three term test) = 8.893e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.979
y[1] (closed_form) = 1.0433610415247260916425737212828
y[1] (numeric) = 1.043361041524722945129470331286
absolute error = 3.1465131033899968e-15
relative error = 3.0157471653262119229888000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.979
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.979
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.98
y[1] (closed_form) = 1.0412328196584756351520199916701
y[1] (numeric) = 1.0412328196584724862732963943549
absolute error = 3.1488787235973152e-15
relative error = 3.0241831261428615180800000000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.98
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.98
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.981
y[1] (closed_form) = 1.0391111027982222887253328013085
y[1] (numeric) = 1.0391111027982191375002268167142
absolute error = 3.1512251059845943e-15
relative error = 3.0326161442204401551422999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.981
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.981
Order of pole (three term test) = 9.749e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.982
y[1] (closed_form) = 1.0369958644604925315557841555328
y[1] (numeric) = 1.0369958644604893780033577798778
absolute error = 3.1535524263756550e-15
relative error = 3.0410462900122771322200000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.982
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.982
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.983
y[1] (closed_form) = 1.0348870782964516826746449561156
y[1] (numeric) = 1.0348870782964485268137861454732
absolute error = 3.1558608588106424e-15
relative error = 3.0494736333992768340536000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.983
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.983
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.984
y[1] (closed_form) = 1.0327847180910833498578888227906
y[1] (numeric) = 1.0327847180910801917073132568812
absolute error = 3.1581505755659094e-15
relative error = 3.0578982436951451720064000000002e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.984
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.984
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.985
y[1] (closed_form) = 1.0306887577623747068978845113247
y[1] (numeric) = 1.0306887577623715464761373376652
absolute error = 3.1604217471736595e-15
relative error = 3.0663201896515637883875000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.985
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.985
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.986
y[1] (closed_form) = 1.0285991713605075519751161288464
y[1] (numeric) = 1.0285991713605043893005736874957
absolute error = 3.1626745424413507e-15
relative error = 3.0747395394633113851372000000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.986
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.986
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.987
y[1] (closed_form) = 1.0265159330670551002957392403166
y[1] (numeric) = 1.0265159330670519353866107694519
absolute error = 3.1649091284708647e-15
relative error = 3.0831563607733337939343000000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.987
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.987
Order of pole (three term test) = 2.341e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.988
y[1] (closed_form) = 1.0244390171941844645871920536315
y[1] (numeric) = 1.024439017194181297461521376188
absolute error = 3.1671256706774435e-15
relative error = 3.0915707206777624078639999999998e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.988
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.988
Order of pole (three term test) = 1.207e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.989
y[1] (closed_form) = 1.0223683981838647774661826093091
y[1] (numeric) = 1.0223683981838616081418498009124
absolute error = 3.1693243328083967e-15
relative error = 3.0999826857308817886006999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.989
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.989
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.99
y[1] (closed_form) = 1.0203040506070809101112131415162
y[1] (numeric) = 1.0203040506070777386059361799327
absolute error = 3.1715052769615835e-15
relative error = 3.1083923219500479883499999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.99
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.99
Order of pole (three term test) = 1.282e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.991
y[1] (closed_form) = 1.0182459491630527420854287986429
y[1] (numeric) = 1.0182459491630495684167651949724
absolute error = 3.1736686636036705e-15
relative error = 3.1167996948205563283104999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.991
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.991
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.992
y[1] (closed_form) = 1.0161940686784599375650364203955
y[1] (numeric) = 1.0161940686784567617503848322255
absolute error = 3.1758146515881700e-15
relative error = 3.1252048693004609228799999999998e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.992
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.992
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.993
y[1] (closed_form) = 1.0141483841066721836338762069633
y[1] (numeric) = 1.0141483841066690056904780337031
absolute error = 3.1779433981732602e-15
relative error = 3.1336079098253450469498000000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.993
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.993
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.994
y[1] (closed_form) = 1.0121088705269848467059904699829
y[1] (numeric) = 1.0121088705269816666509314305906
absolute error = 3.1800550590393923e-15
relative error = 3.1420088803130450105227999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.994
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.994
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.995
y[1] (closed_form) = 1.0100755031438600035352642610035
y[1] (numeric) = 1.0100755031438568213854759543202
absolute error = 3.1821497883066833e-15
relative error = 3.1504078441683241340825000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.995
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.995
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.996
y[1] (closed_form) = 1.0080482572861728036644570248866
y[1] (numeric) = 1.008048257286169619436718472784
absolute error = 3.1842277385521026e-15
relative error = 3.1588048642875026128416000000003e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 15
h = -0.001
Radius of convergence (given) for eq 1 = 0.996
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.996
Order of pole (three term test) = 1.537e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.997
y[1] (closed_form) = 1.0060271084064631205552464816717
y[1] (numeric) = 1.0060271084064599342661856552209
absolute error = 3.1862890608264508e-15
relative error = 3.1672000030630395332572000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 0.997
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.997
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.998
y[1] (closed_form) = 1.0040120320801924490263091312887
y[1] (numeric) = 1.0040120320801892606924044601541
absolute error = 3.1883339046711346e-15
relative error = 3.1755933223880687461383999999998e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 0.998
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.998
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -0.999
y[1] (closed_form) = 1.002003004005006007008009010011
y[1] (numeric) = 1.0020030040050028166455908752692
absolute error = 3.1903624181347418e-15
relative error = 3.1839848836608904511418000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 0.999
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.999
Order of pole (three term test) = 1.682e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1
y[1] (closed_form) = 1
y[1] (numeric) = 0.99999999999999680762525221058232
absolute error = 3.19237474778941768e-15
relative error = 3.1923747477894176800000000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1
Order of pole (three term test) = 1.733e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.001
y[1] (closed_form) = 0.99800299600499400699200899001099
y[1] (numeric) = 0.99800299600499081262097024296627
absolute error = 3.19437103874704472e-15
relative error = 3.2007629751955775564847200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.001
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.001
Order of pole (three term test) = 1.786e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.002
y[1] (closed_form) = 0.99601196807980844697829889123948
y[1] (numeric) = 0.99601196807980525062686421600931
absolute error = 3.19635143467523017e-15
relative error = 3.2091496258196697916006800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.002
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.002
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.003
y[1] (closed_form) = 0.99402689240354708556285281742012
y[1] (numeric) = 0.99402689240354388724677500431781
absolute error = 3.19831607781310231e-15
relative error = 3.2175347591246812417807900000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.003
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.003
Order of pole (three term test) = 1.896e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.004
y[1] (closed_form) = 0.99204774527388454151521404422152
y[1] (numeric) = 0.99204774527388134125010505730298
absolute error = 3.20026510898691854e-15
relative error = 3.2259184341005576790166400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.004
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.004
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.005
y[1] (closed_form) = 0.99007450310635875349620058909433
y[1] (numeric) = 0.99007450310635555129753296360672
absolute error = 3.20219866762548761e-15
relative error = 3.2343007092684331232902500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.005
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.005
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.006
y[1] (closed_form) = 0.98810714243366836752842784248781
y[1] (numeric) = 0.98810714243366516341153606707943
absolute error = 3.20411689177540838e-15
relative error = 3.2426816426848171952616800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.006
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.006
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.007
y[1] (closed_form) = 0.98614563990497500613875660840847
y[1] (numeric) = 0.98614563990497180011883849228096
absolute error = 3.20601991811612751e-15
relative error = 3.2510612919457409853879900000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.007
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.007
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.008
y[1] (closed_form) = 0.98418997228521038044847568657092
y[1] (numeric) = 0.98418997228520717254059371175264
absolute error = 3.20790788197481828e-15
relative error = 3.2594397141908617608499200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.008
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.008
Order of pole (three term test) = 2.201e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.009
y[1] (closed_form) = 0.98224011645438820683226580203343
y[1] (numeric) = 0.98224011645438499705134846095032
absolute error = 3.20978091734108311e-15
relative error = 3.2678169661075272337119100000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.009
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.009
Order of pole (three term test) = 4.536e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.01
y[1] (closed_form) = 0.98029604940692089010881286148417
y[1] (numeric) = 0.98029604940691767846965598000247
absolute error = 3.21163915688148170e-15
relative error = 3.2761931039347994821700000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.01
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.01
Order of pole (three term test) = 1.168e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.011
y[1] (closed_form) = 0.97835774825094093556438034244478
y[1] (numeric) = 0.97835774825093772208164838855752
absolute error = 3.21348273195388726e-15
relative error = 3.2845681834674392000784600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.011
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.011
Order of pole (three term test) = 2.407e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.012
y[1] (closed_form) = 0.97642519020762705244574981643207
y[1] (numeric) = 0.97642519020762383713397719475907
absolute error = 3.21531177262167300e-15
relative error = 3.2929422600598506729120000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.012
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.012
Order of pole (three term test) = 4.958e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.013
y[1] (closed_form) = 0.97449835261053491189073144871849
y[1] (numeric) = 0.97449835261053169476432378098752
absolute error = 3.21712640766773097e-15
relative error = 3.3013153886299878217539300000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.013
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.013
Order of pole (three term test) = 7.661e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.014
y[1] (closed_form) = 0.97257721290493252259296865578158
y[1] (numeric) = 0.97257721290492930366620404745612
absolute error = 3.21892676460832546e-15
relative error = 3.3096876236632218046701600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.014
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.014
Order of pole (three term test) = 5.261e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.015
y[1] (closed_form) = 0.97066174864714018782304836322163
y[1] (numeric) = 0.97066174864713696711007865643853
absolute error = 3.22071296970678310e-15
relative error = 3.3180590192161706191975000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.015
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.015
Order of pole (three term test) = 2.709e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.016
y[1] (closed_form) = 0.968751937503875007750015500031
y[1] (numeric) = 0.96875193750387178526486751300943
absolute error = 3.22248514798702157e-15
relative error = 3.3264296289204909377619200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.016
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.016
Order of pole (three term test) = 8.372e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.017
y[1] (closed_form) = 0.96684775725159989132631208492018
y[1] (numeric) = 0.96684775725159666708288883800086
absolute error = 3.22424342324691932e-15
relative error = 3.3347995059866329365634800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.017
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.017
Order of pole (three term test) = 8.622e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.018
y[1] (closed_form) = 0.96494918577587704231495169464376
y[1] (numeric) = 0.9649491857758738163270336231159
absolute error = 3.22598791807152786e-15
relative error = 3.3431687032075580379866400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.018
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.018
Order of pole (three term test) = 1.184e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.019
y[1] (closed_form) = 0.96305620107072588435043303822081
y[1] (numeric) = 0.96305620107072265663167919209167
absolute error = 3.22771875384612914e-15
relative error = 3.3515372729624204999395400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.019
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.019
Order of pole (three term test) = 1.219e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.02
y[1] (closed_form) = 0.96116878123798539023452518262207
y[1] (numeric) = 0.96116878123798216079847441348258
absolute error = 3.22943605076913949e-15
relative error = 3.3599052672202127253960000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.02
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.02
Order of pole (three term test) = 6.279e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.021
y[1] (closed_form) = 0.95928690448668078097465468069656
y[1] (numeric) = 0.95928690448667754983472681583411
absolute error = 3.23113992786486245e-15
relative error = 3.3682727375433750772404500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.021
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.021
Order of pole (three term test) = 1.617e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.022
y[1] (closed_form) = 0.95741054913239456037622404938706
y[1] (numeric) = 0.95741054913239132754572105329485
absolute error = 3.23283050299609221e-15
relative error = 3.3766397350913703758696400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.022
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.022
Order of pole (three term test) = 3.330e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.023
y[1] (closed_form) = 0.95553969359664185130082396187779
y[1] (numeric) = 0.95553969359663861679293108530816
absolute error = 3.23450789287656963e-15
relative error = 3.3850063106242235383142700000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.023
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.023
Order of pole (three term test) = 6.858e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.024
y[1] (closed_form) = 0.95367431640625
y[1] (numeric) = 0.9536743164062467638277869167074
absolute error = 3.23617221308329260e-15
relative error = 3.3933725145060266213376000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.024
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.024
Order of pole (three term test) = 7.062e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.025
y[1] (closed_form) = 0.95181439619274241522903033908388
y[1] (numeric) = 0.95181439619273917740545227040107
absolute error = 3.23782357806868281e-15
relative error = 3.4017383967084098772562500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.025
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.025
Order of pole (three term test) = 1.091e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.026
y[1] (closed_form) = 0.9499599116917266091370944146157
y[1] (numeric) = 0.94995991169172336967499324200527
absolute error = 3.23946210117261043e-15
relative error = 3.4101040068139788570106800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.026
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.026
Order of pole (three term test) = 7.487e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.027
y[1] (closed_form) = 0.94811084174228640721929519336246
y[1] (numeric) = 0.94811084174228316613140055908365
absolute error = 3.24108789463427881e-15
relative error = 3.4184693940197182549924900000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.027
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.027
Order of pole (three term test) = 7.709e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.028
y[1] (closed_form) = 0.94626716528637829490226952716922
y[1] (numeric) = 0.9462671652863750522011999231985
absolute error = 3.24270106960397072e-15
relative error = 3.4268346071403625933644800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.028
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.028
Order of pole (three term test) = 3.969e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.029
y[1] (closed_form) = 0.94442886136823186861861223734253
y[1] (numeric) = 0.94442886136822862431687608268456
absolute error = 3.24430173615465797e-15
relative error = 3.4351996946117341996127700000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.029
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.029
Order of pole (three term test) = 8.173e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.03
y[1] (closed_form) = 0.94259590913375435950607974361391
y[1] (numeric) = 0.9425959091337511136160764501377
absolute error = 3.24589000329347621e-15
relative error = 3.4435647044940489111890000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.03
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.03
Order of pole (three term test) = 4.207e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.031
y[1] (closed_form) = 0.94076828782993919814555755102962
y[1] (numeric) = 0.94076828782993595067957857796316
absolute error = 3.24746597897306646e-15
relative error = 3.4519296844751896973880600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.031
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.031
Order of pole (three term test) = 4.332e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.032
y[1] (closed_form) = 0.93894597680427858902710173667448
y[1] (numeric) = 0.93894597680427533999733163388934
absolute error = 3.24902977010278514e-15
relative error = 3.4602946818739486409433600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.032
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.032
Order of pole (three term test) = 8.919e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.033
y[1] (closed_form) = 0.93712895550418006370602639517416
y[1] (numeric) = 0.93712895550417681312454383538999
absolute error = 3.25058148255978417e-15
relative error = 3.4686597436432375301811300000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.033
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.033
Order of pole (three term test) = 4.591e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.034
y[1] (closed_form) = 0.93531720347638698188103513425544
y[1] (numeric) = 0.93531720347638372975981393429251
absolute error = 3.25212122119996293e-15
relative error = 3.4770249163732675663870800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.034
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.034
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.035
y[1] (closed_form) = 0.93351070036640294989381315783332
y[1] (numeric) = 0.93351070036639969624472328903991
absolute error = 3.25364908986879341e-15
relative error = 3.4853902462946982206272500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.035
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.035
Order of pole (three term test) = 4.865e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.036
y[1] (closed_form) = 0.93170942591792012641433490854341
y[1] (numeric) = 0.93170942591791687124914349652287
absolute error = 3.25516519141202054e-15
relative error = 3.4937557792817559974998400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.036
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.036
Order of pole (three term test) = 1.502e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.037
y[1] (closed_form) = 0.9299133599722513853384280186615
y[1] (numeric) = 0.92991335997224812866880033242278
absolute error = 3.25666962768623872e-15
relative error = 3.5021215608553228460876800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.037
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.037
Order of pole (three term test) = 1.031e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.038
y[1] (closed_form) = 0.92812248246776630618389447618623
y[1] (numeric) = 0.92812248246776304802139490683953
absolute error = 3.25816249956934670e-15
relative error = 3.5104876361859951858348000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.038
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.038
Order of pole (three term test) = 1.061e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.039
y[1] (closed_form) = 0.92633677343933096252875117760562
y[1] (numeric) = 0.9263367734393277028848442067238
absolute error = 3.25964390697088182e-15
relative error = 3.5188540500971133132082200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.039
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.039
Order of pole (three term test) = 5.462e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.04
y[1] (closed_form) = 0.92455621301775147928994082840237
y[1] (numeric) = 0.92455621301774821817599198616696
absolute error = 3.26111394884223541e-15
relative error = 3.5272208470677618194560000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.04
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.04
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.041
y[1] (closed_form) = 0.9227807814292213298932065801652
y[1] (numeric) = 0.92278078142921806732048339341449
absolute error = 3.26257272318675071e-15
relative error = 3.5355880712357411961635100000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.041
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.041
Order of pole (three term test) = 5.786e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.042
y[1] (closed_form) = 0.92101045899477234463474567217185
y[1] (numeric) = 0.921010458994769080614418602467
absolute error = 3.26402032706970485e-15
relative error = 3.5439557664005110167554000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.042
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.042
Order of pole (three term test) = 5.955e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.043
y[1] (closed_form) = 0.91924522612972940178278419155599
y[1] (numeric) = 0.91924522612972613632592756337974
absolute error = 3.26545685662817625e-15
relative error = 3.5523239760261049053862500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.043
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.043
Order of pole (three term test) = 6.129e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.044
y[1] (closed_form) = 0.91748506334316877321237210258217
y[1] (numeric) = 0.91748506334316550632996502178327
absolute error = 3.26688240708079890e-15
relative error = 3.5606927432440176298704000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.044
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.044
Order of pole (three term test) = 1.262e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.045
y[1] (closed_form) = 0.9157299512373800966095098555436
y[1] (numeric) = 0.91572995123737682831243711813872
absolute error = 3.26829707273740488e-15
relative error = 3.5690621108560645640820000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.045
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.045
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.046
y[1] (closed_form) = 0.91397987050733194652120981687499
y[1] (numeric) = 0.91397987050732867682026280831831
absolute error = 3.26970094700855668e-15
relative error = 3.5774321213372140004948800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.046
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.046
Order of pole (three term test) = 6.681e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.047
y[1] (closed_form) = 0.91223480194014097676629182938655
y[1] (numeric) = 0.91223480194013770567216941441615
absolute error = 3.27109412241497040e-15
relative error = 3.5858028168383922872136000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.047
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.047
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.048
y[1] (closed_form) = 0.91049472641454460695763650136938
y[1] (numeric) = 0.91049472641454133448094590453797
absolute error = 3.27247669059683141e-15
relative error = 3.5941742391892623249286400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.048
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.048
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.049
y[1] (closed_form) = 0.90875962490037722612029614658656
y[1] (numeric) = 0.90875962490037395227155382358283
absolute error = 3.27384874232300373e-15
relative error = 3.6025464299009756274957300000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.049
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.049
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.05
y[1] (closed_form) = 0.90702947845804988662131519274376
y[1] (numeric) = 0.90702947845804661141094769260938
absolute error = 3.27521036750013438e-15
relative error = 3.6109194301688981539500000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.05
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.05
Order of pole (three term test) = 7.491e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.051
y[1] (closed_form) = 0.90530426823803346185636261419282
y[1] (numeric) = 0.9053042682380301852947074325387
absolute error = 3.27656165518165412e-15
relative error = 3.6192932808753103226061200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.051
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.051
Order of pole (three term test) = 7.708e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.052
y[1] (closed_form) = 0.90358397548034524136535153030982
y[1] (numeric) = 0.90358397548034196346265795363412
absolute error = 3.27790269357667570e-15
relative error = 3.6276680225920813038928000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.052
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.052
Order of pole (three term test) = 3.173e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.053
y[1] (closed_form) = 0.90186858151403893727413828711708
y[1] (numeric) = 0.901868581514035658040568228326
absolute error = 3.27923357005879108e-15
relative error = 3.6360436955833180786237200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.053
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.053
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.054
y[1] (closed_form) = 0.90015806775669807618217759038487
y[1] (numeric) = 0.90015806775669479562780641561625
absolute error = 3.28055437117476862e-15
relative error = 3.6444203398079892562559200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.054
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.054
Order of pole (three term test) = 2.519e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.055
y[1] (closed_form) = 0.8984524157139327508366838121336
y[1] (numeric) = 0.89845241571392946897150115898188
absolute error = 3.28186518265315172e-15
relative error = 3.6527979949225241931530000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.055
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.055
Order of pole (three term test) = 1.728e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.056
y[1] (closed_form) = 0.8967516069788797061524334251607
y[1] (numeric) = 0.89675160697887642298634401240077
absolute error = 3.28316608941275993e-15
relative error = 3.6611767002833874573004800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.056
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.056
Order of pole (three term test) = 2.666e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.057
y[1] (closed_form) = 0.89505562323170573435286135856913
y[1] (numeric) = 0.89505562323170244989568578747531
absolute error = 3.28445717557109382e-15
relative error = 3.6695564949496289993011800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.057
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.057
Order of pole (three term test) = 2.743e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=142.8MB, alloc=44.3MB, time=1.16
x[1] = -1.058
y[1] (closed_form) = 0.8933644462391143542225763915938
y[1] (numeric) = 0.89336444623911106848405193894904
absolute error = 3.28573852445264476e-15
relative error = 3.6779374176854102491326400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.058
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.058
Order of pole (three term test) = 9.407e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.059
y[1] (closed_form) = 0.89167805785385574967386875033995
y[1] (numeric) = 0.89167805785385246266365015322916
absolute error = 3.28701021859711079e-15
relative error = 3.6863195069625064058799900000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.059
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.059
Order of pole (three term test) = 9.677e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.06
y[1] (closed_form) = 0.88999644001423994304022783908864
y[1] (numeric) = 0.8899964400142366547678880715689
absolute error = 3.28827233976751974e-15
relative error = 3.6947028009627851798640000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.06
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.06
Order of pole (three term test) = 9.955e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.061
y[1] (closed_form) = 0.88831957474365317871835028395135
y[1] (numeric) = 0.88831957474364988919338132569072
absolute error = 3.28952496895826063e-15
relative error = 3.7030873375806621146642300000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.061
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.061
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.062
y[1] (closed_form) = 0.88664744415007749298661871677289
y[1] (numeric) = 0.88664744415007420221843231374822
absolute error = 3.29076818640302467e-15
relative error = 3.7114731544255329559114800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.062
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.062
Order of pole (three term test) = 1.053e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.063
y[1] (closed_form) = 0.88498003042561344603259027460045
y[1] (numeric) = 0.88498003042561015403051869194371
absolute error = 3.29200207158265674e-15
relative error = 3.7198602888241830538410600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.063
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.063
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.064
y[1] (closed_form) = 0.88331731584600599242467069930465
y[1] (numeric) = 0.883317315846002699197967466386
absolute error = 3.29322670323291865e-15
relative error = 3.7282487778231742719904000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.064
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.064
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.065
y[1] (closed_form) = 0.88165928277017346646388503162953
y[1] (numeric) = 0.88165928277017017202172567946448
absolute error = 3.29444215935216505e-15
relative error = 3.7366386581912094038362500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.065
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.065
Order of pole (three term test) = 2.293e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.066
y[1] (closed_form) = 0.88000591363973965905050881941927
y[1] (numeric) = 0.88000591363973636340199161048607
absolute error = 3.29564851720893320e-15
relative error = 3.7450299664214744954192000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.066
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.066
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.067
y[1] (closed_form) = 0.87835719097856896289731389587426
y[1] (numeric) = 0.87835719097856566605146054642663
absolute error = 3.29684585334944763e-15
relative error = 3.7534227387339592828310700000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.067
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.067
Order of pole (three term test) = 1.213e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.068
y[1] (closed_form) = 0.87671309739230456311632930746679
y[1] (numeric) = 0.87671309739230126508208570242611
absolute error = 3.29803424360504068e-15
relative error = 3.7618170110777559205843200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.068
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.068
Order of pole (three term test) = 2.495e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.069
y[1] (closed_form) = 0.87507361556790965039933984446442
y[1] (numeric) = 0.87507361556790635118557674497458
absolute error = 3.29921376309948984e-15
relative error = 3.7702128191333361090482400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.069
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.069
Order of pole (three term test) = 1.283e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.07
y[1] (closed_form) = 0.87343872827321163420386059917897
y[1] (numeric) = 0.87343872827320833381937434290576
absolute error = 3.30038448625627321e-15
relative error = 3.7786101983148071981290000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.07
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.07
Order of pole (three term test) = 1.319e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.071
y[1] (closed_form) = 0.87180841835644933354605458741231
y[1] (numeric) = 0.87180841835644603199956778166857
absolute error = 3.30154648680574374e-15
relative error = 3.7870091837721471052733400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.071
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.071
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.072
y[1] (closed_form) = 0.87018266874582312319002004900868
y[1] (numeric) = 0.87018266874581982049018225678531
absolute error = 3.30269983779222337e-15
relative error = 3.7954098103934184212300800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.072
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.072
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.073
y[1] (closed_form) = 0.86856146244904801320908272092513
y[1] (numeric) = 0.86856146244904470936447113990698
absolute error = 3.30384461158101815e-15
relative error = 3.8038121128069620456213500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.073
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.073
Order of pole (three term test) = 1.435e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.074
y[1] (closed_form) = 0.86694478255290964007920407533403
y[1] (numeric) = 0.86694478255290633509832420997908
absolute error = 3.30498087986535495e-15
relative error = 3.8122161253835701663062000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.074
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.074
Order of pole (three term test) = 1.476e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.075
y[1] (closed_form) = 0.8653326122228231476473769605192
y[1] (numeric) = 0.86533261222281984153866328727797
absolute error = 3.30610871367324123e-15
relative error = 3.8206218822386393964187500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.075
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.075
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.076
y[1] (closed_form) = 0.86372493470239493649894280067993
y[1] (numeric) = 0.8637249347023916292707594264317
absolute error = 3.30722818337424823e-15
relative error = 3.8290294172343036187364800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.076
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.076
Order of pole (three term test) = 1.560e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.077
y[1] (closed_form) = 0.86212173331298726042714683398725
y[1] (numeric) = 0.86212173331298395208778814776832
absolute error = 3.30833935868621893e-15
relative error = 3.8374387639815472372559700000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.077
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.077
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.078
y[1] (closed_form) = 0.86052299145328564888596693526457
y[1] (numeric) = 0.86052299145328233944365825336305
absolute error = 3.30944230868190152e-15
relative error = 3.8458499558422988459676800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.078
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.078
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.079
y[1] (closed_form) = 0.85892869259886913448332432889753
y[1] (numeric) = 0.85892869259886582394622253338833
absolute error = 3.31053710179550920e-15
relative error = 3.8542630259315054265172000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.079
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.079
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.08
y[1] (closed_form) = 0.85733882030178326474622770919068
y[1] (numeric) = 0.8573388203017799531224218799833
absolute error = 3.31162380582920738e-15
relative error = 3.8626780071191874880320000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.08
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.08
Order of pole (three term test) = 1.744e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.081
y[1] (closed_form) = 0.85575335819011587756223252359098
y[1] (numeric) = 0.85575335819011256485974456406209
absolute error = 3.31270248795952889e-15
relative error = 3.8710949320324750392272900000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.081
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.081
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.082
y[1] (closed_form) = 0.85417228996757561987283082946963
y[1] (numeric) = 0.85417228996757230609961608575114
absolute error = 3.31377321474371849e-15
relative error = 3.8795138330576250854867600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.082
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.082
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.083
y[1] (closed_form) = 0.85259559941307318936404041644179
y[1] (numeric) = 0.85259559941306987452798829043484
absolute error = 3.31483605212600695e-15
relative error = 3.8879347423420201655785500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.083
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.083
Order of pole (three term test) = 1.896e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.084
y[1] (closed_form) = 0.8510232703803052790675508231097
y[1] (numeric) = 0.85102327038030196317648537929359
absolute error = 3.31589106544381611e-15
relative error = 3.8963576917961487829521600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.084
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.084
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.085
y[1] (closed_form) = 0.8494552867973412049523243220285
y[1] (numeric) = 0.84945528679733788801400488813321
absolute error = 3.31693831943389529e-15
relative error = 3.9047827130955673827702500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.085
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.085
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.086
y[1] (closed_form) = 0.84789163266621219675155757692921
y[1] (numeric) = 0.84789163266620887877367933853904
absolute error = 3.31797787823839017e-15
relative error = 3.9132098376828444129373200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.086
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.086
Order of pole (three term test) = 2.060e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.087
y[1] (closed_form) = 0.84633229206250333243339999610687
y[1] (numeric) = 0.84633229206250001342359458526204
absolute error = 3.31900980541084483e-15
relative error = 3.9216390967694865149382700000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.087
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.087
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.088
y[1] (closed_form) = 0.84477724913494809688581314878892
y[1] (numeric) = 0.84477724913494477685164922665117
absolute error = 3.32003416392213775e-15
relative error = 3.9300705213378470287360000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.088
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.088
Order of pole (three term test) = 2.176e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.089
y[1] (closed_form) = 0.8432264881050255455464571417489
y[1] (numeric) = 0.84322648810502222449544097539634
absolute error = 3.32105101616635256e-15
relative error = 3.9385041421430169943077600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.089
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.089
Order of pole (three term test) = 2.237e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.09
y[1] (closed_form) = 0.84167999326656005386751956905984
y[1] (numeric) = 0.84167999326655673180709560247557
absolute error = 3.32206042396658427e-15
relative error = 3.9469399897146987711870000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.09
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.09
Order of pole (three term test) = 2.300e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.091
y[1] (closed_form) = 0.84013774898532363366297538144354
y[1] (numeric) = 0.84013774898532031060052680076162
absolute error = 3.32306244858068192e-15
relative error = 3.9553780943590626564195200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.091
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.091
Order of pole (three term test) = 2.364e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.092
y[1] (closed_form) = 0.83859973969864079754189644299535
y[1] (numeric) = 0.8385997396986374734847457360672
absolute error = 3.32405715070692815e-15
relative error = 3.9638184861605863694616000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.092
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.092
Order of pole (three term test) = 9.719e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.093
y[1] (closed_form) = 0.83706594991499595278613216099457
y[1] (numeric) = 0.83706594991499262774154167133794
absolute error = 3.32504459048965663e-15
relative error = 3.9722611949838778033728700000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.093
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.093
Order of pole (three term test) = 4.995e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.094
y[1] (closed_form) = 0.83553636421364330618397173881802
y[1] (numeric) = 0.83553636421363998015914421400994
absolute error = 3.32602482752480808e-15
relative error = 3.9807062504754812032348800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.094
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.094
Order of pole (three term test) = 5.134e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.095
y[1] (closed_form) = 0.83401096724421926148328850524384
y[1] (numeric) = 0.83401096724421593448536763981842
absolute error = 3.32699792086542542e-15
relative error = 3.9891536820656667142155000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.095
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.095
Order of pole (three term test) = 2.638e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.096
y[1] (closed_form) = 0.8324897437263572912781714529277
y[1] (numeric) = 0.83248974372635396331424242583864
absolute error = 3.32796392902708906e-15
relative error = 3.9976035189702038122969600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.096
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.096
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.097
y[1] (closed_form) = 0.83097267844930526529218245833295
y[1] (numeric) = 0.83097267844930193636927246504023
absolute error = 3.32892290999329272e-15
relative error = 4.0060557901921183988824800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.097
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.097
Order of pole (three term test) = 8.360e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.098
y[1] (closed_form) = 0.82945975627154521716915338701597
y[1] (numeric) = 0.82945975627154188729423216625515
absolute error = 3.32987492122076082e-15
relative error = 4.0145105245234341276352800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.098
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.098
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.099
y[1] (closed_form) = 0.82795096212041553202886899414722
y[1] (numeric) = 0.82795096212041220120884934943945
absolute error = 3.33082001964470777e-15
relative error = 4.0229677505468976893137700000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.099
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.099
Order of pole (three term test) = 2.943e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.1
y[1] (closed_form) = 0.8264462809917355371900826446281
y[1] (numeric) = 0.82644628099173220543182096058792
absolute error = 3.33175826168404018e-15
relative error = 4.0314274966376886178000000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.1
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.1
Order of pole (three term test) = 6.049e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.101
y[1] (closed_form) = 0.82494569794943247860709568792634
y[1] (numeric) = 0.82494569794942914591739244142389
absolute error = 3.33268970324650245e-15
relative error = 4.0398897909651135163924500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.101
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.101
Order of pole (three term test) = 6.216e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.102
y[1] (closed_form) = 0.82344919812517086570861097295464
y[1] (numeric) = 0.82344919812516753209421123918819
absolute error = 3.33361439973376645e-15
relative error = 4.0483546614942849119458000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.102
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.102
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.103
y[1] (closed_form) = 0.82195676671798416746875947818897
y[1] (numeric) = 0.82195676671798083293635343172302
absolute error = 3.33453240604646595e-15
relative error = 4.0568221359877848929635500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.103
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.103
Order of pole (three term test) = 3.282e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.104
y[1] (closed_form) = 0.82046838899390884268010922075194
y[1] (numeric) = 0.82046838899390550723633263157538
absolute error = 3.33544377658917656e-15
relative error = 4.0652922420073138181529600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.104
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.104
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.105
y[1] (closed_form) = 0.81898405028562068753711021477857
y[1] (numeric) = 0.81898405028561735118854493943692
absolute error = 3.33634856527534165e-15
relative error = 4.0737650069153240381912500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.105
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.105
Order of pole (three term test) = 6.931e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.106
y[1] (closed_form) = 0.81750373599207348377582085550131
y[1] (numeric) = 0.81750373599207014652899532335642
absolute error = 3.33724682553214489e-15
relative error = 4.0822404578766387866640400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.106
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.106
Order of pole (three term test) = 3.561e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.107
y[1] (closed_form) = 0.81602743157813993075191215627904
y[1] (numeric) = 0.81602743157813659261330185094877
absolute error = 3.33813861030533027e-15
relative error = 4.0907186218600566740412300000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.107
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.107
Order of pole (three term test) = 7.317e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.108
y[1] (closed_form) = 0.81455512257425484497386907166782
y[1] (numeric) = 0.81455512257425150594989700769789
absolute error = 3.33902397206396993e-15
relative error = 4.0991995256399415801435200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.108
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.108
Order of pole (three term test) = 7.518e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.109
y[1] (closed_form) = 0.81308679457606061074201487786216
y[1] (numeric) = 0.8130867945760572708390520726817
absolute error = 3.33990296280518046e-15
relative error = 4.1076831957977981493252600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.109
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.109
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.11
y[1] (closed_form) = 0.81162243324405486567648729810892
y[1] (numeric) = 0.81162243324405152490085323932033
absolute error = 3.34077563405878859e-15
relative error = 4.1161696587238334217390000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.11
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.11
Order of pole (three term test) = 3.968e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.111
y[1] (closed_form) = 0.81016202430324040504860567064807
y[1] (numeric) = 0.81016202430323706340656877870178
absolute error = 3.34164203689194629e-15
relative error = 4.1246589406185040366190900000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.111
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.111
Order of pole (three term test) = 4.077e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.112
y[1] (closed_form) = 0.80870555354277728896019874747683
y[1] (numeric) = 0.80870555354277394645797683378039
absolute error = 3.34250222191369644e-15
relative error = 4.1331510674940498507033600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.112
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.112
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.113
y[1] (closed_form) = 0.80725300681563713654442434384457
y[1] (numeric) = 0.80725300681563379318818506435529
absolute error = 3.34335623927948928e-15
relative error = 4.1416460651760136558963200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.113
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.113
Order of pole (three term test) = 4.303e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.114
y[1] (closed_form) = 0.80580437003825959148941656540391
y[1] (numeric) = 0.80580437003825624728527786975359
absolute error = 3.34420413869565032e-15
relative error = 4.1501439593047472645187200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.114
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.114
Order of pole (three term test) = 8.840e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.115
y[1] (closed_form) = 0.80435962919021094331275513281988
y[1] (numeric) = 0.8043596291902075982667857090195
absolute error = 3.34504596942380038e-15
relative error = 4.1586447753369042274255000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.115
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.115
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.116
y[1] (closed_form) = 0.80291877031384488894027569018898
y[1] (numeric) = 0.80291877031384154305849540496091
absolute error = 3.34588178028522807e-15
relative error = 4.1671485385469190111499200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.116
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.116
Order of pole (three term test) = 4.665e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.117
y[1] (closed_form) = 0.80148177951396541926714109044802
y[1] (numeric) = 0.8014817795139620725555214252325
absolute error = 3.34671161966521552e-15
relative error = 4.1756552740284730869332800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.117
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.117
Order of pole (three term test) = 4.792e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.118
y[1] (closed_form) = 0.80004864295749181550238254485873
y[1] (numeric) = 0.8000486429574884679668470275409
absolute error = 3.34753553551731783e-15
relative error = 4.1841650066959479713449200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.118
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.118
Order of pole (three term test) = 4.922e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.119
y[1] (closed_form) = 0.79861934687312574022030713302842
y[1] (numeric) = 0.79861934687312239186673176543184
absolute error = 3.34835357536759658e-15
relative error = 4.1926777612858651012093800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.119
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.119
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.12
y[1] (closed_form) = 0.79719387755102040816326530612245
y[1] (numeric) = 0.79719387755101705899747898731421
absolute error = 3.34916578631880824e-15
relative error = 4.2011935623583130562560000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.12
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.12
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.121
y[1] (closed_form) = 0.79577222134245182196028937461057
y[1] (numeric) = 0.79577222134244847198807432006277
absolute error = 3.34997221505454780e-15
relative error = 4.2097124342983620019398000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.121
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.121
Order of pole (three term test) = 5.334e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.122
y[1] (closed_form) = 0.7943543646594920580450621343984
y[1] (numeric) = 0.79435436465948870727215429105024
absolute error = 3.35077290784334816e-15
relative error = 4.2182344013174655050534400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.122
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.122
Order of pole (three term test) = 5.479e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.123
y[1] (closed_form) = 0.79294029397468458817456421983794
y[1] (numeric) = 0.79294029397468123660665367710203
absolute error = 3.35156791054273591e-15
relative error = 4.2267594874548499954423900000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.123
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.123
Order of pole (three term test) = 5.627e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.124
y[1] (closed_form) = 0.79152999582072162206658983548841
y[1] (numeric) = 0.79152999582071826970932123224462
absolute error = 3.35235726860324379e-15
relative error = 4.2352877165788917264350400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.124
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.124
Order of pole (three term test) = 1.156e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.125
y[1] (closed_form) = 0.79012345679012345679012345679012
y[1] (numeric) = 0.79012345679012010364909638440956
absolute error = 3.35314102707238056e-15
relative error = 4.2438191123884816462500000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.125
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.125
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.126
y[1] (closed_form) = 0.78872066353491981865734504005123
y[1] (numeric) = 0.78872066353491646473811444149257
absolute error = 3.35391923059855866e-15
relative error = 4.2523536984143781596061600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.126
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.126
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.127
y[1] (closed_form) = 0.78732160276633318347978827347459
y[1] (numeric) = 0.78732160276632982878786483849452
absolute error = 3.35469192343498007e-15
relative error = 4.2608914980205478013290300000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.127
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.127
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.128
y[1] (closed_form) = 0.78592626125446406116392535586741
y[1] (numeric) = 0.78592626125446070570477591238645
absolute error = 3.35545914944348096e-15
relative error = 4.2694325344054940778086400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.128
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.128
Order of pole (three term test) = 6.429e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.129
y[1] (closed_form) = 0.78453462582797823073320252526005
y[1] (numeric) = 0.78453462582797487451225042692438
absolute error = 3.35622095209833567e-15
relative error = 4.2779768306035746767444700000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.129
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.129
Order of pole (three term test) = 6.602e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.13
y[1] (closed_form) = 0.78314668337379591197431278878534
y[1] (numeric) = 0.78314668337379255499693829876507
absolute error = 3.35697737449002027e-15
relative error = 4.2865244094863068827630000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.13
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.13
Order of pole (three term test) = 6.780e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.131
y[1] (closed_form) = 0.78176242083678286001527563770315
y[1] (numeric) = 0.78176242083677950228681630876683
absolute error = 3.35772845932893632e-15
relative error = 4.2950752937636615120275200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.131
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.131
Order of pole (three term test) = 6.962e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.132
y[1] (closed_form) = 0.78038182521944336925170747543358
y[1] (numeric) = 0.78038182521944001077745852633829
absolute error = 3.35847424894909529e-15
relative error = 4.3036295059853454828929600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.132
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.132
Order of pole (three term test) = 7.149e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.133
y[1] (closed_form) = 0.7790048835816151731455204492677
y[1] (numeric) = 0.7790048835816118139307351375037
absolute error = 3.35921478531176400e-15
relative error = 4.3121870685420730173960000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.133
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.133
Order of pole (three term test) = 7.341e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.134
y[1] (closed_form) = 0.77763158304016622652719066593258
y[1] (numeric) = 0.77763158304016286657708065686097
absolute error = 3.35995011000907161e-15
relative error = 4.3207480036668256913091600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.134
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.134
Order of pole (three term test) = 7.538e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.135
y[1] (closed_form) = 0.7762619107686933571386985969066
y[1] (numeric) = 0.77626191076868999645843432932801
absolute error = 3.36068026426757859e-15
relative error = 4.3293123334361014291027500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.135
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.135
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.136
y[1] (closed_form) = 0.77489585399722277325927395358064
y[1] (numeric) = 0.77489585399721941185398500177269
absolute error = 3.36140528895180795e-15
relative error = 4.3378800797711523522432000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.136
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.136
Order of pole (three term test) = 7.948e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.137
y[1] (closed_form) = 0.77353340001191241436018345118114
y[1] (numeric) = 0.77353340001190905223495888344165
absolute error = 3.36212522456773949e-15
relative error = 4.3464512644392120127478100000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.137
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.137
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.138
y[1] (closed_form) = 0.77217453615475613183799160491844
y[1] (numeric) = 0.77217453615475276899788033865129
absolute error = 3.36284011126626715e-15
relative error = 4.3550259090547116750046000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.138
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.138
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.139
y[1] (closed_form) = 0.77081924982328968697801083926029
y[1] (numeric) = 0.77081924982328632342802199264025
absolute error = 3.36354998884662004e-15
relative error = 4.3636040350804859569128400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.139
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.139
Order of pole (three term test) = 8.602e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.14
y[1] (closed_form) = 0.76946752847029855340104647583872
y[1] (numeric) = 0.76946752847029518914614971609113
absolute error = 3.36425489675974759e-15
relative error = 4.3721856638289679679640000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.14
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.14
Order of pole (three term test) = 8.831e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.141
y[1] (closed_form) = 0.76811935960352751134704323974311
y[1] (numeric) = 0.76811935960352414639216912807395
absolute error = 3.36495487411166916e-15
relative error = 4.3807708164633739576899600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.141
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.141
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.142
y[1] (closed_form) = 0.76677473078539202124886133952478
y[1] (numeric) = 0.76677473078538865559890167273626
absolute error = 3.36564995966678852e-15
relative error = 4.3893595139988775833972800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.142
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.142
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.143
y[1] (closed_form) = 0.76543362963269136414816039508622
y[1] (numeric) = 0.76543362963268799780796854391256
absolute error = 3.36634019185117366e-15
relative error = 4.3979517773037739769333400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.143
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.143
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.144
y[1] (closed_form) = 0.76409604381632353660325688297716
y[1] (numeric) = 0.76409604381632016957764812717493
absolute error = 3.36702560875580223e-15
relative error = 4.4065476271006335872812800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.144
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.144
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.145
y[1] (closed_form) = 0.76276196106100188783585362597967
y[1] (numeric) = 0.76276196106099852012960548620661
absolute error = 3.36770624813977306e-15
relative error = 4.4151470839674459759865000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.145
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.145
Order of pole (three term test) = 1.007e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.146
y[1] (closed_form) = 0.76143136914497348695972637202318
y[1] (numeric) = 0.76143136914497011857757893853901
absolute error = 3.36838214743348417e-15
relative error = 4.4237501683387536962077200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.146
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.146
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.147
y[1] (closed_form) = 0.76010425589973920822980079947765
y[1] (numeric) = 0.76010425589973583917645705770009
absolute error = 3.36905334374177756e-15
relative error = 4.4323569005067762339340400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.147
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.147
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.148
y[1] (closed_form) = 0.75878060920977552234457138000947
y[1] (numeric) = 0.75878060920977215262469753295823
absolute error = 3.36971987384705124e-15
relative error = 4.4409673006225242174009600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.148
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.148
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.149
y[1] (closed_form) = 0.75746041701225798192850937092155
y[1] (numeric) = 0.75746041701225461154673515858277
absolute error = 3.37038177421233878e-15
relative error = 4.4495813886969038696947800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.149
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.149
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.15
y[1] (closed_form) = 0.75614366729678638941398865784499
y[1] (numeric) = 0.75614366729678301837490767348807
absolute error = 3.37103908098435692e-15
relative error = 4.4581991846018120267000000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.15
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.15
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.151
y[1] (closed_form) = 0.75483034810511163563433300548535
y[1] (numeric) = 0.754830348105108263942503008964
absolute error = 3.37169182999652135e-15
relative error = 4.4668207080712214810013500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.151
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.151
Order of pole (three term test) = 1.178e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.152
y[1] (closed_form) = 0.75352044753086419753086419753087
y[1] (numeric) = 0.75352044753086082519080742559964
absolute error = 3.37234005677193123e-15
relative error = 4.4754459787022570230579200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.152
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.152
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.153
y[1] (closed_form) = 0.75221395371928428346731517538997
y[1] (numeric) = 0.75221395371928091048351864906731
absolute error = 3.37298379652632266e-15
relative error = 4.4840750159562620811079400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.153
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.153
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.154
y[1] (closed_form) = 0.75091085486695361473467315854131
y[1] (numeric) = 0.75091085486695024111158898754971
absolute error = 3.37362308417099160e-15
relative error = 4.4927078391598562495856000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.154
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.154
Order of pole (three term test) = 1.274e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.155
y[1] (closed_form) = 0.7496111392215288319184423080527
y[1] (numeric) = 0.74961113922152545766048799236626
absolute error = 3.37425795431568644e-15
relative error = 4.5013444675059836031210000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.155
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.155
Order of pole (three term test) = 1.307e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.156
y[1] (closed_form) = 0.74831479508147651488847116294106
y[1] (numeric) = 0.74831479508147314000002989147049
absolute error = 3.37488844127147057e-15
relative error = 4.5099849200549518956315200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.156
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.156
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.157
y[1] (closed_form) = 0.74702181079580980525888414364035
y[1] (numeric) = 0.74702181079580642974430509008493
absolute error = 3.37551457905355542e-15
relative error = 4.5186292157354629094275800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.157
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.157
Order of pole (three term test) = 1.377e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.158
y[1] (closed_form) = 0.7457321747638266202522961093661
y[1] (numeric) = 0.74573217476382324411589472526197
absolute error = 3.37613640138410413e-15
relative error = 4.5272773733456338105813200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.158
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.158
Order of pole (three term test) = 1.413e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.159
y[1] (closed_form) = 0.74444587543484944698838143322209
y[1] (numeric) = 0.74444587543484607023443973821572
absolute error = 3.37675394169500637e-15
relative error = 4.5359294115540098516999700000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.159
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.159
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.16
y[1] (closed_form) = 0.74316290130796670630202140309156
y[1] (numeric) = 0.74316290130796332893478827246719
absolute error = 3.37736723313062437e-15
relative error = 4.5445853489005681522720000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.16
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.16
Order of pole (three term test) = 1.488e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.161
y[1] (closed_form) = 0.74188324093177567528067297712551
y[1] (numeric) = 0.74188324093177229730436442661476
absolute error = 3.37797630855051075e-15
relative error = 4.5532452037977130006507500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.161
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.161
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.162
y[1] (closed_form) = 0.74060688290412695779429495705961
y[1] (numeric) = 0.74060688290412357921309442496126
absolute error = 3.37858120053209835e-15
relative error = 4.5619089945312626044974000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.162
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.162
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.163
y[1] (closed_form) = 0.7393338158718704923741413561896
y[1] (numeric) = 0.73933381587186711319219998282732
absolute error = 3.37918194137336228e-15
relative error = 4.5705767392614272456973199999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.163
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.163
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.164
y[1] (closed_form) = 0.73806402853060308687899292639435
y[1] (numeric) = 0.73806402853059970710042983093972
absolute error = 3.37977856309545463e-15
relative error = 4.5792484560237790963684800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.164
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.164
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.165
y[1] (closed_form) = 0.7367975096244174694689531949382
y[1] (numeric) = 0.73679750962441408909785574962598
absolute error = 3.38037109744531222e-15
relative error = 4.5879241627302138777895000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.165
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.165
Order of pole (three term test) = 1.693e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.166
y[1] (closed_form) = 0.7355342479456528454877916025526
y[1] (numeric) = 0.73553424794564946452821570431521
absolute error = 3.38095957589823739e-15
relative error = 4.5966038771699040329988400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.166
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.166
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.167
y[1] (closed_form) = 0.73427423233464694993498001672677
y[1] (numeric) = 0.73427423233464356839095035627436
absolute error = 3.38154402966045241e-15
relative error = 4.6052876170102438722024900000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.167
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.167
Order of pole (three term test) = 1.782e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.168
y[1] (closed_form) = 0.73301745167948958528804653781197
y[1] (numeric) = 0.73301745167948620316355686618424
absolute error = 3.38212448967162773e-15
relative error = 4.6139753997977866683315200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.168
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.168
Order of pole (three term test) = 1.829e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.169
y[1] (closed_form) = 0.73176389491577763451466857315553
y[1] (numeric) = 0.73176389491577425181368196577124
absolute error = 3.38270098660738429e-15
relative error = 4.6226672429591736827266900000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.169
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.169
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.17
y[1] (closed_form) = 0.73051355102637153919205201256483
y[1] (numeric) = 0.7305135510263681559185011307946
absolute error = 3.38327355088177023e-15
relative error = 4.6313631638020552678470000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.17
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.17
Order of pole (three term test) = 1.925e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.171
y[1] (closed_form) = 0.72926640904115323272860131807611
y[1] (numeric) = 0.7292664090411498488863886683638
absolute error = 3.38384221264971231e-15
relative error = 4.6400631795160041576767100000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.171
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.171
Order of pole (three term test) = 1.975e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.172
y[1] (closed_form) = 0.72802245803678551875968269869189
y[1] (numeric) = 0.72802245803678213435268088924965
absolute error = 3.38440700180944224e-15
relative error = 4.6487673071734209097881600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.172
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.172
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.173
y[1] (closed_form) = 0.72678168713647288486542546890137
y[1] (numeric) = 0.72678168713646949989747746400306
absolute error = 3.38496794800489831e-15
relative error = 4.6574755637304317267799900000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.173
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.173
Order of pole (three term test) = 2.079e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.174
y[1] (closed_form) = 0.72554408550972374183400131758806
y[1] (numeric) = 0.72554408550972035630892068948558
absolute error = 3.38552508062810248e-15
relative error = 4.6661879660277785737244800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.174
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.174
Order of pole (three term test) = 8.531e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.175
y[1] (closed_form) = 0.7243096423721140787686736079674
y[1] (numeric) = 0.72430964237211069269024478645418
absolute error = 3.38607842882151322e-15
relative error = 4.6749045307917016893625000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.175
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.175
Order of pole (three term test) = 8.751e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.176
y[1] (closed_form) = 0.72307834698505252441112499421537
y[1] (numeric) = 0.72307834698504913778310351386084
absolute error = 3.38662802148035453e-15
relative error = 4.6836252746348147864812800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.176
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.176
Order of pole (three term test) = 4.489e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.177
y[1] (closed_form) = 0.72185018865554680512715751998262
y[1] (numeric) = 0.72185018865554341795327026506152
absolute error = 3.38717388725492110e-15
relative error = 4.6923502140569725925419000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.177
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.177
Order of pole (three term test) = 1.151e-29
NO COMPLEX POLE (six term test) for Equation 1
memory used=186.6MB, alloc=44.3MB, time=1.50
TOP MAIN SOLVE Loop
x[1] = -1.178
y[1] (closed_form) = 0.72062515673597159007382084105604
y[1] (numeric) = 0.72062515673596820235776628819588
absolute error = 3.38771605455286016e-15
relative error = 4.7010793654461311982694400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.178
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.178
Order of pole (three term test) = 1.417e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.179
y[1] (closed_form) = 0.7194032406238377141393671121931
y[1] (numeric) = 0.71940324062383432588481557076301
absolute error = 3.38825455154143009e-15
relative error = 4.7098127450792010237336900000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.179
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.179
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.18
y[1] (closed_form) = 0.71818442976156276931916116058604
y[1] (numeric) = 0.71818442976155938052975501084985
absolute error = 3.38878940614973619e-15
relative error = 4.7185503691228926709560000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.18
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.18
Order of pole (three term test) = 4.970e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.181
y[1] (closed_form) = 0.7169687136362430552617975409407
y[1] (numeric) = 0.71696871363623966594115146999698
absolute error = 3.38932064607094372e-15
relative error = 4.7272922536345555338509200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.181
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.181
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.182
y[1] (closed_form) = 0.71575608177942687979019757730882
y[1] (numeric) = 0.71575608177942348994189881284026
absolute error = 3.38984829876446856e-15
relative error = 4.7360384145630093724214400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.182
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.182
Order of pole (three term test) = 7.844e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.183
y[1] (closed_form) = 0.71454652376688920027238513485994
y[1] (numeric) = 0.71454652376688580989999367671432
absolute error = 3.39037239145814562e-15
relative error = 4.7447888677493687555881800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.183
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.183
Order of pole (three term test) = 5.364e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.184
y[1] (closed_form) = 0.71334002921840759678597516435354
y[1] (numeric) = 0.71334002921840420589302401397807
absolute error = 3.39089295115037547e-15
relative error = 4.7535436289278607548723200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.184
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.184
Order of pole (three term test) = 2.751e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.185
y[1] (closed_form) = 0.71213658779753956808915950079225
y[1] (numeric) = 0.71213658779753617667915488854307
absolute error = 3.39141000461224918e-15
relative error = 4.7623027137266356047855000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.185
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.185
Order of pole (three term test) = 2.821e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.186
y[1] (closed_form) = 0.71093618921140114147914539782567
y[1] (numeric) = 0.71093618921139774955556700817397
absolute error = 3.39192357838965170e-15
relative error = 4.7710661376685705226132000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.186
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.186
Order of pole (three term test) = 5.787e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.187
y[1] (closed_form) = 0.70973882321044678768659920835731
y[1] (numeric) = 0.70973882321044339525290040301324
absolute error = 3.39243369880534407e-15
relative error = 4.7798339161720668289638300000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.187
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.187
Order of pole (three term test) = 1.187e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.188
y[1] (closed_form) = 0.70854447958825063202167579271956
y[1] (numeric) = 0.70854447958824723908128383169489
absolute error = 3.39294039196102467e-15
relative error = 4.7886060645518404018564800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.188
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.188
Order of pole (three term test) = 3.044e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.189
y[1] (closed_form) = 0.70735314818128895305367890835603
y[1] (numeric) = 0.70735314818128555960999516898642
absolute error = 3.39344368373936961e-15
relative error = 4.7973825980197053444188100000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.189
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.189
Order of pole (three term test) = 6.243e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.19
y[1] (closed_form) = 0.70616481886872396017230421580397
y[1] (numeric) = 0.70616481886872056622870440975126
absolute error = 3.39394359980605271e-15
relative error = 4.8061635316853512426310000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.19
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.19
Order of pole (three term test) = 6.402e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.191
y[1] (closed_form) = 0.70497948157218884144376977908058
y[1] (numeric) = 0.70497948157218544700360416733548
absolute error = 3.39444016561174510e-15
relative error = 4.8149488805571138011931000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.191
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.191
Order of pole (three term test) = 6.565e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.192
y[1] (closed_form) = 0.70379712625557407323994414666006
y[1] (numeric) = 0.70379712625557067830653775256529
absolute error = 3.39493340639409477e-15
relative error = 4.8237386595427390712812800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.192
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.192
Order of pole (three term test) = 2.357e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.193
y[1] (closed_form) = 0.70261774292481498318284432309455
y[1] (numeric) = 0.70261774292481158775949714340832
absolute error = 3.39542334717968623e-15
relative error = 4.8325328834501412471612700000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.193
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.193
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.194
y[1] (closed_form) = 0.70144132162768055801060018125244
y[1] (numeric) = 0.70144132162767716210058739527189
absolute error = 3.39591001278598055e-15
relative error = 4.8413315669881541673798000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.194
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.194
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.195
y[1] (closed_form) = 0.70026785245356348803417307119973
y[1] (numeric) = 0.70026785245356009164074524796383
absolute error = 3.39639342782323590e-15
relative error = 4.8501347247672764460975000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.195
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.195
Order of pole (three term test) = 7.260e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.196
y[1] (closed_form) = 0.69909732553327143991677945436852
y[1] (numeric) = 0.69909732553326804304316275795952
absolute error = 3.39687361669640900e-15
relative error = 4.8589423713004105761440000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.196
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.196
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.197
y[1] (closed_form) = 0.69792973103881954957011018216664
y[1] (numeric) = 0.69792973103881615221950657512928
absolute error = 3.39735060360703736e-15
relative error = 4.8677545210035955927442400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.197
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.197
Order of pole (three term test) = 1.908e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.198
y[1] (closed_form) = 0.69676505918322412702305734933849
y[1] (numeric) = 0.69676505918322072919864479423562
absolute error = 3.39782441255510287e-15
relative error = 4.8765711881967338594354800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.198
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.198
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.199
y[1] (closed_form) = 0.69560330022029756517976823889244
y[1] (numeric) = 0.69560330022029416688470089801572
absolute error = 3.39829506734087672e-15
relative error = 4.8853923871043117135487199999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.199
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.199
Order of pole (three term test) = 8.026e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.2
y[1] (closed_form) = 0.69444444444444444444444444444444
y[1] (numeric) = 0.69444444444444104568185287769858
absolute error = 3.39876259156674586e-15
relative error = 4.8942181318561140384000000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.2
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.2
Order of pole (three term test) = 4.115e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.201
y[1] (closed_form) = 0.69328848219045882525039846755514
y[1] (numeric) = 0.69328848219045542602338982853373
absolute error = 3.39922700863902141e-15
relative error = 4.9030484364879331208054100000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.201
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.201
Order of pole (three term test) = 2.109e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.202
y[1] (closed_form) = 0.69213540383332272059047455571829
y[1] (numeric) = 0.69213540383331932090213278598945
absolute error = 3.39968834176972884e-15
relative error = 4.9118833149422713069473600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.202
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.202
Order of pole (three term test) = 4.325e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.203
y[1] (closed_form) = 0.6909851997880057407050398387517
y[1] (numeric) = 0.69098519978800234055842586037119
absolute error = 3.40014661397838051e-15
relative error = 4.9207227810690380794965900000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.203
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.203
Order of pole (three term test) = 4.435e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.204
y[1] (closed_form) = 0.68983786050926590214236045959757
y[1] (numeric) = 0.68983786050926250154051236586706
absolute error = 3.40060184809373051e-15
relative error = 4.9295668486262412469841600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.204
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.204
Order of pole (three term test) = 9.093e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.205
y[1] (closed_form) = 0.68869337649145159346429985709612
y[1] (numeric) = 0.68869337649144819241023310158401
absolute error = 3.40105406675551211e-15
relative error = 4.9384155312806724715227500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.205
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.205
Order of pole (three term test) = 1.864e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.206
y[1] (closed_form) = 0.68755173826830468992791707575995
y[1] (numeric) = 0.68755173826830128842462465960212
absolute error = 3.40150329241615783e-15
relative error = 4.9472688426085869296338800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.206
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.206
Order of pole (three term test) = 1.911e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.207
y[1] (closed_form) = 0.68641293641276480953070633950396
y[1] (numeric) = 0.68641293641276140758115899700133
absolute error = 3.40194954734250263e-15
relative error = 4.9561267960963776140128700000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.207
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.207
Order of pole (three term test) = 1.470e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.208
y[1] (closed_form) = 0.68527696153677470286390947765449
y[1] (numeric) = 0.68527696153677130047105586018441
absolute error = 3.40239285361747008e-15
relative error = 4.9649894051412438588211200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.208
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.208
Order of pole (three term test) = 1.507e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.209
y[1] (closed_form) = 0.68414380429108676927455443424386
y[1] (numeric) = 0.68414380429108336644132129250191
absolute error = 3.40283323314174195e-15
relative error = 4.9738566830518545152179500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.209
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.209
Order of pole (three term test) = 1.030e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.21
y[1] (closed_form) = 0.68301345536507069189263028481661
y[1] (numeric) = 0.68301345536506728862192264940547
absolute error = 3.40327070763541114e-15
relative error = 4.9827286430490054500740000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.21
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.21
Order of pole (three term test) = 5.278e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.211
y[1] (closed_form) = 0.68188590548652218413510614576948
y[1] (numeric) = 0.6818859054865187804298075061511
absolute error = 3.40370529863961838e-15
relative error = 4.9916052982662717862559800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.211
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.211
Order of pole (three term test) = 1.082e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.212
y[1] (closed_form) = 0.68076114542147284035334226491956
y[1] (numeric) = 0.68076114542146943621631474674686
absolute error = 3.40413702751817270e-15
relative error = 5.0004866617506546786288000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.212
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.212
Order of pole (three term test) = 1.109e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.213
y[1] (closed_form) = 0.67963916597400108334483056255772
y[1] (numeric) = 0.67963916597399767877891510340175
absolute error = 3.40456591545915597e-15
relative error = 5.0093727464632228604229300000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.213
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.213
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.214
y[1] (closed_form) = 0.67851995798604420150414304286346
y[1] (numeric) = 0.67851995798604079651215956635191
absolute error = 3.40499198347651155e-15
relative error = 5.0182635652797488163438000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.214
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.214
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.215
y[1] (closed_form) = 0.67740351233721146844146386899016
y[1] (numeric) = 0.67740351233720806302621145737289
absolute error = 3.40541525241161727e-15
relative error = 5.0271591309913397044057500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.215
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.215
Order of pole (three term test) = 5.973e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.216
y[1] (closed_form) = 0.67628981994459833795013850415512
y[1] (numeric) = 0.6762898199445949321143955693121
absolute error = 3.40583574293484302e-15
relative error = 5.0360594563050632405811200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.216
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.216
Order of pole (three term test) = 1.837e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.217
y[1] (closed_form) = 0.67517887176260170725729513891468
y[1] (numeric) = 0.67517887176259830100381959182175
absolute error = 3.40625347554709293e-15
relative error = 5.0449645538445683206007700000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.217
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.217
Order of pole (three term test) = 6.275e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.218
y[1] (closed_form) = 0.67407065878273624154378358557057
y[1] (numeric) = 0.67407065878273283487531300423817
absolute error = 3.40666847058133240e-15
relative error = 5.0538744361507005673776000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.218
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.218
Order of pole (three term test) = 6.431e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.219
y[1] (closed_form) = 0.67296517203345175277143881972676
y[1] (numeric) = 0.67296517203344834569069061562656
absolute error = 3.40708074820410020e-15
relative error = 5.0627891156821129372922000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.219
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.219
Order of pole (three term test) = 1.977e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.22
y[1] (closed_form) = 0.67186240257995162590701424348293
y[1] (numeric) = 0.67186240257994821841668582647732
absolute error = 3.40749032841700561e-15
relative error = 5.0717086048158711499240000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.22
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.22
Order of pole (three term test) = 1.351e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.221
y[1] (closed_form) = 0.67076234152401228568304735380903
y[1] (numeric) = 0.67076234152400887778581629559802
absolute error = 3.40789723105821101e-15
relative error = 5.0806329158480543603594100000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.221
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.221
Order of pole (three term test) = 6.924e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.222
y[1] (closed_form) = 0.66966498000380369708642160499945
y[1] (numeric) = 0.66966498000380028878494580109964
absolute error = 3.40830147580389981e-15
relative error = 5.0895620609943507238760400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.222
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.222
Order of pole (three term test) = 1.419e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.223
y[1] (closed_form) = 0.66857030919371089281547660037347
y[1] (numeric) = 0.6685703091937074841123944306433
absolute error = 3.40870308216973017e-15
relative error = 5.0984960523906483374439299999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.223
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.223
Order of pole (three term test) = 1.454e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.224
y[1] (closed_form) = 0.66747832030415652099619804348755
y[1] (numeric) = 0.66747832030415311189412853121322
absolute error = 3.40910206951227433e-15
relative error = 5.1074349020936211066220800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.224
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.224
Order of pole (three term test) = 1.491e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.225
y[1] (closed_form) = 0.66638900458142440649729279466889
y[1] (numeric) = 0.66638900458142099699883576422489
absolute error = 3.40949845703044400e-15
relative error = 5.1163786220813100275000000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.225
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.225
Order of pole (three term test) = 7.638e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.226
y[1] (closed_form) = 0.66530235330748411923282655035407
y[1] (numeric) = 0.66530235330748070934056278345232
absolute error = 3.40989226376690175e-15
relative error = 5.1253272242536996147830000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.226
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.226
Order of pole (three term test) = 1.565e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.227
y[1] (closed_form) = 0.66421835779981654288957569067086
y[1] (numeric) = 0.66421835779981313260606708121217
absolute error = 3.41028350860945869e-15
relative error = 5.1342807204332897320970100000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.227
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.227
Order of pole (three term test) = 8.021e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.228
y[1] (closed_form) = 0.66313700941124043756432428991289
y[1] (numeric) = 0.66313700941123702689211399745446
absolute error = 3.41067221029245843e-15
relative error = 5.1432391223656626331051200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.228
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.228
Order of pole (three term test) = 8.219e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.229
y[1] (closed_form) = 0.66205829952973998984402568521379
y[1] (numeric) = 0.66205829952973657878563828706607
absolute error = 3.41105838739814772e-15
relative error = 5.1522024417200456403445200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.229
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.229
Order of pole (three term test) = 1.684e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.23
y[1] (closed_form) = 0.66098221957829334390904884658602
y[1] (numeric) = 0.66098221957828993246699048855249
absolute error = 3.41144205835803353e-15
relative error = 5.1611706900898689275370000000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.23
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.23
Order of pole (three term test) = 1.726e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.231
y[1] (closed_form) = 0.65990876101470210728664654824824
y[1] (numeric) = 0.6599087610146986954634050940211
absolute error = 3.41182324145422714e-15
relative error = 5.1701438789933190930975400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.231
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.231
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.232
y[1] (closed_form) = 0.65883791533142182492831843481194
y[1] (numeric) = 0.65883791533141841272636361403695
absolute error = 3.41220195482077499e-15
relative error = 5.1791220198738879784217600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.232
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.232
Order of pole (three term test) = 1.812e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.233
y[1] (closed_form) = 0.65776967405539341533090090107868
y[1] (numeric) = 0.65776967405539000275268445610191
absolute error = 3.41257821644497677e-15
relative error = 5.1881051241009172886865300000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.233
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.233
Order of pole (three term test) = 9.285e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.234
y[1] (closed_form) = 0.65670402874787556246700062255542
y[1] (numeric) = 0.65670402874787214951495645386485
absolute error = 3.41295204416869057e-15
relative error = 5.1970932029701385776109200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.234
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.234
Order of pole (three term test) = 9.513e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.235
y[1] (closed_form) = 0.65564097100427805733580291432411
y[1] (numeric) = 0.65564097100427464401234722469861
absolute error = 3.41332345568962550e-15
relative error = 5.2060862677042090532375000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.235
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.235
Order of pole (three term test) = 9.747e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.236
y[1] (closed_form) = 0.65458049245399608299033315528744
y[1] (numeric) = 0.65458049245399266929786459266573
absolute error = 3.41369246856262171e-15
relative error = 5.2150843294532429358801600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.236
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.236
Order of pole (three term test) = 9.987e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.237
y[1] (closed_form) = 0.6535225847602454369419325577763
y[1] (numeric) = 0.65352258476024202288283235685827
absolute error = 3.41405910020091803e-15
relative error = 5.2240873992953385410470700000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.237
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.237
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.238
y[1] (closed_form) = 0.65246723961989868488703182213221
y[1] (numeric) = 0.65246723961989527046366394472484
absolute error = 3.41442336787740737e-15
relative error = 5.2330954882371011411862800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.238
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.238
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.239
y[1] (closed_form) = 0.65141444876332223974527089395559
y[1] (numeric) = 0.65141444876331882495998216807557
absolute error = 3.41478528872588002e-15
relative error = 5.2421086072141616621824200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.239
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.239
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.24
y[1] (closed_form) = 0.65036420395421436004162330905307
y[1] (numeric) = 0.65036420395421094489674356679821
absolute error = 3.41514487974225486e-15
relative error = 5.2511267670916910727360000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.24
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.24
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.241
y[1] (closed_form) = 0.64931649698944406170844260788881
y[1] (numeric) = 0.64931649698944064620628482209005
absolute error = 3.41550215778579876e-15
relative error = 5.2601499786649107400995600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.241
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.241
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.242
y[1] (closed_form) = 0.64827131969889093742625913738425
y[1] (numeric) = 0.64827131969888752156911955705007
absolute error = 3.41585713958033418e-15
relative error = 5.2691782526595986140375200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.242
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.242
Order of pole (three term test) = 1.155e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.243
y[1] (closed_form) = 0.64722866394528587766472131304574
y[1] (numeric) = 0.64722866394528246145487959761053
absolute error = 3.41620984171543521e-15
relative error = 5.2782115997325914557752900000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.243
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.243
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.244
y[1] (closed_form) = 0.64618852162405268762729913875994
y[1] (numeric) = 0.64618852162404927106701849114798
absolute error = 3.41656028064761196e-15
relative error = 5.2872500304722828221305600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.244
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.244
Order of pole (three term test) = 1.212e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.245
y[1] (closed_form) = 0.64515088466315059434525249592749
y[1] (numeric) = 0.64515088466314717743677979444373
absolute error = 3.41690847270148376e-15
relative error = 5.2962935553991173650940000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.245
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.245
Order of pole (three term test) = 1.242e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.246
y[1] (closed_form) = 0.64411574502291763820791540956744
y[1] (numeric) = 0.64411574502291422095348133862658
absolute error = 3.41725443407094086e-15
relative error = 5.3053421849660808202037600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.246
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.246
Order of pole (three term test) = 1.272e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.247
y[1] (closed_form) = 0.64308309469591494325756313950594
y[1] (numeric) = 0.64308309469591152565938231921078
absolute error = 3.41759818082029516e-15
relative error = 5.3143959295591863564564400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.247
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.247
Order of pole (three term test) = 1.303e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.248
y[1] (closed_form) = 0.64205292570677186061801446416831
y[1] (numeric) = 0.64205292570676844267828557874849
absolute error = 3.41793972888541982e-15
relative error = 5.3234547994979569113292800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.248
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.248
Order of pole (three term test) = 1.335e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.249
y[1] (closed_form) = 0.64102523011203197946667982905139
y[1] (numeric) = 0.64102523011202856118758575417349
absolute error = 3.41827909407487790e-15
relative error = 5.3325188050359035988779000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.249
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.249
Order of pole (three term test) = 1.367e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.25
y[1] (closed_form) = 0.64
y[1] (numeric) = 0.63999999999999658138370792895969
absolute error = 3.41861629207104031e-15
relative error = 5.3415879563610004843750000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.25
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.25
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.251
y[1] (closed_form) = 0.6389772274905894628821323436854
y[1] (numeric) = 0.63897722749058604393079391249246
absolute error = 3.41895133843119294e-15
relative error = 5.3506622635961553822929400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.251
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.251
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.252
y[1] (closed_form) = 0.63795690473517132970633567761231
y[1] (numeric) = 0.63795690473516791042208708897902
absolute error = 3.41928424858863329e-15
relative error = 5.3597417367996770366081600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.252
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.252
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.253
y[1] (closed_form) = 0.6369390239164234090377825859597
y[1] (numeric) = 0.63693902391641998942274473220317
absolute error = 3.41961503785375653e-15
relative error = 5.3688263859657384359087700000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.253
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.253
Order of pole (three term test) = 1.505e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.254
y[1] (closed_form) = 0.63592357724818062264549295523861
y[1] (numeric) = 0.63592357724817720270177154010731
absolute error = 3.41994372141513130e-15
relative error = 5.3779162210248366113508000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.254
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.254
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.255
y[1] (closed_form) = 0.63491055697528610656973698830177
y[1] (numeric) = 0.63491055697528268629942264773661
absolute error = 3.42027031434056516e-15
relative error = 5.3870112518442486411290000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.255
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.255
Order of pole (three term test) = 1.578e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.256
y[1] (closed_form) = 0.63389995537344314170960282364396
y[1] (numeric) = 0.63389995537343972111477124548404
absolute error = 3.42059483157815992e-15
relative error = 5.3961114882284840875571200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.256
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.256
Order of pole (three term test) = 1.616e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.257
y[1] (closed_form) = 0.63289176474906790865346581023753
y[1] (numeric) = 0.63289176474906448773617785288065
absolute error = 3.42091728795735688e-15
relative error = 5.4052169399197337808871200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.257
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.257
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.258
y[1] (closed_form) = 0.6318859774391430615128361317457
y[1] (numeric) = 0.6318859774391396402751379417735
absolute error = 3.42123769818997220e-15
relative error = 5.4143276165983151647208000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.258
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.258
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.259
y[1] (closed_form) = 0.63088258581107211555750147784245
y[1] (numeric) = 0.63088258581106869400142460662015
absolute error = 3.42155607687122230e-15
relative error = 5.4234435278831139145063000000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.259
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.259
Order of pole (three term test) = 1.736e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.26
y[1] (closed_form) = 0.62988158226253464348702443940539
y[1] (numeric) = 0.6298815822625312216145859586657
absolute error = 3.42187243848073969e-15
relative error = 5.4325646833320223318440000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.26
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.26
Order of pole (three term test) = 1.778e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.261
y[1] (closed_form) = 0.62888295922134227521050284852536
y[1] (numeric) = 0.62888295922133885302370546494642
absolute error = 3.42218679738357894e-15
relative error = 5.4416910924423739276517400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.261
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.261
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.262
y[1] (closed_form) = 0.62788670914529549604305795896635
y[1] (numeric) = 0.62788670914529207354389012775305
absolute error = 3.42249916783121330e-15
relative error = 5.4508227646513748749652000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.262
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.262
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.263
y[1] (closed_form) = 0.62689282452204123826378270891674
y[1] (numeric) = 0.62689282452203781545421874639501
absolute error = 3.42280956396252173e-15
relative error = 5.4599597093365318255223700000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.263
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.263
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.264
y[1] (closed_form) = 0.62590129786893126101586284249319
y[1] (numeric) = 0.62590129786892783789786303772651
absolute error = 3.42311799980476668e-15
relative error = 5.4691019358160765055692800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.264
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.264
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.265
y[1] (closed_form) = 0.62491212173288131356527988251652
y[1] (numeric) = 0.62491212173287789014079060795395
absolute error = 3.42342448927456257e-15
relative error = 5.4782494533493868885782500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.265
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.265
Order of pole (three term test) = 2.003e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.266
y[1] (closed_form) = 0.62392528869023107696991931398167
y[1] (numeric) = 0.62392528869022765324087313514659
absolute error = 3.42372904617883508e-15
relative error = 5.4874022711374049974804800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.266
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.266
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.267
y[1] (closed_form) = 0.62294079134660487924604230141738
y[1] (numeric) = 0.62294079134660145521435808564595
absolute error = 3.42403168421577143e-15
relative error = 5.4965603983230515030932700000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.267
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.267
Order of pole (three term test) = 2.100e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.268
y[1] (closed_form) = 0.62195862233677317915393724686284
y[1] (numeric) = 0.62195862233676975482152027110119
absolute error = 3.42433241697576165e-15
relative error = 5.5057238439916369991496000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.268
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.268
Order of pole (three term test) = 6.450e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.269
y[1] (closed_form) = 0.62097877432451481375915089846314
y[1] (numeric) = 0.62097877432451138912789295613212
absolute error = 3.42463125794233102e-15
relative error = 5.5148926171712701236982200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.269
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.269
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.27
y[1] (closed_form) = 0.62000124000248000496000992001984
y[1] (numeric) = 0.62000124000247658003178942695623
absolute error = 3.42492822049306361e-15
relative error = 5.5240667268332622965690000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.27
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.27
Order of pole (three term test) = 2.254e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.271
y[1] (closed_form) = 0.61902601209205412020618518410762
y[1] (numeric) = 0.61902601209205069498286728359037
absolute error = 3.42522331790051725e-15
relative error = 5.5332461818925294868572500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.271
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.271
Order of pole (three term test) = 6.924e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.272
y[1] (closed_form) = 0.61805308334322218266682488825601
y[1] (numeric) = 0.6180530833432187571502615551262
absolute error = 3.42551656333312981e-15
relative error = 5.5424309912079907025030399999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.272
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.272
Order of pole (three term test) = 2.363e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.273
y[1] (closed_form) = 0.61708244653443412614029122588982
y[1] (numeric) = 0.61708244653443070033232136977289
absolute error = 3.42580796985611693e-15
relative error = 5.5516211635829633124559700000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.273
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.273
Order of pole (three term test) = 2.420e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.274
y[1] (closed_form) = 0.61611409447247079003078106015984
y[1] (numeric) = 0.61611409447246736393323062779843
absolute error = 3.42609755043236141e-15
relative error = 5.5608167077655554278971600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.274
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.274
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.275
y[1] (closed_form) = 0.61514801999231064975009611687813
y[1] (numeric) = 0.61514801999230722336477819358394
absolute error = 3.42638531792329419e-15
relative error = 5.5700176324490551176187499999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.275
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.275
Order of pole (three term test) = 2.536e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.276
y[1] (closed_form) = 0.61418421595699727793555487858806
y[1] (numeric) = 0.61418421595699385126426978882109
absolute error = 3.42667128508976697e-15
relative error = 5.5792239462723164261467200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.276
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.276
Order of pole (three term test) = 7.790e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.277
y[1] (closed_form) = 0.61322267525750753190750885033626
y[1] (numeric) = 0.61322267525750410495204425741938
absolute error = 3.42695546459291688e-15
relative error = 5.5884356578201427508055200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.277
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.277
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.278
y[1] (closed_form) = 0.61226339081262046282214238307606
y[1] (numeric) = 0.61226339081261703558427338805326
absolute error = 3.42723786899502280e-15
relative error = 5.5976527756236668188752000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.278
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.278
Order of pole (three term test) = 2.721e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.279
y[1] (closed_form) = 0.61130635556878694200719996625589
y[1] (numeric) = 0.61130635556878351448868920590208
absolute error = 3.42751851076035381e-15
relative error = 5.6068753081607279369042100000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.279
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.279
Order of pole (three term test) = 5.572e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.28
y[1] (closed_form) = 0.6103515625
y[1] (numeric) = 0.61035156249999657220259774399032
absolute error = 3.42779740225600968e-15
relative error = 5.6161032638562462597120000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.28
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.28
Order of pole (three term test) = 5.704e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.281
y[1] (closed_form) = 0.60939900460766587383856167209336
y[1] (numeric) = 0.60939900460766244576400591933991
absolute error = 3.42807455575275345e-15
relative error = 5.6253366510825940540654500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.281
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.281
Order of pole (three term test) = 8.759e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.282
y[1] (closed_form) = 0.60844867492047575818789381840484
y[1] (numeric) = 0.60844867492047232983791039256853
absolute error = 3.42834998342583631e-15
relative error = 5.6345754781599641955564400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.282
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.282
Order of pole (three term test) = 2.989e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.283
y[1] (closed_form) = 0.60750056649427825591447364024667
y[1] (numeric) = 0.60750056649427482729077628443196
absolute error = 3.42862369735581471e-15
relative error = 5.6438197533567356801691900000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.283
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.283
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.284
y[1] (closed_form) = 0.60655467241195252375268097165206
y[1] (numeric) = 0.60655467241194909485697144229215
absolute error = 3.42889570952935991e-15
relative error = 5.6530694848898363917809600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.284
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.284
Order of pole (three term test) = 9.396e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.285
y[1] (closed_form) = 0.6056109857832821087374524973883
y[1] (numeric) = 0.60561098578327867957142065732837
absolute error = 3.42916603184005993e-15
relative error = 5.6623246809251029579142500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.285
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.285
Order of pole (three term test) = 3.206e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.286
y[1] (closed_form) = 0.60466949974482947110768196319256
y[1] (numeric) = 0.60466949974482604167300587397847
absolute error = 3.42943467608921409e-15
relative error = 5.6715853495776379051856400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.286
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.286
Order of pole (three term test) = 6.564e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.287
y[1] (closed_form) = 0.60373020745981118941491901864862
y[1] (numeric) = 0.60373020745980775971326503202854
absolute error = 3.42970165398662008e-15
relative error = 5.6808514989121639152895200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.287
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.287
Order of pole (three term test) = 3.359e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.288
y[1] (closed_form) = 0.60279310211797384360171289687898
y[1] (numeric) = 0.60279310211797041363473574552513
absolute error = 3.42996697715135385e-15
relative error = 5.6901231369433755613344000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.288
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.288
Order of pole (three term test) = 6.877e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.289
y[1] (closed_form) = 0.60185817693547057184350965169866
y[1] (numeric) = 0.6018581769354671416128525391566
absolute error = 3.43023065711254206e-15
relative error = 5.6994002716362879960732599999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.289
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.289
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.29
y[1] (closed_form) = 0.60092542515473829697734511147167
y[1] (numeric) = 0.60092542515473486648463980134415
absolute error = 3.43049270531012752e-15
relative error = 5.7086829109065832060320000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.29
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.29
Order of pole (three term test) = 1.441e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.291
y[1] (closed_form) = 0.59999484004437561836968202073462
y[1] (numeric) = 0.59999484004437218761654892510713
absolute error = 3.43075313309562749e-15
relative error = 5.7179710626209535206606900000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.291
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.291
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.292
y[1] (closed_form) = 0.59906641489902136510462095869796
y[1] (numeric) = 0.59906641489901793409266922581305
absolute error = 3.43101195173288491e-15
relative error = 5.7272647345974423964062400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.292
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.292
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.293
y[1] (closed_form) = 0.59814014303923380640237246306335
y[1] (numeric) = 0.59814014303923037513320006425063
absolute error = 3.43126917239881272e-15
relative error = 5.7365639346057826471192800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.293
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.293
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.294
y[1] (closed_form) = 0.59721601781137051520631424551311
y[1] (numeric) = 0.59721601781136708368150806138189
absolute error = 3.43152480618413122e-15
relative error = 5.7458686703677319434919200000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.294
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.294
Order of pole (three term test) = 3.953e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.295
y[1] (closed_form) = 0.59629403258746888090517434146778
y[1] (numeric) = 0.59629403258746544912631024736903
absolute error = 3.43177886409409875e-15
relative error = 5.7551789495574059562187500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.295
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.295
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=230.4MB, alloc=44.3MB, time=1.84
x[1] = -1.296
y[1] (closed_form) = 0.59537418076512726718488035360463
y[1] (numeric) = 0.59537418076512383515352330436919
absolute error = 3.43203135704923544e-15
relative error = 5.7644947798016086327910400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.296
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.296
Order of pole (three term test) = 4.140e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.297
y[1] (closed_form) = 0.59445645576738681103239847129577
y[1] (numeric) = 0.59445645576738337875010258525531
absolute error = 3.43228229588604046e-15
relative error = 5.7738161686801602361761400000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.297
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.297
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.298
y[1] (closed_form) = 0.59354085104261385894145550461656
y[1] (numeric) = 0.59354085104261042640976414691404
absolute error = 3.43253169135770252e-15
relative error = 5.7831431237262226365060800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.298
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.298
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.299
y[1] (closed_form) = 0.59262736006438303639739457307421
y[1] (numeric) = 0.59262736006437960361784043827039
absolute error = 3.43277955413480382e-15
relative error = 5.7924756524266221006718200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.299
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.299
Order of pole (three term test) = 8.875e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.3
y[1] (closed_form) = 0.59171597633136094674556213017752
y[1] (numeric) = 0.59171597633135751371966732415988
absolute error = 3.43302589480601764e-15
relative error = 5.8018137622221698115999999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.3
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.3
Order of pole (three term test) = 4.541e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.301
y[1] (closed_form) = 0.59080669336719049557456246333306
y[1] (numeric) = 0.59080669336718706230383858453369
absolute error = 3.43327072387879937e-15
relative error = 5.8111574605079796924613700000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.301
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.301
Order of pole (three term test) = 4.647e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.302
y[1] (closed_form) = 0.58989950472037583677244744585313
y[1] (numeric) = 0.58989950472037240325839566578183
absolute error = 3.43351405178007130e-15
relative error = 5.8205067546337839880451999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.302
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.302
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.303
y[1] (closed_form) = 0.58899440396416793644043587941871
y[1] (numeric) = 0.58899440396416450268454702251772
absolute error = 3.43375588885690099e-15
relative error = 5.8298616519042462129309100000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.303
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.303
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.304
y[1] (closed_form) = 0.58809138469645075087507998042832
y[1] (numeric) = 0.58809138469644731687883460325478
absolute error = 3.43399624537717354e-15
relative error = 5.8392221595792719221926400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.304
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.304
Order of pole (three term test) = 9.960e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.305
y[1] (closed_form) = 0.58719044053962801485591814565259
y[1] (numeric) = 0.587190440539624580620786615395
absolute error = 3.43423513153025759e-15
relative error = 5.8485882848743169322097500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.305
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.305
Order of pole (three term test) = 5.096e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.306
y[1] (closed_form) = 0.58629156514051063650157477914397
y[1] (numeric) = 0.5862915651405072020290173514787
absolute error = 3.43447255742766527e-15
relative error = 5.8579600349606932804617200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.306
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.306
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.307
y[1] (closed_form) = 0.58539475217020469498299135547569
y[1] (numeric) = 0.5853947521702012602744582517696
absolute error = 3.43470853310370609e-15
relative error = 5.8673374169658728245364100000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.307
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.307
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.308
y[1] (closed_form) = 0.584499995324000037407999700736
y[1] (numeric) = 0.58449999532399660246493118460113
absolute error = 3.43494306851613487e-15
relative error = 5.8767204379737885682276800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.308
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.308
Order of pole (three term test) = 1.092e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.309
y[1] (closed_form) = 0.58360728832125947121678034363964
y[1] (numeric) = 0.58360728832125603604060679684599
absolute error = 3.43517617354679365e-15
relative error = 5.8861091050251335301956500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.309
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.309
Order of pole (three term test) = 1.117e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.31
y[1] (closed_form) = 0.5827166249053085484528873608764
y[1] (numeric) = 0.58271662490530511304502935862856
absolute error = 3.43540785800224784e-15
relative error = 5.8955034251176575182240000000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.31
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.31
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.311
y[1] (closed_form) = 0.58182799884332593829946803466066
y[1] (numeric) = 0.58182799884332250266133642024414
absolute error = 3.43563813161441652e-15
relative error = 5.9049034052064615756709200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.311
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.311
Order of pole (three term test) = 5.847e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.312
y[1] (closed_form) = 0.58094140392623438429506246281975
y[1] (numeric) = 0.58094140392623094842805842162281
absolute error = 3.43586700404119694e-15
relative error = 5.9143090522042901054873600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.312
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.312
Order of pole (three term test) = 5.983e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.313
y[1] (closed_form) = 0.5800568339685922426679366044285
y[1] (numeric) = 0.58005683396858880657345173734507
absolute error = 3.43609448486708343e-15
relative error = 5.9237203729818209537336700000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.313
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.313
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.314
y[1] (closed_form) = 0.57917428280848559825228368419712
y[1] (numeric) = 0.57917428280848216193170008041655
absolute error = 3.43632058360378057e-15
relative error = 5.9331373743679531170397199999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.314
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.314
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.315
y[1] (closed_form) = 0.57829374430742095447382497939829
y[1] (numeric) = 0.5782937443074175179285152885875
absolute error = 3.43654530969081079e-15
relative error = 5.9425600631500922883377500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.315
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.315
Order of pole (three term test) = 1.281e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.316
y[1] (closed_form) = 0.5774152123502184939163533226781
y[1] (numeric) = 0.57741521235021505714768082656159
absolute error = 3.43676867249611651e-15
relative error = 5.9519884460744343545425600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.316
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.316
Order of pole (three term test) = 1.311e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.317
y[1] (closed_form) = 0.57653868084490590600459270713161
y[1] (numeric) = 0.57653868084490246901391139047488
absolute error = 3.43699068131665673e-15
relative error = 5.9614225298462466149609700000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.317
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.317
Order of pole (three term test) = 6.706e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.318
y[1] (closed_form) = 0.57566414372261277836239669706941
y[1] (numeric) = 0.57566414372260934115105131807115
absolute error = 3.43721134537899826e-15
relative error = 5.9708623211301469734042400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.318
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.318
Order of pole (three term test) = 1.372e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.319
y[1] (closed_form) = 0.57479159493746554842877843565869
y[1] (numeric) = 0.57479159493746211099810459575719
absolute error = 3.43743067383990150e-15
relative error = 5.9803078265503808735415000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.319
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.319
Order of pole (three term test) = 1.404e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.32
y[1] (closed_form) = 0.57392102846648301193755739210285
y[1] (numeric) = 0.57392102846647957428888160520185
absolute error = 3.43764867578690100e-15
relative error = 5.9897590526910963024000000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.32
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.32
Order of pole (three term test) = 7.180e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.321
y[1] (closed_form) = 0.57305243830947238488952408568051
y[1] (numeric) = 0.57305243830946894702416384679982
absolute error = 3.43786536023888069e-15
relative error = 5.9992160060966165981582900000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.321
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.321
Order of pole (three term test) = 7.345e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.322
y[1] (closed_form) = 0.57218581848892591566896532782814
y[1] (numeric) = 0.57218581848892247758822918118421
absolute error = 3.43808073614664393e-15
relative error = 6.0086786932717112501581200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.322
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.322
Order of pole (three term test) = 7.513e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.323
y[1] (closed_form) = 0.57132116304991804397916048925659
y[1] (numeric) = 0.57132116304991460568434809577819
absolute error = 3.43829481239347840e-15
relative error = 6.0181471206818646543936000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.323
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.323
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.324
y[1] (closed_form) = 0.57045846606000310329405536641688
y[1] (numeric) = 0.57045846605999966478645757070102
absolute error = 3.43850759779571586e-15
relative error = 6.0276212947535428053993600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.324
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.324
Order of pole (three term test) = 7.862e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.325
y[1] (closed_form) = 0.56959772160911356354574581701673
y[1] (numeric) = 0.56959772160911012482664471372985
absolute error = 3.43871910110328688e-15
relative error = 6.0371012218744580287000000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.325
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.325
Order of pole (three term test) = 1.608e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.326
y[1] (closed_form) = 0.568738923809458810789659871374
y[1] (numeric) = 0.56873892380945537186032887110348
absolute error = 3.43892933100027052e-15
relative error = 6.0465869083938316488235200000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.326
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.326
Order of pole (three term test) = 1.645e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.327
y[1] (closed_form) = 0.56788206679542446061141590603596
y[1] (numeric) = 0.56788206679542102147311980059685
absolute error = 3.43913829610543911e-15
relative error = 6.0560783606226547865331900000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.327
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.327
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.328
y[1] (closed_form) = 0.56702714472347220206125707649877
y[1] (numeric) = 0.56702714472346876271525210370072
absolute error = 3.43934600497279805e-15
relative error = 6.0655755848339470762112000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.328
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.328
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.329
y[1] (closed_form) = 0.56617415177204016892371992270591
y[1] (numeric) = 0.56617415177203672937125383058512
absolute error = 3.43955246609212079e-15
relative error = 6.0750785872630135162503899999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.329
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.329
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.33
y[1] (closed_form) = 0.56532308214144383515178924755498
y[1] (numeric) = 0.56532308214144039539410135807601
absolute error = 3.43975768788947897e-15
relative error = 6.0845873741076993500330000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.33
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.33
Order of pole (three term test) = 9.004e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.331
y[1] (closed_form) = 0.5644739300537774313162233758815
y[1] (numeric) = 0.56447393005377399135454464811367
absolute error = 3.43996167872776783e-15
relative error = 6.0941019515286431046826300000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.331
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.331
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.332
y[1] (closed_form) = 0.56362668975281587894200506813119
y[1] (numeric) = 0.56362668975281243877755816090436
absolute error = 3.44016444690722683e-15
relative error = 6.1036223256495276152299200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.332
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.332
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.333
y[1] (closed_form) = 0.56278135550391723962498501594641
y[1] (numeric) = 0.56278135550391379925898434999073
absolute error = 3.44036600066595568e-15
relative error = 6.1131485025573293222795200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.333
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.333
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.334
y[1] (closed_form) = 0.56193792159392567584273830101441
y[1] (numeric) = 0.5619379215939222352763901205888
absolute error = 3.44056634818042561e-15
relative error = 6.1226804883025654768291600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.334
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.334
Order of pole (three term test) = 9.853e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.335
y[1] (closed_form) = 0.56109638233107492039445075677875
y[1] (numeric) = 0.56109638233107147962895319079254
absolute error = 3.44076549756598621e-15
relative error = 6.1322182888995397731172500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.335
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.335
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.336
y[1] (closed_form) = 0.56025673204489225142529312632221
y[1] (numeric) = 0.56025673204488881046183624895462
absolute error = 3.44096345687736759e-15
relative error = 6.1417619103265859019206400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.336
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.336
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.337
y[1] (closed_form) = 0.55941896508610297001122753862927
y[1] (numeric) = 0.55941896508609952885099342945114
absolute error = 3.44116023410917813e-15
relative error = 6.1513113585263094406659700000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.337
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.337
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.338
y[1] (closed_form) = 0.55858307582653537730052439779158
y[1] (numeric) = 0.55858307582653193594468720139381
absolute error = 3.44135583719639777e-15
relative error = 6.1608666394058279293558800000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.338
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.338
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.339
y[1] (closed_form) = 0.55774905865902624822844955243426
y[1] (numeric) = 0.55774905865902280667817553756746
absolute error = 3.44155027401486680e-15
relative error = 6.1704277588370089979228000000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.339
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.339
Order of pole (three term test) = 1.102e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.34
y[1] (closed_form) = 0.55691690799732679884161283136556
y[1] (numeric) = 0.55691690799732335709806044959517
absolute error = 3.44174355238177039e-15
relative error = 6.1799947226567069122840000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.34
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.34
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.341
y[1] (closed_form) = 0.55608661827600914428835093069437
y[1] (numeric) = 0.55608661827600570235267087457564
absolute error = 3.44193568005611873e-15
relative error = 6.1895675366669972459031300000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.341
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.341
Order of pole (three term test) = 1.153e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.342
y[1] (closed_form) = 0.55525818395037324455125144089499
y[1] (numeric) = 0.55525818395036980242458670167208
absolute error = 3.44212666473922291e-15
relative error = 6.1991462066354098488852400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.342
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.342
Order of pole (three term test) = 1.179e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.343
y[1] (closed_form) = 0.55443159949635433501751172207009
y[1] (numeric) = 0.55443159949635089270099764690354
absolute error = 3.44231651407516655e-15
relative error = 6.2087307382951600727409500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.343
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.343
Order of pole (three term test) = 1.205e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.344
y[1] (closed_form) = 0.55360685941043083900226757369615
y[1] (numeric) = 0.5536068594104273964970319224229
absolute error = 3.44250523565127325e-15
relative error = 6.2183211373453783173119999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.344
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.344
Order of pole (three term test) = 1.233e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.345
y[1] (closed_form) = 0.55278395820953275935932339243515
y[1] (numeric) = 0.55278395820952931666648639386536
absolute error = 3.44269283699856979e-15
relative error = 6.2279174094513377143547500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.345
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.345
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.346
y[1] (closed_form) = 0.55196289043095054633286894855485
y[1] (numeric) = 0.55196289043094710345354335630949
absolute error = 3.44287932559224536e-15
relative error = 6.2375195602446803946377600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.346
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.346
Order of pole (three term test) = 1.289e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.347
y[1] (closed_form) = 0.55114365063224443882277920799555
y[1] (numeric) = 0.55114365063224099575807035588899
absolute error = 3.44306470885210656e-15
relative error = 6.2471275953236418114230400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.347
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.347
Order of pole (three term test) = 1.318e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.348
y[1] (closed_form) = 0.55032623339115427625496394262519
y[1] (numeric) = 0.55032623339115083300596979959675
absolute error = 3.44324899414302844e-15
relative error = 6.2567415202532735504377600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.348
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.348
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.349
y[1] (closed_form) = 0.54951063330550977826696435489375
y[1] (numeric) = 0.54951063330550633483477557949225
absolute error = 3.44343218877540150e-15
relative error = 6.2663613405656644251015000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.349
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.349
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.35
y[1] (closed_form) = 0.54869684499314128943758573388203
y[1] (numeric) = 0.54869684499313784582328572830725
absolute error = 3.44361430000557478e-15
relative error = 6.2759870617601600365500000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.35
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.35
Order of pole (three term test) = 1.409e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.351
y[1] (closed_form) = 0.54788486309179098630780938647305
y[1] (numeric) = 0.54788486309178754251247435017811
absolute error = 3.44379533503629494e-15
relative error = 6.2856186893035805607829400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.351
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.351
Order of pole (three term test) = 1.441e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.352
y[1] (closed_form) = 0.54707468225902454395854486887714
y[1] (numeric) = 0.54707468225902109998324385173564
absolute error = 3.44397530101714150e-15
relative error = 6.2952562286304370164160000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.352
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.352
Order of pole (three term test) = 1.473e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.353
y[1] (closed_form) = 0.54626629717214325942896598891407
y[1] (numeric) = 0.54626629717213981527476094395582
absolute error = 3.44415420504495825e-15
relative error = 6.3048996851431459770742500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.353
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.353
Order of pole (three term test) = 1.506e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.354
y[1] (closed_form) = 0.54545970252809662927722225737407
y[1] (numeric) = 0.54545970252809318494516809309329
absolute error = 3.44433205416428078e-15
relative error = 6.3145490642122425824664800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.354
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.354
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.355
y[1] (closed_form) = 0.54465489304339537860323252679021
y[1] (numeric) = 0.54465489304339193409437715902994
absolute error = 3.44450885536776027e-15
relative error = 6.3242043711765920497267500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.355
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.355
Order of pole (three term test) = 1.574e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.356
y[1] (closed_form) = 0.5438518634540249388710505477676
y[1] (numeric) = 0.54385186345402149418643495118402
absolute error = 3.44468461559658358e-15
relative error = 6.3338656113435997055548800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.356
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.356
Order of pole (three term test) = 1.609e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.357
y[1] (closed_form) = 0.54305060851535937188594416679474
y[1] (numeric) = 0.54305060851535592702660242590524
absolute error = 3.44485934174088950e-15
relative error = 6.3435327899894192288855000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.357
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.357
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.358
y[1] (closed_form) = 0.54225112300207573729885194592238
y[1] (numeric) = 0.54225112300207229226581130574088
absolute error = 3.44503304064018150e-15
relative error = 6.3532059123591596757660000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.358
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.358
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.359
y[1] (closed_form) = 0.5414534017080689010282741551838
y[1] (numeric) = 0.54145340170806545582255507144708
absolute error = 3.44520571908373672e-15
relative error = 6.3628849836670907571703199999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.359
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.359
Order of pole (three term test) = 1.720e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.36
y[1] (closed_form) = 0.54065743944636678200692041522491
y[1] (numeric) = 0.54065743944636333662953660421354
absolute error = 3.44537738381101137e-15
relative error = 6.3725700090968466299520000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.36
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.36
Order of pole (three term test) = 1.758e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.361
y[1] (closed_form) = 0.53986323104904603467757478320442
y[1] (numeric) = 0.53986323104904258912953327116177
absolute error = 3.44554804151204265e-15
relative error = 6.3822609938016283534906500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.361
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.361
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.362
y[1] (closed_form) = 0.53907077136714816467965180340736
y[1] (numeric) = 0.53907077136714471896195297556032
absolute error = 3.44571769882784704e-15
relative error = 6.3919579429044046844697600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.362
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.362
Order of pole (three term test) = 1.837e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.363
y[1] (closed_form) = 0.53828005527059607518480499997577
y[1] (numeric) = 0.53828005527059262929844264916068
absolute error = 3.44588636235081509e-15
relative error = 6.4016608614981113989342100000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.363
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.363
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.364
y[1] (closed_form) = 0.53749107764811104135671347855625
y[1] (numeric) = 0.53749107764810759530267485345337
absolute error = 3.44605403862510288e-15
relative error = 6.4113697546458494078284800000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.364
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.364
Order of pole (three term test) = 1.920e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.365
y[1] (closed_form) = 0.53670383340713011042681372351702
y[1] (numeric) = 0.53670383340712666420607957649718
absolute error = 3.44622073414701984e-15
relative error = 6.4210846273810810413840000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.365
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.365
Order of pole (three term test) = 1.963e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.366
y[1] (closed_form) = 0.53591831747372392489426331596244
y[1] (numeric) = 0.53591831747372047850780795054912
absolute error = 3.44638645536541332e-15
relative error = 6.4308054847078251769339199999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.366
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.366
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.367
y[1] (closed_form) = 0.53513452479251496637482213466232
y[1] (numeric) = 0.53513452479251151982361345261258
absolute error = 3.44655120868204974e-15
relative error = 6.4405323316008508465908600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.367
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.367
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.368
y[1] (closed_form) = 0.53435245032659621763961560822133
y[1] (numeric) = 0.53435245032659277092461515622889
absolute error = 3.44671500045199244e-15
relative error = 6.4502651730058695000345600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.368
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.368
Order of pole (three term test) = 2.096e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.369
y[1] (closed_form) = 0.53357208905745024040090472483421
y[1] (numeric) = 0.53357208905744679352306774085806
absolute error = 3.44687783698397615e-15
relative error = 6.4600040138397257252601499999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.369
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.369
Order of pole (three term test) = 2.143e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.37
y[1] (closed_form) = 0.53279343598486866641802972987373
y[1] (numeric) = 0.53279343598486521937830518909551
absolute error = 3.44703972454077822e-15
relative error = 6.4697488589905866411180000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.37
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.37
Order of pole (three term test) = 1.095e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.371
y[1] (closed_form) = 0.53201648612687209951261969705918
y[1] (numeric) = 0.5320164861268686523119503574725
absolute error = 3.44720066933958668e-15
relative error = 6.4794997133181300467818799999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.371
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.371
Order of pole (three term test) = 2.239e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.372
y[1] (closed_form) = 0.53124123451963042609796938350517
y[1] (numeric) = 0.53124123451962697873729183114022
absolute error = 3.44736067755236495e-15
relative error = 6.4892565816537309440408000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.372
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.372
Order of pole (three term test) = 4.577e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.373
y[1] (closed_form) = 0.53046767621738353184317890181521
y[1] (numeric) = 0.53046767621738008432342359560168
absolute error = 3.44751975530621353e-15
relative error = 6.4990194688006470055953700000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.373
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.373
Order of pole (three term test) = 2.339e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.374
y[1] (closed_form) = 0.52969580629236242210823168470811
y[1] (numeric) = 0.52969580629235897443032300097977
absolute error = 3.44767790868372834e-15
relative error = 6.5087883795342023236058399999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.374
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.374
Order of pole (three term test) = 4.781e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.375
y[1] (closed_form) = 0.52892561983471074380165289256199
y[1] (numeric) = 0.52892561983470729596650916920584
absolute error = 3.44783514372335615e-15
relative error = 6.5185633186019702210937499999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.375
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.375
Order of pole (three term test) = 7.330e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.376
y[1] (closed_form) = 0.5281571119524067063277447268794
y[1] (numeric) = 0.52815711195240325833627830713265
absolute error = 3.44799146641974675e-15
relative error = 6.5283442907239544225279999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.376
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.376
Order of pole (three term test) = 7.491e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.377
y[1] (closed_form) = 0.52739027777118539930563796028646
y[1] (numeric) = 0.5273902777711819511587552361843
absolute error = 3.44814688272410216e-15
relative error = 6.5381313005927691045386400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.377
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.377
Order of pole (three term test) = 7.656e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.378
y[1] (closed_form) = 0.52662511243446150475753126573292
y[1] (numeric) = 0.52662511243445805645613272121016
absolute error = 3.44830139854452276e-15
relative error = 6.5479243528738175565998400000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.378
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.378
Order of pole (three term test) = 1.043e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.379
y[1] (closed_form) = 0.5258616111032524014785125057779
y[1] (numeric) = 0.52586161110324895302349275942748
absolute error = 3.44845501974635042e-15
relative error = 6.5577234522054695590392200000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.379
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.379
Order of pole (three term test) = 2.666e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.38
y[1] (closed_form) = 0.52509976895610165931526990128125
y[1] (numeric) = 0.5250997689560982107075177487726
absolute error = 3.44860775215250865e-15
relative error = 6.5675286031992374730599999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.38
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.38
Order of pole (three term test) = 1.090e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.381
y[1] (closed_form) = 0.52433958118900292109580680393527
y[1] (numeric) = 0.5243395811889994723362052600955
absolute error = 3.44875960154383977e-15
relative error = 6.5773398104399509995929700000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.381
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.381
Order of pole (three term test) = 1.392e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.382
y[1] (closed_form) = 0.52358104301532416996697250780659
y[1] (numeric) = 0.52358104301532072105639884836731
absolute error = 3.44891057365943928e-15
relative error = 6.5871570784859309074147200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.382
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.382
Order of pole (three term test) = 1.138e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.383
y[1] (closed_form) = 0.52282414966573237991121400290377
y[1] (numeric) = 0.52282414966572893085053980591659
absolute error = 3.44906067419698718e-15
relative error = 6.5969804118691612123270199999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.383
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.383
Order of pole (three term test) = 5.815e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.384
y[1] (closed_form) = 0.52206889638811854722844064285475
y[1] (numeric) = 0.52206889638811509801853182977829
absolute error = 3.44920990881307646e-15
relative error = 6.6068098150954601837657600000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.384
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.384
Order of pole (three term test) = 5.943e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.385
y[1] (closed_form) = 0.5213152784475231007832762058674
y[1] (numeric) = 0.52131527844751965142499308232849
absolute error = 3.44935828312353891e-15
relative error = 6.6166452926446504256347500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.385
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.385
Order of pole (three term test) = 3.037e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.386
y[1] (closed_form) = 0.52056329112606168883225160281437
y[1] (numeric) = 0.52056329112605823932644889904655
absolute error = 3.44950580270376782e-15
relative error = 6.6264868489707271671487200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.386
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.386
Order of pole (three term test) = 1.551e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.387
y[1] (closed_form) = 0.51981292972285134025966735091376
y[1] (numeric) = 0.51981292972284789060719426187558
absolute error = 3.44965247308903818e-15
relative error = 6.6363344885020258905004199999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.387
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.387
Order of pole (three term test) = 6.342e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.388
y[1] (closed_form) = 0.51906418955393699806492870134293
y[1] (numeric) = 0.51906418955393354826662892651901
absolute error = 3.44979829977482392e-15
relative error = 6.6461882156413883741324799999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.388
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.388
Order of pole (three term test) = 9.720e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.389
y[1] (closed_form) = 0.51831706595221842295812879246118
y[1] (numeric) = 0.51831706595221497301484057534865
absolute error = 3.44994328821711253e-15
relative error = 6.6560480347663277634921300000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.389
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.389
Order of pole (three term test) = 6.622e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.39
y[1] (closed_form) = 0.51757155426737746493452719838518
y[1] (numeric) = 0.51757155426737401484708336566823
absolute error = 3.45008744383271695e-15
relative error = 6.6659139502291924190950000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.39
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.39
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.391
y[1] (closed_form) = 0.51682764986580570071234354981004
y[1] (numeric) = 0.51682764986580225048157155022537
absolute error = 3.45023077199958467e-15
relative error = 6.6757859663573283858742700000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.391
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.391
Order of pole (three term test) = 1.037e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.392
y[1] (closed_form) = 0.51608534813053243493195930770247
y[1] (numeric) = 0.51608534813052898455868125059813
absolute error = 3.45037327805710434e-15
relative error = 6.6856640874532410238617600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.392
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.392
Order of pole (three term test) = 1.413e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.393
y[1] (closed_form) = 0.5153446444611530630281960515324
y[1] (numeric) = 0.5153446444611496125132287451228
absolute error = 3.45051496730640960e-15
relative error = 6.6955483177947552019104000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.393
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.393
Order of pole (three term test) = 1.083e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.394
y[1] (closed_form) = 0.51460553427375779370081657606179
y[1] (numeric) = 0.51460553427375434304497156538138
absolute error = 3.45065584501068041e-15
relative error = 6.7054386616351745572067599999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.394
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.394
Order of pole (three term test) = 1.475e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.395
y[1] (closed_form) = 0.51386801300086072892177644172095
y[1] (numeric) = 0.51386801300085727812586004627928
absolute error = 3.45079591639544167e-15
relative error = 6.7153351232034393758617499999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.395
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.395
Order of pole (three term test) = 7.536e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.396
y[1] (closed_form) = 0.51313207609132929943103915402994
y[1] (numeric) = 0.51313207609132584849585250517052
absolute error = 3.45093518664885942e-15
relative error = 6.7252377067042836194467199999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.396
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.396
Order of pole (three term test) = 3.850e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.397
y[1] (closed_form) = 0.51239771901031405368595861158664
y[1] (numeric) = 0.51239771901031060261229768955227
absolute error = 3.45107366092203437e-15
relative error = 6.7351464163183905748013300000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.397
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.397
Order of pole (three term test) = 7.867e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.398
y[1] (closed_form) = 0.51166493723917879824232860759597
y[1] (numeric) = 0.51166493723917534703098427830293
absolute error = 3.45121134432929304e-15
relative error = 6.7450612562025476345481600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.398
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.398
Order of pole (three term test) = 4.019e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.399
y[1] (closed_form) = 0.51093372627543108755820173809435
y[1] (numeric) = 0.51093372627542763620995978961807
absolute error = 3.45134824194847628e-15
relative error = 6.7549822304897997236922800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.399
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.399
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.4
y[1] (closed_form) = 0.51020408163265306122448979591836
y[1] (numeric) = 0.51020408163264960974013097469297
absolute error = 3.45148435882122539e-15
relative error = 6.7649093432896017644000000000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.4
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.4
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.401
y[1] (closed_form) = 0.50947599884043262663917534176924
y[1] (numeric) = 0.50947599884042917501947538850339
absolute error = 3.45161969995326585e-15
relative error = 6.7748425986879701636458500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.401
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.401
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.402
y[1] (closed_form) = 0.50874947344429498515469036489547
y[1] (numeric) = 0.508749473444291533400420050207
absolute error = 3.45175427031468847e-15
relative error = 6.7847820007476329153858800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.402
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.402
Order of pole (three term test) = 1.314e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.403
y[1] (closed_form) = 0.50802450100563449974065349223662
y[1] (numeric) = 0.5080245010056310478525786520083
absolute error = 3.45188807484022832e-15
relative error = 6.7947275535081789871428800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.403
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.403
Order of pole (three term test) = 1.342e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.404
y[1] (closed_form) = 0.50730107710164690221670278650335
y[1] (numeric) = 0.50730107710164345019558435696221
absolute error = 3.45202111842954114e-15
relative error = 6.8046792609862063678262400000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.404
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.404
Order of pole (three term test) = 4.570e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.405
y[1] (closed_form) = 0.50657919732526183812261749471258
y[1] (numeric) = 0.5065791973252583859692115472351
absolute error = 3.45215340594747748e-15
relative error = 6.8146371271754692324570000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.405
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.405
Order of pole (three term test) = 4.668e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.406
y[1] (closed_form) = 0.5058588572850757473052898672424
y[1] (numeric) = 0.50585885728507229502034764288796
absolute error = 3.45228494222435444e-15
relative error = 6.8246011560470239337518400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.406
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.406
Order of pole (three term test) = 9.538e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.407
y[1] (closed_form) = 0.50514005260528507831438805566037
y[1] (numeric) = 0.50514005260528162589865599943519
absolute error = 3.45241573205622518e-15
relative error = 6.8345713515493741213618200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.407
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.407
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.408
y[1] (closed_form) = 0.50442277892561983471074380165289
y[1] (numeric) = 0.50442277892561638216496359650686
absolute error = 3.45254578020514603e-15
relative error = 6.8445477176086146192179200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.408
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.408
Order of pole (three term test) = 9.954e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.409
y[1] (closed_form) = 0.50370703190127745140360482974451
y[1] (numeric) = 0.50370703190127399872851343030307
absolute error = 3.45267509139944144e-15
relative error = 6.8545302581285745014446399999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.409
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.409
Order of pole (three term test) = 1.017e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.41
y[1] (closed_form) = 0.50299280720285699914491222775514
y[1] (numeric) = 0.50299280720285354634124189378858
absolute error = 3.45280367033396656e-15
relative error = 6.8645189769909589179360000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.41
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.41
Order of pole (three term test) = 5.193e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.411
y[1] (closed_form) = 0.50228010051629371532069830997814
y[1] (numeric) = 0.50228010051629026238917663961039
absolute error = 3.45293152167036775e-15
relative error = 6.8745138780554902311977500000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.411
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.411
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.412
y[1] (closed_form) = 0.50156890754279385919155117206623
y[1] (numeric) = 0.50156890754279040613290113472551
absolute error = 3.45305865003734072e-15
relative error = 6.8845149651600478364556799999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.412
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.412
Order of pole (three term test) = 5.419e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.413
y[1] (closed_form) = 0.50085922399876988974585902115079
y[1] (numeric) = 0.50085922399876643656079899026425
absolute error = 3.45318506003088654e-15
relative error = 6.8945222421208071082812599999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.413
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.413
Order of pole (three term test) = 2.214e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.414
y[1] (closed_form) = 0.50015104561577596434123105177764
y[1] (numeric) = 0.50015104561577251103047483721209
absolute error = 3.45331075621456555e-15
relative error = 6.9045357127323775024078000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.414
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.414
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.415
y[1] (closed_form) = 0.49944436814044375632109278427749
y[1] (numeric) = 0.49944436814044030288534966452846
absolute error = 3.45343574311974903e-15
relative error = 6.9145553807679395015917500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
memory used=274.2MB, alloc=44.3MB, time=2.19
Radius of convergence (given) for eq 1 = 1.415
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.415
Order of pole (three term test) = 5.775e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.416
y[1] (closed_form) = 0.49873918733441858980497302818475
y[1] (numeric) = 0.49873918733441513624494778231598
absolute error = 3.45356002524586877e-15
relative error = 6.9245812499793806525011200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.416
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.416
Order of pole (three term test) = 1.770e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.417
y[1] (closed_form) = 0.49803549897429588986243761482831
y[1] (numeric) = 0.49803549897429243617883055416377
absolute error = 3.45368360706066454e-15
relative error = 6.9346133240974306625560600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.417
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.417
Order of pole (three term test) = 1.205e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.418
y[1] (closed_form) = 0.49733329885155794629198239042255
y[1] (numeric) = 0.49733329885155449248548938999309
absolute error = 3.45380649300042946e-15
relative error = 6.9446516068317955255290400000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.418
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.418
Order of pole (three term test) = 6.154e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.419
y[1] (closed_form) = 0.49663258277251098923747529873691
y[1] (numeric) = 0.49663258277250753530878782848359
absolute error = 3.45392868747025332e-15
relative error = 6.9546961018712907452725200000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.419
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.419
Order of pole (three term test) = 1.886e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.42
y[1] (closed_form) = 0.49593334655822257488593533029161
y[1] (numeric) = 0.49593334655821912083574048602779
absolute error = 3.45405019484426382e-15
relative error = 6.9647468128839735666480000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.42
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.42
Order of pole (three term test) = 6.420e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.421
y[1] (closed_form) = 0.49523558604445927950155528735797
y[1] (numeric) = 0.49523558604445582533053582149221
absolute error = 3.45417101946586576e-15
relative error = 6.9748037435172742430881600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.421
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.421
Order of pole (three term test) = 1.967e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.422
y[1] (closed_form) = 0.49453929708162470006191631999462
y[1] (numeric) = 0.49453929708162124577075067201632
absolute error = 3.45429116564797830e-15
relative error = 6.9848668973981265527772000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.422
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.422
Order of pole (three term test) = 6.697e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.423
y[1] (closed_form) = 0.49384447553469775977330563195056
y[1] (numeric) = 0.49384447553469430536266795868043
absolute error = 3.45441063767327013e-15
relative error = 6.9949362781330972110707699999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.423
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.423
Order of pole (three term test) = 1.368e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.424
y[1] (closed_form) = 0.49315111728317131675293523545007
y[1] (numeric) = 0.49315111728316786222349544105739
absolute error = 3.45452943979439268e-15
relative error = 7.0050118893085144110796800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.424
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.424
Order of pole (three term test) = 6.985e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.425
y[1] (closed_form) = 0.49245921822099107417666974453678
y[1] (numeric) = 0.49245921822098761952909351032534
absolute error = 3.45464757623421144e-15
relative error = 7.0150937344905956053500000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.425
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.425
Order of pole (three term test) = 2.854e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.426
y[1] (closed_form) = 0.49176877425649479020160552669419
y[1] (numeric) = 0.49176877425649133543655434065894
absolute error = 3.45476505118603525e-15
relative error = 7.0251818172255742160290000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.426
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.426
Order of pole (three term test) = 7.286e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.427
y[1] (closed_form) = 0.49107978131235178598350266582659
y[1] (numeric) = 0.49107978131234833110163385198289
absolute error = 3.45488186881384370e-15
relative error = 7.0352761410398255277773000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.427
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.427
Order of pole (three term test) = 7.440e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.428
y[1] (closed_form) = 0.49039223532550275011965570541943
y[1] (numeric) = 0.49039223532549929512162245290679
absolute error = 3.45499803325251264e-15
relative error = 7.0453767094399917352857599999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.428
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.428
Order of pole (three term test) = 1.520e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.429
y[1] (closed_form) = 0.48970613224709983785829961298524
y[1] (numeric) = 0.4897061322470963827447510049475
absolute error = 3.45511354860803774e-15
relative error = 7.0554835259131059946273400000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.429
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.429
Order of pole (three term test) = 1.552e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.43
y[1] (closed_form) = 0.48902146804244706342608440510538
y[1] (numeric) = 0.48902146804244360819766544734906
absolute error = 3.45522841895775632e-15
relative error = 7.0655965939267158987680000000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.43
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.43
Order of pole (three term test) = 7.924e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.431
y[1] (closed_form) = 0.48833823869094098383551596109116
y[1] (numeric) = 0.48833823869093752849286761052405
absolute error = 3.45534264835056711e-15
relative error = 7.0757159169290056557407100000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.431
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.431
Order of pole (three term test) = 8.092e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.432
y[1] (closed_form) = 0.48765644018601167254455229237539
y[1] (numeric) = 0.48765644018600821708831148522704
absolute error = 3.45545624080714835e-15
relative error = 7.0858414983489177780704000000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.432
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.432
Order of pole (three term test) = 8.264e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.433
y[1] (closed_form) = 0.48697606853506398135076447938119
y[1] (numeric) = 0.4869760685350605257815641592072
absolute error = 3.45556920032017399e-15
relative error = 7.0959733415962737665511100000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.433
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.433
Order of pole (three term test) = 1.688e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.434
y[1] (closed_form) = 0.48629711975941908891262018833315
y[1] (numeric) = 0.48629711975941563323108933380506
absolute error = 3.45568153085452809e-15
relative error = 7.1061114500618939650400400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.434
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.434
Order of pole (three term test) = 8.617e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.435
y[1] (closed_form) = 0.48561958989425633430052568320606
y[1] (numeric) = 0.48561958989425287850728933568861
absolute error = 3.45579323634751745e-15
relative error = 7.1162558271177166209762500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.435
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.435
Order of pole (three term test) = 2.640e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.436
y[1] (closed_form) = 0.48494347498855533399027009411783
y[1] (numeric) = 0.48494347498855187808594938503537
absolute error = 3.45590432070908246e-15
relative error = 7.1264064761169161044361600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.436
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.436
Order of pole (three term test) = 1.797e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.437
y[1] (closed_form) = 0.48426877110503838072145392981686
y[1] (numeric) = 0.48426877110503492470666610781071
absolute error = 3.45601478782200615e-15
relative error = 7.1365634003940202175593500000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.437
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.437
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.438
y[1] (closed_form) = 0.48359547432011312265335296086165
y[1] (numeric) = 0.48359547432010966652871141874007
absolute error = 3.45612464154212158e-15
relative error = 7.1467266032650268564735200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.438
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.438
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.439
y[1] (closed_form) = 0.48292358072381552126046917957562
y[1] (numeric) = 0.48292358072381206502658348105817
absolute error = 3.45623388569851745e-15
relative error = 7.1568960880275197525814499999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.439
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.439
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.44
y[1] (closed_form) = 0.48225308641975308641975308641975
y[1] (numeric) = 0.48225308641974963007722899267779
absolute error = 3.45634252409374196e-15
relative error = 7.1670718579607833282560000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.44
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.44
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.441
y[1] (closed_form) = 0.4815839875250483871511465792367
y[1] (numeric) = 0.48158398752504493070058607523157
absolute error = 3.45645056050400513e-15
relative error = 7.1772539163259170763475300000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.441
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.441
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.442
y[1] (closed_form) = 0.48091628017028283648269374674179
y[1] (numeric) = 0.48091628017027937992469506736257
absolute error = 3.45655799867937922e-15
relative error = 7.1874422663659486924160800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.442
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.442
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.443
y[1] (closed_form) = 0.48024996049944074892099840124788
y[1] (numeric) = 0.4802499604994372922561560572502
absolute error = 3.45666484234399768e-15
relative error = 7.1976369113059468251823200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.443
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.443
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.444
y[1] (closed_form) = 0.47958502466985366901727273424851
y[1] (numeric) = 0.47958502466985021224617753799618
absolute error = 3.45677109519625233e-15
relative error = 7.2078378543531327983668800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.444
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.444
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.445
y[1] (closed_form) = 0.47892146885214496952862154428228
y[1] (numeric) = 0.47892146885214151265186063529332
absolute error = 3.45687676090898896e-15
relative error = 7.2180450986969916732039999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.445
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.445
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.446
y[1] (closed_form) = 0.47825928923017471768354156742786
y[1] (numeric) = 0.47825928923017126070169843772656
absolute error = 3.45698184312970130e-15
relative error = 7.2282586475093825233908000000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.446
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.446
Order of pole (three term test) = 1.106e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.447
y[1] (closed_form) = 0.47759848200098480806988603067424
y[1] (numeric) = 0.47759848200098135098354054995084
absolute error = 3.45708634548072340e-15
relative error = 7.2384785039446479814306000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.447
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.447
Order of pole (three term test) = 1.130e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.448
y[1] (closed_form) = 0.47693904337474436067275113702268
y[1] (numeric) = 0.47693904337474090348247957760235
absolute error = 3.45719027155942033e-15
relative error = 7.2487046711397228435923200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.448
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.448
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.449
y[1] (closed_form) = 0.47628096957469538259888426420068
y[1] (numeric) = 0.47628096957469192530525932582321
absolute error = 3.45729362493837747e-15
relative error = 7.2589371522142422743894699999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.449
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.449
Order of pole (three term test) = 1.177e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.45
y[1] (closed_form) = 0.4756242568370986920332936979786
y[1] (numeric) = 0.47562425683709523463688453239055
absolute error = 3.45739640916558805e-15
relative error = 7.2691759502706488751250000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.45
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.45
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.451
y[1] (closed_form) = 0.47496890141118010298275720397207
y[1] (numeric) = 0.47496890141117664548412943933278
absolute error = 3.45749862776463929e-15
relative error = 7.2794210683942993258052900000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.451
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.451
Order of pole (three term test) = 1.227e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.452
y[1] (closed_form) = 0.47431489955907686936988214223376
y[1] (numeric) = 0.47431489955907341176959790733682
absolute error = 3.45760028423489694e-15
relative error = 7.2896725096535701581897600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.452
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.452
Order of pole (three term test) = 1.253e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.453
y[1] (closed_form) = 0.47366224755578438705026361672387
y[1] (numeric) = 0.47366224755578092934888156503561
absolute error = 3.45770138205168826e-15
relative error = 7.2999302770999627197063400000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.453
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.453
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.454
y[1] (closed_form) = 0.47301094168910315233411979285905
y[1] (numeric) = 0.47301094168909969453219512637542
absolute error = 3.45780192466648363e-15
relative error = 7.3101943737682077059210800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.454
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.454
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.455
y[1] (closed_form) = 0.47236097825958597560255547289238
y[1] (numeric) = 0.47236097825958251770063996581595
absolute error = 3.45790191550707643e-15
relative error = 7.3204648026763684792207500000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.455
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.455
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.456
y[1] (closed_form) = 0.47171235358048544861731674918488
y[1] (numeric) = 0.47171235358048199061595877142314
absolute error = 3.45800135797776174e-15
relative error = 7.3307415668259443120486400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.456
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.456
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.457
y[1] (closed_form) = 0.47106506397770166413155151402667
y[1] (numeric) = 0.47106506397769820603129605451338
absolute error = 3.45810025545951329e-15
relative error = 7.3410246692019723281632100000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.457
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.457
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.458
y[1] (closed_form) = 0.47041910578973018641768324235428
y[1] (numeric) = 0.47041910578972672821907193219512
absolute error = 3.45819861131015916e-15
relative error = 7.3513141127731291765982400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.458
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.458
Order of pole (three term test) = 1.418e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.459
y[1] (closed_form) = 0.46977447536761027133703922757802
y[1] (numeric) = 0.46977447536760681304061036302211
absolute error = 3.45829642886455591e-15
relative error = 7.3616099004918317390547099999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.459
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.459
Order of pole (three term test) = 1.447e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.46
y[1] (closed_form) = 0.46913116907487333458434978419966
y[1] (numeric) = 0.46913116907486987619063834943831
absolute error = 3.45839371143476135e-15
relative error = 7.3719120352943372936600000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.46
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.46
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.461
y[1] (closed_form) = 0.46848918328749166674865227374198
y[1] (numeric) = 0.46848918328748820825818996353608
absolute error = 3.45849046231020590e-15
relative error = 7.3822205201008430078739000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.461
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.461
Order of pole (three term test) = 1.508e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.462
y[1] (closed_form) = 0.46784851439382739384049359889663
y[1] (numeric) = 0.46784851439382393525380884103419
absolute error = 3.45858668475786244e-15
relative error = 7.3925353578155845252033599999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.462
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.462
Order of pole (three term test) = 1.539e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.463
y[1] (closed_form) = 0.46720915879458168194362747731816
y[1] (numeric) = 0.46720915879457822326124545490323
absolute error = 3.45868238202241493e-15
relative error = 7.4028565513269342213091700000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.463
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.463
Order of pole (three term test) = 1.571e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.464
y[1] (closed_form) = 0.46657111290274418465764878019648
y[1] (numeric) = 0.46657111290274072588009145377095
absolute error = 3.45877755732642553e-15
relative error = 7.4131841035074985327468800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.464
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.464
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.465
y[1] (closed_form) = 0.46593437314354273200619692716281
y[1] (numeric) = 0.46593437314353927313398305666241
absolute error = 3.45887221387050040e-15
relative error = 7.4235180172142147209900000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.465
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.465
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.466
y[1] (closed_form) = 0.46529893595439325949349419027748
y[1] (numeric) = 0.46529893595438980052713935682336
absolute error = 3.45896635483345412e-15
relative error = 7.4338582952884469227227200000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.466
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.466
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.467
y[1] (closed_form) = 0.4646647977848499760000631944125
y[1] (numeric) = 0.46466479778484651694007982193966
absolute error = 3.45905998337247284e-15
relative error = 7.4442049405560817017627600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.467
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.467
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.468
y[1] (closed_form) = 0.46403195509655576921649132445857
y[1] (numeric) = 0.46403195509655231006338870118261
absolute error = 3.45915310262327596e-15
relative error = 7.4545579558276226524230400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.468
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.468
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.469
y[1] (closed_form) = 0.46340040436319284732207857324577
y[1] (numeric) = 0.46340040436318938807636287296911
absolute error = 3.45924571570027666e-15
relative error = 7.4649173438982847214902599999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.469
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.469
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.47
y[1] (closed_form) = 0.46277014207043361562311999629784
y[1] (numeric) = 0.46277014207043015628529429955687
absolute error = 3.45933782569674097e-15
relative error = 7.4752831075480875620730000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.47
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.47
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.471
y[1] (closed_form) = 0.46214116471589178687343478564275
y[1] (numeric) = 0.46214116471588832744399910069708
absolute error = 3.45942943568494567e-15
relative error = 7.4856552495419485235184700000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.471
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.471
Order of pole (three term test) = 1.850e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.472
y[1] (closed_form) = 0.46151346880907372400756143667297
y[1] (numeric) = 0.46151346880907026448701272033815
absolute error = 3.45952054871633482e-15
relative error = 7.4960337726297748266188800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.472
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.472
Order of pole (three term test) = 1.888e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.473
y[1] (closed_form) = 0.46088705087133001402479295801457
y[1] (numeric) = 0.46088705087132655441362513633955
absolute error = 3.45961116782167502e-15
relative error = 7.5064186795465551194695800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.473
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.473
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.474
y[1] (closed_form) = 0.46026190743580727176992795980625
y[1] (numeric) = 0.46026190743580381206863194859675
absolute error = 3.45970129601120950e-15
relative error = 7.5168099730124506116220000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.474
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.474
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.475
y[1] (closed_form) = 0.45963803504740017236426314277506
y[1] (numeric) = 0.45963803504739671257332686796426
absolute error = 3.45979093627481080e-15
relative error = 7.5272076557328852467500000000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.475
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.475
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.476
y[1] (closed_form) = 0.45901543026270371104795058790696
y[1] (numeric) = 0.45901543026270025116785900577455
absolute error = 3.45988009158213241e-15
relative error = 7.5376117303986356972481600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.476
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.476
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.477
y[1] (closed_form) = 0.45839408964996568920238970006817
y[1] (numeric) = 0.45839408964996222923362481730918
absolute error = 3.45996876488275899e-15
relative error = 7.5480221996859203366957099999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.477
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.477
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.478
y[1] (closed_form) = 0.45777400978903942532881907123147
y[1] (numeric) = 0.457774009789035965271859964876
absolute error = 3.46005695910635547e-15
relative error = 7.5584390662564878225274800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.478
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.478
Order of pole (three term test) = 6.401e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.479
y[1] (closed_form) = 0.45715518727133668976671827948731
y[1] (numeric) = 0.45715518727133322962204111667233
absolute error = 3.46014467716281498e-15
relative error = 7.5688623327577051626661800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.479
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.479
Order of pole (three term test) = 4.355e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.48
y[1] (closed_form) = 0.45653761869978086194302410518627
y[1] (numeric) = 0.4565376186997774017111021627808
absolute error = 3.46023192194240547e-15
relative error = 7.5792920018226449414880000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.48
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.48
Order of pole (three term test) = 4.444e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.481
y[1] (closed_form) = 0.45592130068876030895051019873153
y[1] (numeric) = 0.45592130068875684863181388281631
absolute error = 3.46031869631591522e-15
relative error = 7.5897280760701721228544200000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.481
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.481
Order of pole (three term test) = 1.134e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.482
y[1] (closed_form) = 0.45530622986408198426097424605841
y[1] (numeric) = 0.4553062298640785238559711112612
absolute error = 3.46040500313479721e-15
relative error = 7.6001705581050303474560400000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.482
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.482
Order of pole (three term test) = 2.314e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.483
y[1] (closed_form) = 0.45469240286292524538612251504918
y[1] (numeric) = 0.45469240286292178489527728373698
absolute error = 3.46049084523131220e-15
relative error = 7.6106194505179273770258000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.483
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.483
Order of pole (three term test) = 1.181e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.484
y[1] (closed_form) = 0.45407981633379588930623869341257
y[1] (numeric) = 0.45407981633379242873001327474181
absolute error = 3.46057622541867076e-15
relative error = 7.6210747558856201932345600000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.484
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.484
Order of pole (three term test) = 4.819e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.485
y[1] (closed_form) = 0.45346846693648040449387250734052
y[1] (numeric) = 0.45346846693647694383272601616638
absolute error = 3.46066114649117414e-15
relative error = 7.6315364767709994928815000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.485
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.485
Order of pole (three term test) = 4.917e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.486
y[1] (closed_form) = 0.45285835134200043836688409905643
y[1] (numeric) = 0.45285835134199697762127287470246
absolute error = 3.46074561122435397e-15
relative error = 7.6420046157231735391381199999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.486
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.486
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.487
y[1] (closed_form) = 0.45224946623256747901223289581213
y[1] (numeric) = 0.45224946623256401818261052070129
absolute error = 3.46082962237511084e-15
relative error = 7.6524791752775514609719599999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.487
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.487
Order of pole (three term test) = 2.560e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.488
y[1] (closed_form) = 0.4516418083015377500289050757313
y[1] (numeric) = 0.4516418083015342891157223938795
absolute error = 3.46091318268185180e-15
relative error = 7.6629601579559260718592000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.488
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.488
Order of pole (three term test) = 2.612e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.489
y[1] (closed_form) = 0.45103537425336731734533207704947
y[1] (numeric) = 0.45103537425336385634903721242275
absolute error = 3.46099629486462672e-15
relative error = 7.6734475662665560580731200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.489
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.489
Order of pole (three term test) = 5.330e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.49
y[1] (closed_form) = 0.45043016080356740687356425386244
y[1] (numeric) = 0.45043016080356394579460262859887
absolute error = 3.46107896162526357e-15
relative error = 7.6839414027042476517570000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.49
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.49
Order of pole (three term test) = 2.719e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.491
y[1] (closed_form) = 0.44982616467865993186932909777017
y[1] (numeric) = 0.44982616467865647070814345026757
absolute error = 3.46116118564750260e-15
relative error = 7.6944416697504357275105999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.491
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.491
Order of pole (three term test) = 5.549e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.492
y[1] (closed_form) = 0.44922338261613322887392276232849
y[1] (numeric) = 0.44922338261612976763095316519904
absolute error = 3.46124296959712945e-15
relative error = 7.7049483698732643719847999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.492
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.492
Order of pole (three term test) = 2.831e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.493
y[1] (closed_form) = 0.44862181136439800112065728478827
y[1] (numeric) = 0.44862181136439453979634116268107
absolute error = 3.46132431612210720e-15
relative error = 7.7154615055276669320527999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.493
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.493
Order of pole (three term test) = 2.889e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.494
y[1] (closed_form) = 0.44802144768274346829531423328298
y[1] (numeric) = 0.44802144768274000689008638057563
absolute error = 3.46140522785270735e-15
relative error = 7.7259810791554455026645999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.494
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.494
Order of pole (three term test) = 2.947e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.495
y[1] (closed_form) = 0.44742228834129372154673885079585
y[1] (numeric) = 0.44742228834129026006103144915611
absolute error = 3.46148570740163974e-15
relative error = 7.7365070931853498598935000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.495
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.495
Order of pole (three term test) = 6.014e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.496
y[1] (closed_form) = 0.4468243301209642826503474505991
y[1] (numeric) = 0.44682433012096082108459008641762
absolute error = 3.46156575736418148e-15
relative error = 7.7470395500331559791436800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.496
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.496
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.497
y[1] (closed_form) = 0.44622756981341886623391516946161
y[1] (numeric) = 0.44622756981341540458853485115683
absolute error = 3.46164538031830478e-15
relative error = 7.7575784521017438767230200000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.497
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.497
Order of pole (three term test) = 3.130e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.498
y[1] (closed_form) = 0.44563200422102634398156153019335
y[1] (numeric) = 0.44563200422102288225698270538955
absolute error = 3.46172457882480380e-15
relative error = 7.7681238017811750264152000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.498
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.498
Order of pole (three term test) = 3.193e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.499
y[1] (closed_form) = 0.4450376301568179097383579268545
y[1] (numeric) = 0.44503763015681444793500249943403
absolute error = 3.46180335542742047e-15
relative error = 7.7786756014487692235104700000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.499
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.499
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.5
y[1] (closed_form) = 0.44444444444444444444444444444445
y[1] (numeric) = 0.4444444444444409825627317914751
absolute error = 3.46188171265296935e-15
relative error = 7.7892338534691810374999999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.5
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.5
Order of pole (three term test) = 9.971e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.501
y[1] (closed_form) = 0.44385244391813407983396367777911
y[1] (numeric) = 0.44385244391813061787431066631774
absolute error = 3.46195965301146137e-15
relative error = 7.7997985601944754780713699999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.501
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.501
Order of pole (three term test) = 3.391e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.502
y[1] (closed_form) = 0.44326162542264995984049673670792
y[1] (numeric) = 0.44326162542264649780331774048115
absolute error = 3.46203717899622677e-15
relative error = 7.8103697239642035780270799999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.502
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.502
Order of pole (three term test) = 3.459e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.503
y[1] (closed_form) = 0.44267198581324819865702172943977
y[1] (numeric) = 0.44267198581324473654272864540287
absolute error = 3.46211429308403690e-15
relative error = 7.8209473471054771134321000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.503
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.503
Order of pole (three term test) = 3.529e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.504
y[1] (closed_form) = 0.44208352195563603440470801267542
y[1] (numeric) = 0.4420835219556325722137102774503
absolute error = 3.46219099773522512e-15
relative error = 7.8315314319330429850419200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.504
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.504
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.505
y[1] (closed_form) = 0.44149623072593017737111069414245
y[1] (numeric) = 0.44149623072592671510381530033573
absolute error = 3.46226729539380672e-15
relative error = 7.8421219807493570659680000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.505
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.505
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.506
y[1] (closed_form) = 0.44091010901061535178453957520956
y[1] (numeric) = 0.44091010901061188944135108761165
absolute error = 3.46234318848759791e-15
relative error = 7.8527189958446576134047600000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.506
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.506
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.507
y[1] (closed_form) = 0.4403251537065030300975452313006
y[1] (numeric) = 0.44032515370649956767886580296675
absolute error = 3.46241867942833385e-15
relative error = 7.8633224794970381617086500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.507
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.507
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.508
y[1] (closed_form) = 0.43974136172069035875859254620802
y[1] (numeric) = 0.43974136172068689626482193442231
absolute error = 3.46249377061178571e-15
relative error = 7.8739324339725198588254400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.508
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.508
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.509
y[1] (closed_form) = 0.4391587299705192744570790411057
y[1] (numeric) = 0.43915872997051581188861462322884
absolute error = 3.46256846441787686e-15
relative error = 7.8845488615251234582456599999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.509
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.509
Order of pole (three term test) = 3.977e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.51
y[1] (closed_form) = 0.43857725538353580983290206569887
y[1] (numeric) = 0.43857725538353234719013885490081
absolute error = 3.46264276321079806e-15
relative error = 7.8951717643969406566060000000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.51
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.51
Order of pole (three term test) = 4.057e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.511
y[1] (closed_form) = 0.43799693489744958764778564079609
y[1] (numeric) = 0.4379969348974461249311163016742
absolute error = 3.46271666933912189e-15
relative error = 7.9058011448182053086186899999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.511
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.511
Order of pole (three term test) = 4.138e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.512
y[1] (closed_form) = 0.43741776546009350242154474958708
y[1] (numeric) = 0.43741776546009003963135961367104
absolute error = 3.46279018513591604e-15
relative error = 7.9164370050073636393497600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.512
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.512
Order of pole (three term test) = 4.221e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.513
y[1] (closed_form) = 0.43683974402938358854239245769972
y[1] (numeric) = 0.43683974402938012567907953884379
absolute error = 3.46286331291885593e-15
relative error = 7.9270793471711445104221699999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.513
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.513
Order of pole (three term test) = 8.612e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.514
y[1] (closed_form) = 0.43626286757327907386628368603732
y[1] (numeric) = 0.43626286757327561093022869570103
absolute error = 3.46293605499033629e-15
relative error = 7.9377281735046288825928400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.514
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.514
Order of pole (three term test) = 4.392e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.515
y[1] (closed_form) = 0.43568713306974261782613904954852
y[1] (numeric) = 0.43568713306973915481772541196659
absolute error = 3.46300841363758193e-15
relative error = 7.9483834861913189852842500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.515
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.515
Order of pole (three term test) = 4.480e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.516
y[1] (closed_form) = 0.43511253750670073307760319128939
y[1] (numeric) = 0.4351125375066972699972120585318
absolute error = 3.46308039113275759e-15
relative error = 7.9590452874032069277630400000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.516
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.516
Order of pole (three term test) = 4.569e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.517
y[1] (closed_form) = 0.43453907788200438971376476400835
y[1] (numeric) = 0.43453907788200092656177503093135
absolute error = 3.46315198973307700e-15
relative error = 7.9697135793008430362529999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.517
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.517
Order of pole (three term test) = 4.661e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.518
y[1] (closed_form) = 0.43396675120338980108699991841425
y[1] (numeric) = 0.43396675120338633786378823750331
absolute error = 3.46322321168091094e-15
relative error = 7.9803883640334034209045600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.518
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.518
Order of pole (three term test) = 4.754e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.519
y[1] (closed_form) = 0.43339555448843939028179812348393
y[1] (numeric) = 0.4333955544884359269877389195893
absolute error = 3.46329405920389463e-15
relative error = 7.9910696437387575173714300000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.519
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.519
Order of pole (three term test) = 4.849e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.52
y[1] (closed_form) = 0.43282548476454293628808864265928
y[1] (numeric) = 0.43282548476453947292355412762519
absolute error = 3.46336453451503409e-15
relative error = 8.0017574205435347615360000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.52
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.52
Order of pole (three term test) = 4.945e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.521
y[1] (closed_form) = 0.43225653906885889893020829145848
y[1] (numeric) = 0.43225653906885543549556847864667
absolute error = 3.46343463981281181e-15
relative error = 8.0124516965631911665382100000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.521
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.521
Order of pole (three term test) = 1.009e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.522
y[1] (closed_form) = 0.43168871444827592161223647562426
y[1] (numeric) = 0.43168871444827245810785919433275
absolute error = 3.46350437728129151e-15
relative error = 8.0231524739020752822508400000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.522
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.522
Order of pole (three term test) = 1.029e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.523
y[1] (closed_form) = 0.43112200795937451094597222108454
y[1] (numeric) = 0.43112200795937104737222313086244
absolute error = 3.46357374909022210e-15
relative error = 8.0338597546534937773909000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.523
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.523
Order of pole (three term test) = 5.247e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.524
y[1] (closed_form) = 0.430556416668388892333340222236
y[1] (numeric) = 0.43055641666838542869058282709522
absolute error = 3.46364275739514078e-15
relative error = 8.0445735408997764922492800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.524
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.524
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.525
y[1] (closed_form) = 0.42999193765116904058048911582908
y[1] (numeric) = 0.42999193765116557686908477835367
absolute error = 3.46371140433747541e-15
relative error = 8.0552938347123412503812500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.525
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.525
Order of pole (three term test) = 5.457e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.526
y[1] (closed_form) = 0.42942856799314288462628549441829
y[1] (numeric) = 0.42942856799313942084659344977227
absolute error = 3.46377969204464602e-15
relative error = 8.0660206381517581152695200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.526
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.526
Order of pole (three term test) = 1.113e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.527
y[1] (closed_form) = 0.42886630478927868547331186428612
y[1] (numeric) = 0.42886630478927522162568923412058
absolute error = 3.46384762263016554e-15
relative error = 8.0767539532678132644186599999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.527
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.527
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.528
y[1] (closed_form) = 0.42830514514404758641484608426304
y[1] (numeric) = 0.42830514514404412249964789052332
absolute error = 3.46391519819373972e-15
relative error = 8.0874937820995723984204800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.528
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.528
Order of pole (three term test) = 5.789e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.529
y[1] (closed_form) = 0.42774508617138633465663404825221
y[1] (numeric) = 0.42774508617138287067421322688589
absolute error = 3.46398242082136632e-15
relative error = 8.0982401266754438589151200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.529
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.529
Order of pole (three term test) = 5.903e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.53
y[1] (closed_form) = 0.42718612499466017343756674783203
y[1] (numeric) = 0.42718612499465670938827416239858
absolute error = 3.46404929258543345e-15
relative error = 8.1089929890132411631050000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.53
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.53
Order of pole (three term test) = 6.020e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.531
y[1] (closed_form) = 0.42662825874662590375863762238365
y[1] (numeric) = 0.42662825874662243964282207756645
absolute error = 3.46411581554481720e-15
relative error = 8.1197523711202452689292000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.531
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.531
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.532
y[1] (closed_form) = 0.42607148456939511483478652114337
y[1] (numeric) = 0.4260714845693916506527947761649
absolute error = 3.46418199174497847e-15
relative error = 8.1305182749932663485732800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.532
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.532
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.533
y[1] (closed_form) = 0.4255157996143975823894329108387
y[1] (numeric) = 0.4255157996143941181416096927796
absolute error = 3.46424782321805910e-15
relative error = 8.1412907026187052922598999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.533
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.533
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=318.1MB, alloc=44.3MB, time=2.53
x[1] = -1.534
y[1] (closed_form) = 0.42496120104234483391666340863079
y[1] (numeric) = 0.42496120104234136960335142565365
absolute error = 3.46431331198297714e-15
relative error = 8.1520696559726145548538400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.534
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.534
Order of pole (three term test) = 1.953e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.535
y[1] (closed_form) = 0.42440768602319388004116754554425
y[1] (numeric) = 0.42440768602319041566270750002273
absolute error = 3.46437846004552152e-15
relative error = 8.1628551370207589434620000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.535
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.535
Order of pole (three term test) = 6.639e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.536
y[1] (closed_form) = 0.42385525173611111111111111111111
y[1] (numeric) = 0.42385525173610764666784171266527
absolute error = 3.46444326939844584e-15
relative error = 8.1736471477186756765286400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.536
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.536
Order of pole (three term test) = 6.770e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.537
y[1] (closed_form) = 0.42330389536943635816419873440601
y[1] (numeric) = 0.42330389536943289365645671284448
absolute error = 3.46450774202156153e-15
relative error = 8.1844456900117342900645700000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.537
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.537
Order of pole (three term test) = 2.071e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.538
y[1] (closed_form) = 0.42275361412064711741220675695557
y[1] (numeric) = 0.4227536141206436528403268751253
absolute error = 3.46457187988183027e-15
relative error = 8.1952507658351961211898799999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.538
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.538
Order of pole (three term test) = 1.408e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.539
y[1] (closed_form) = 0.42220440519632293739426418427365
y[1] (numeric) = 0.42220440519631947275857925081805
absolute error = 3.46463568493345560e-15
relative error = 8.2060623771142731911675999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.539
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.539
Order of pole (three term test) = 1.436e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.54
y[1] (closed_form) = 0.42165626581210996795412379827964
y[1] (numeric) = 0.42165626581210650325496468030568
absolute error = 3.46469915911797396e-15
relative error = 8.2168805257641870435360000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.54
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.54
Order of pole (three term test) = 1.464e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.541
y[1] (closed_form) = 0.42110919319268567020159760405713
y[1] (numeric) = 0.42110919319268220543929323971219
absolute error = 3.46476230436434494e-15
relative error = 8.2277052136902270064641400000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.541
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.541
Order of pole (three term test) = 1.493e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.542
y[1] (closed_form) = 0.4205631845717236866232309009641
y[1] (numeric) = 0.42056318457172022179810831192331
absolute error = 3.46482512258904079e-15
relative error = 8.2385364427878079849935600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.542
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.542
Order of pole (three term test) = 1.522e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.543
y[1] (closed_form) = 0.42001823719185887051215763788463
y[1] (numeric) = 0.42001823719185540562454194174931
absolute error = 3.46488761569613532e-15
relative error = 8.2493742149425280804866800000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.543
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.543
Order of pole (three term test) = 7.760e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.544
y[1] (closed_form) = 0.41947434830465247389191656151843
y[1] (numeric) = 0.41947434830464900894213098412633
absolute error = 3.46494978557739210e-15
relative error = 8.2602185320302258133056000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.544
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.544
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.545
y[1] (closed_form) = 0.41893151517055749311381321938396
y[1] (numeric) = 0.41893151517055402810217910703207
absolute error = 3.46501163411235189e-15
relative error = 8.2710693959170367702272500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.545
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.545
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.546
y[1] (closed_form) = 0.41838973505888417131218735827048
y[1] (numeric) = 0.41838973505888070623902418985098
absolute error = 3.46507316316841950e-15
relative error = 8.2819268084594501416619999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.546
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.546
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.547
y[1] (closed_form) = 0.41784900524776565690668888509111
y[1] (numeric) = 0.4178490052477621917723142841412
absolute error = 3.46513437460094991e-15
relative error = 8.2927907715043647331611899999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.547
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.547
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.548
y[1] (closed_form) = 0.4173093230241238173453785496331
y[1] (numeric) = 0.41730932302412035215010829629935
absolute error = 3.46519527025333375e-15
relative error = 8.3036612868891446784600000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.548
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.548
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.549
y[1] (closed_form) = 0.41677068568363520728715208504123
y[1] (numeric) = 0.4167706856836317420313001279591
absolute error = 3.46525585195708213e-15
relative error = 8.3145383564416748198041299999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.549
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.549
Order of pole (three term test) = 8.718e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.55
y[1] (closed_form) = 0.41623309053069719042663891779397
y[1] (numeric) = 0.41623309053069372511051738588321
absolute error = 3.46531612153191076e-15
relative error = 8.3254219819804156008999999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.55
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.55
Order of pole (three term test) = 8.889e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.551
y[1] (closed_form) = 0.41569653487839421416934894855797
y[1] (numeric) = 0.41569653487839074879326816273449
absolute error = 3.46537608078582348e-15
relative error = 8.3363121653144577493114800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.551
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.551
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.552
y[1] (closed_form) = 0.41516101604846423636943352109682
y[1] (numeric) = 0.41516101604846077093370200590168
absolute error = 3.46543573151519514e-15
relative error = 8.3472089082435765944985600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.552
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.552
Order of pole (three term test) = 1.848e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.553
y[1] (closed_form) = 0.41462653137126530334698974918827
y[1] (numeric) = 0.41462653137126183785191424433447
absolute error = 3.46549507550485380e-15
relative error = 8.3581122125582859385241999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.553
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.553
Order of pole (three term test) = 9.419e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.554
y[1] (closed_form) = 0.41409307818574227840637107046373
y[1] (numeric) = 0.41409307818573881285225654230143
absolute error = 3.46555411452816230e-15
relative error = 8.3690220800398915888668000000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.554
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.554
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.555
y[1] (closed_form) = 0.41356065383939372008147144880636
y[1] (numeric) = 0.41356065383939025446862110170705
absolute error = 3.46561285034709931e-15
relative error = 8.3799385124605448090627500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.555
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.555
Order of pole (three term test) = 9.790e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.556
y[1] (closed_form) = 0.4130292556882389093384262594088
y[1] (numeric) = 0.41302925568823544366714154706926
absolute error = 3.46567128471233954e-15
relative error = 8.3908615115832949045174400000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.556
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.556
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.557
y[1] (closed_form) = 0.41249888109678502497061976719388
y[1] (numeric) = 0.41249888109678155924120040386031
absolute error = 3.46572941936333357e-15
relative error = 8.4017910791621420437389300000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.557
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.557
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.558
y[1] (closed_form) = 0.41196952743799446642530745285832
y[1] (numeric) = 0.41196952743799100063805142447143
absolute error = 3.46578725602838689e-15
relative error = 8.4127272169420893148579600000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.558
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.558
Order of pole (three term test) = 1.037e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.559
y[1] (closed_form) = 0.41144119209325232330555145257256
y[1] (numeric) = 0.41144119209324885746075502783411
absolute error = 3.46584479642473845e-15
relative error = 8.4236699266591947326944499999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.559
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.559
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.56
y[1] (closed_form) = 0.41091387245233399079552925706772
y[1] (numeric) = 0.41091387245233052489348699842922
absolute error = 3.46590204225863850e-15
relative error = 8.4346192100406226536000000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.56
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.56
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.561
y[1] (closed_form) = 0.4103875659133729302616097616428
y[1] (numeric) = 0.41038756591336946430261453621685
absolute error = 3.46595899522542595e-15
relative error = 8.4455750688046951463099500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.561
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.561
Order of pole (three term test) = 1.099e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.562
y[1] (closed_form) = 0.40986226988282857428589696718315
y[1] (numeric) = 0.40986226988282510827023995757812
absolute error = 3.46601565700960503e-15
relative error = 8.4565375046609427748153200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.562
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.562
Order of pole (three term test) = 1.120e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.563
y[1] (closed_form) = 0.40933798177545437539322029874305
y[1] (numeric) = 0.40933798177545090932119101382162
absolute error = 3.46607202928492143e-15
relative error = 8.4675065193101552209256699999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.563
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.563
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.564
y[1] (closed_form) = 0.40881469901426599773680182625702
y[1] (numeric) = 0.40881469901426253160868811181919
absolute error = 3.46612811371443783e-15
relative error = 8.4784821144444315182116800000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.564
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.564
Order of pole (three term test) = 1.164e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.565
y[1] (closed_form) = 0.40829241903050965101205483367188
y[1] (numeric) = 0.40829241903050618482814288306301
absolute error = 3.46618391195060887e-15
relative error = 8.4894642917472300096257499999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.565
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.565
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.566
y[1] (closed_form) = 0.40777113926363056587216537892541
y[1] (numeric) = 0.40777113926362709963273974356992
absolute error = 3.46623942563535549e-15
relative error = 8.5004530528934178480344400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.566
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.566
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.567
y[1] (closed_form) = 0.40725085716124161012327890697128
y[1] (numeric) = 0.40725085716123814382862250683247
absolute error = 3.46629465640013881e-15
relative error = 8.5114483995493204464280900000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.567
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.567
Order of pole (three term test) = 1.233e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.568
y[1] (closed_form) = 0.40673157017909204498125780924615
y[1] (numeric) = 0.40673157017908857863165194321282
absolute error = 3.46634960586603333e-15
relative error = 8.5224503333727703299379199999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.568
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.568
Order of pole (three term test) = 1.257e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.569
y[1] (closed_form) = 0.40621327578103642067609325194444
y[1] (numeric) = 0.40621327578103295427181760814481
absolute error = 3.46640427564379963e-15
relative error = 8.5334588560131558209484300000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.569
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.569
Order of pole (three term test) = 2.562e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.57
y[1] (closed_form) = 0.40569597143900361069414580713213
y[1] (numeric) = 0.40569597143900014423547847317558
absolute error = 3.46645866733395655e-15
relative error = 8.5444739691114695000950000000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.57
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.57
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.571
y[1] (closed_form) = 0.40517965463296598395245459860675
y[1] (numeric) = 0.40517965463296251743967207175402
absolute error = 3.46651278252685273e-15
relative error = 8.5554956743003561386019300000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.571
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.571
Order of pole (three term test) = 1.331e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.572
y[1] (closed_form) = 0.40466432285090871420339400060861
y[1] (numeric) = 0.40466432285090524763677119787098
absolute error = 3.46656662280273763e-15
relative error = 8.5665239732041603874539200000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.572
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.572
Order of pole (three term test) = 1.357e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.573
y[1] (closed_form) = 0.40414997358879922597197058273172
y[1] (numeric) = 0.40414997358879575935178085089959
absolute error = 3.46662018973183213e-15
relative error = 8.5775588674389744623907700000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.573
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.573
Order of pole (three term test) = 1.383e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.574
y[1] (closed_form) = 0.40363660435055677633204115801727
y[1] (numeric) = 0.40363660435055330965855628361889
absolute error = 3.46667348487439838e-15
relative error = 8.5886003586126850008888800000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.574
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.574
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.575
y[1] (closed_form) = 0.40312421264802217183169564121945
y[1] (numeric) = 0.40312421264801870510518586041014
absolute error = 3.46672650978080931e-15
relative error = 8.5996484483250200946187500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.575
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.575
Order of pole (three term test) = 1.436e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.576
y[1] (closed_form) = 0.40261279600092761988198613723621
y[1] (numeric) = 0.40261279600092415310272014561871
absolute error = 3.46677926599161750e-15
relative error = 8.6107031381675957476800000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.576
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.576
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.577
y[1] (closed_form) = 0.40210235193686671392709643097973
y[1] (numeric) = 0.40210235193686324709534139335617
absolute error = 3.46683175503762356e-15
relative error = 8.6217644297239621224472400000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.577
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.577
Order of pole (three term test) = 1.492e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.578
y[1] (closed_form) = 0.40159287799126455171793401347103
y[1] (numeric) = 0.401592877991261084833955573527
absolute error = 3.46688397843994403e-15
relative error = 8.6328323245696495899985200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.578
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.578
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.579
y[1] (closed_form) = 0.40108437170734798601499012730819
y[1] (numeric) = 0.40108437170734451907905241722953
absolute error = 3.46693593771007866e-15
relative error = 8.6439068242722142283370600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.579
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.579
Order of pole (three term test) = 1.550e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.58
y[1] (closed_form) = 0.40057683063611600705015221919564
y[1] (numeric) = 0.40057683063611254006251786921835
absolute error = 3.46698763434997729e-15
relative error = 8.6549879303912833067560000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.58
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.58
Order of pole (three term test) = 1.580e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.581
y[1] (closed_form) = 0.40007025233631025608096781794883
y[1] (numeric) = 0.40007025233630678904189796584264
absolute error = 3.46703906985210619e-15
relative error = 8.6660756444786004003825900000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.581
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.581
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.582
y[1] (closed_form) = 0.39956463437438566937464938203334
y[1] (numeric) = 0.39956463437438220228440368251947
absolute error = 3.46709024569951387e-15
relative error = 8.6771699680780701507818799999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.582
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.582
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.583
y[1] (closed_form) = 0.39905997432448125196287624870854
y[1] (numeric) = 0.39905997432447778482171288281215
absolute error = 3.46714116336589639e-15
relative error = 8.6882709027258027388407100000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.583
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.583
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.584
y[1] (closed_form) = 0.39855626976839098051219263340475
y[1] (numeric) = 0.39855626976838751332036831774251
absolute error = 3.46719182431566224e-15
relative error = 8.6993784499501582372454400000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.584
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.584
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.585
y[1] (closed_form) = 0.39805351829553483465851983799222
y[1] (numeric) = 0.39805351829553136741628983399557
absolute error = 3.46724223000399665e-15
relative error = 8.7104926112717904840462500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.585
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.585
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.586
y[1] (closed_form) = 0.39755171750292995615799659377689
y[1] (numeric) = 0.39755171750292648886561471685144
absolute error = 3.46729238187692545e-15
relative error = 8.7216133882036907692281999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.586
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.586
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.587
y[1] (closed_form) = 0.39705086499516193521003395181946
y[1] (numeric) = 0.397050864995158467867752580441
absolute error = 3.46734228137137846e-15
relative error = 8.7327407822512312766237400000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.587
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.587
Order of pole (three term test) = 1.804e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.588
y[1] (closed_form) = 0.39655095838435622331212050073283
y[1] (numeric) = 0.3965509583843527559201905854804
absolute error = 3.46739192991525243e-15
relative error = 8.7438747949122083238379199999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.588
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.588
Order of pole (three term test) = 1.838e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.589
y[1] (closed_form) = 0.39605199529014967200954010046255
y[1] (numeric) = 0.3960519952901462045682111729892
absolute error = 3.46744132892747335e-15
relative error = 8.7550154276768849383553500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.589
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.589
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.59
y[1] (closed_form) = 0.39555397333966219690676792848384
y[1] (numeric) = 0.3955539733396587294162881104253
absolute error = 3.46749047981805854e-15
relative error = 8.7661626820280337949740000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.59
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.59
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.591
y[1] (closed_form) = 0.39505689016746856631089159994485
y[1] (numeric) = 0.39505689016746509877150761176681
absolute error = 3.46753938398817804e-15
relative error = 8.7773165594409792972692400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.591
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.591
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.592
y[1] (closed_form) = 0.3945607434155703138809626019545
y[1] (numeric) = 0.39456074341556684629291977173881
absolute error = 3.46758804283021569e-15
relative error = 8.7884770613836397785401599999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.592
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.592
Order of pole (three term test) = 1.982e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.593
y[1] (closed_form) = 0.39406553073336777466071942967684
y[1] (numeric) = 0.39406553073336430702426170184719
absolute error = 3.46763645772782965e-15
relative error = 8.7996441893165691834928500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.593
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.593
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.594
y[1] (closed_form) = 0.39357124977763224387563778221026
y[1] (numeric) = 0.39357124977762877619100772619769
absolute error = 3.46768463005601257e-15
relative error = 8.8108179446929987543085200000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.594
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.594
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.595
y[1] (closed_form) = 0.39307789821247825787875512229636
y[1] (numeric) = 0.39307789821247479014619394114515
absolute error = 3.46773256118115121e-15
relative error = 8.8219983289588782070202500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.595
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.595
Order of pole (three term test) = 6.293e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.596
y[1] (closed_form) = 0.39258547370933599663318697746873
y[1] (numeric) = 0.39258547370933252885293451638309
absolute error = 3.46778025246108564e-15
relative error = 8.8331853435529167195782400000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.596
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.596
Order of pole (three term test) = 4.275e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.597
y[1] (closed_form) = 0.39209397394692380712270071192503
y[1] (numeric) = 0.39209397394692033929499546675696
absolute error = 3.46782770524516807e-15
relative error = 8.8443789899066238522406300000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.597
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.597
Order of pole (three term test) = 2.178e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.598
y[1] (closed_form) = 0.39160339661122084708513927766404
y[1] (numeric) = 0.39160339661121737921021840334294
absolute error = 3.46787492087432110e-15
relative error = 8.8555792694443498582444000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.598
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.598
Order of pole (three term test) = 2.219e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.599
y[1] (closed_form) = 0.39111373939543984846689280863079
y[1] (numeric) = 0.39111373939543638054499212753513
absolute error = 3.46792190068109566e-15
relative error = 8.8667861835833260645836599999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.599
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.599
Order of pole (three term test) = 4.522e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.6
y[1] (closed_form) = 0.390625
y[1] (numeric) = 0.39062499999999653203135401027155
absolute error = 3.46796864598972845e-15
relative error = 8.8779997337337048320000000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.6
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.6
Order of pole (three term test) = 2.304e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.601
y[1] (closed_form) = 0.39013717613249994830682416244375
y[1] (numeric) = 0.39013717613249648029166604624478
absolute error = 3.46801515811619897e-15
relative error = 8.8892199212985993161029700000002e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.601
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.601
Order of pole (three term test) = 1.174e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.602
y[1] (closed_form) = 0.38965026550769091694059080331857
y[1] (numeric) = 0.38965026550768744887915243503242
absolute error = 3.46806143836828615e-15
relative error = 8.9004467476741230485046000000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.602
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.602
Order of pole (three term test) = 2.392e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.603
y[1] (closed_form) = 0.38916426584744994277339470713248
y[1] (numeric) = 0.38916426584744647466590666150802
absolute error = 3.46810748804562446e-15
relative error = 8.9116802142494290230361400000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.603
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.603
Order of pole (three term test) = 2.437e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.604
y[1] (closed_form) = 0.38867917488075322914658490929783
y[1] (numeric) = 0.38867917488074976099327646953809
absolute error = 3.46815330843975974e-15
relative error = 8.9229203224067488952278399999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.604
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.604
Order of pole (three term test) = 9.933e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.605
y[1] (closed_form) = 0.38819499034364961520171582185732
y[1] (numeric) = 0.38819499034364614700281498765285
absolute error = 3.46819890083420447e-15
relative error = 8.9341670735214315698317500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.605
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.605
Order of pole (three term test) = 5.060e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.606
y[1] (closed_form) = 0.38771170997923416081351221834683
y[1] (numeric) = 0.38771170997923069256924571385405
absolute error = 3.46824426650449278e-15
relative error = 8.9454204689619819399160800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.606
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.606
Order of pole (three term test) = 5.156e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.607
y[1] (closed_form) = 0.38722933153762184654953495693429
y[1] (numeric) = 0.38722933153761837826012823869938
absolute error = 3.46828940671823491e-15
relative error = 8.9566805100900990250945900000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.607
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.607
Order of pole (three term test) = 2.626e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.608
y[1] (closed_form) = 0.38674785277592138808445335511498
y[1] (numeric) = 0.38674785277591791975013061994362
absolute error = 3.46833432273517136e-15
relative error = 8.9679471982607141193830399999998e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.608
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.608
Order of pole (three term test) = 5.352e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.609
y[1] (closed_form) = 0.38626727145820916450002916317899
y[1] (numeric) = 0.38626727145820569612101335595246
absolute error = 3.46837901580722653e-15
relative error = 8.9792205348220284262129300000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.609
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.609
Order of pole (three term test) = 5.452e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.61
y[1] (closed_form) = 0.38578758535550325990509625400255
y[1] (numeric) = 0.38578758535549979148160907544039
absolute error = 3.46842348717856216e-15
relative error = 8.9905005211155509749359999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.61
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.61
Order of pole (three term test) = 5.555e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.611
y[1] (closed_form) = 0.38530879224573761781297958903735
y[1] (numeric) = 0.38530879224573414934524150340725
absolute error = 3.46846773808563010e-15
relative error = 9.0017871584761355967621000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.611
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.611
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.612
y[1] (closed_form) = 0.38483088991373630771693686926217
y[1] (numeric) = 0.38483088991373283920516711203723
absolute error = 3.46851176975722494e-15
relative error = 9.0130804482320183244873600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.612
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.612
Order of pole (three term test) = 5.766e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.613
y[1] (closed_form) = 0.38435387615118790330732666889335
y[1] (numeric) = 0.38435387615118443475174325435726
absolute error = 3.46855558341453609e-15
relative error = 9.0243803917048541483432100000002e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.613
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.613
Order of pole (three term test) = 5.874e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.614
y[1] (closed_form) = 0.3838777487566199717773079114133
y[1] (numeric) = 0.38387774875661650317812764021376
absolute error = 3.46859918027119954e-15
relative error = 9.0356869902097537169018400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.614
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.614
Order of pole (three term test) = 5.984e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.615
y[1] (closed_form) = 0.3834025055353736736669574135667
y[1] (numeric) = 0.3834025055353702050243958802175
absolute error = 3.46864256153334920e-15
relative error = 9.0470002450553197171699999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.615
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.615
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.616
y[1] (closed_form) = 0.38292814429957847269875502401725
y[1] (numeric) = 0.38292814429957500401302662434935
absolute error = 3.46868572839966790e-15
relative error = 9.0583201575436831354624000000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.616
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.616
Order of pole (three term test) = 3.105e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.617
y[1] (closed_form) = 0.38245466286812695506042974900648
y[1] (numeric) = 0.38245466286812348633174768756847
absolute error = 3.46872868206143801e-15
relative error = 9.0696467289705392889288900000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.617
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.617
Order of pole (three term test) = 6.327e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.618
y[1] (closed_form) = 0.38198205906664975759418531630407
y[1] (numeric) = 0.38198205906664628882276161371246
absolute error = 3.46877142370259161e-15
relative error = 9.0809799606251834380176399999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.618
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.618
Order of pole (three term test) = 6.446e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.619
y[1] (closed_form) = 0.38151033072749060435433000872514
y[1] (numeric) = 0.38151033072748713554037550896475
absolute error = 3.46881395449976039e-15
relative error = 9.0923198537905464436127900000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.619
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.619
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.62
y[1] (closed_form) = 0.38103947568968145099832342630696
y[1] (numeric) = 0.38103947568967798214204780398181
absolute error = 3.46885627562232515e-15
relative error = 9.1036664097432301236600000000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.62
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.62
Order of pole (three term test) = 1.672e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.621
y[1] (closed_form) = 0.380569491798917736479222237741
y[1] (numeric) = 0.38056949179891426758083400527611
absolute error = 3.46889838823246489e-15
relative error = 9.1150196297535422760244900000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.621
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.621
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.622
y[1] (closed_form) = 0.38010037690753374151045808177023
y[1] (numeric) = 0.38010037690753027257016459656468
absolute error = 3.46894029348520555e-15
relative error = 9.1263795150855315182062000000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.622
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.622
Order of pole (three term test) = 1.735e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.623
y[1] (closed_form) = 0.3796321288744780532768137019865
y[1] (numeric) = 0.37963212887447458429482117351803
absolute error = 3.46898199252846847e-15
relative error = 9.1377460669970221224126300000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.623
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.623
Order of pole (three term test) = 7.071e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.624
y[1] (closed_form) = 0.37916474556528913586837826688345
y[1] (numeric) = 0.37916474556528566684489176376507
absolute error = 3.46902348650311838e-15
relative error = 9.1491192867396483405708799999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.624
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.624
Order of pole (three term test) = 7.203e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.625
y[1] (closed_form) = 0.37869822485207100591715976331361
y[1] (numeric) = 0.37869822485206753685238322030252
absolute error = 3.46906477654301109e-15
relative error = 9.1604991755588886595312500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.625
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.625
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.626
y[1] (closed_form) = 0.37823256461346901291891147693765
y[1] (numeric) = 0.37823256461346554381304770189677
absolute error = 3.46910586377504088e-15
relative error = 9.1718857346940999816508799999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.626
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.626
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.627
y[1] (closed_form) = 0.3777677627346457237255910082206
y[1] (numeric) = 0.37776776273464225457884168903319
absolute error = 3.46914674931918741e-15
relative error = 9.1832789653785512494458900000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.627
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.627
Order of pole (three term test) = 3.806e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.628
y[1] (closed_form) = 0.37730381710725691069671413651757
y[1] (numeric) = 0.37730381710725344150927984795514
absolute error = 3.46918743428856243e-15
relative error = 9.1946788688394572474731200000002e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.628
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.628
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.629
y[1] (closed_form) = 0.37684072562942764300069225641298
y[1] (numeric) = 0.37684072562942417377277246695695
absolute error = 3.46922791978945603e-15
relative error = 9.2060854462980118889052300000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.629
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.629
Order of pole (three term test) = 1.580e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.63
y[1] (closed_form) = 0.37637848620572848056005118747412
y[1] (numeric) = 0.37637848620572501129184426609151
absolute error = 3.46926820692138261e-15
relative error = 9.2174986989694214565090000000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.63
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.63
Order of pole (three term test) = 1.207e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.631
y[1] (closed_form) = 0.37591709674715177013722101782561
y[1] (numeric) = 0.37591709674714830082892424069907
absolute error = 3.46930829677712654e-15
relative error = 9.2289186280629377137729400000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.631
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.631
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.632
y[1] (closed_form) = 0.37545655517108804306036139946175
y[1] (numeric) = 0.37545655517108457371217095667436
absolute error = 3.46934819044278739e-15
relative error = 9.2403452347818905614233599999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.632
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.632
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.633
y[1] (closed_form) = 0.37499685940130251409144448415244
y[1] (numeric) = 0.37499685940129904470355548632755
absolute error = 3.46938788899782489e-15
relative error = 9.2517785203237206580892100000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.633
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.633
Order of pole (three term test) = 8.502e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.634
y[1] (closed_form) = 0.37453800736791168094155858748234
y[1] (numeric) = 0.37453800736790821151416507237871
absolute error = 3.46942739351510363e-15
relative error = 9.2632184858800120275402800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.634
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.634
Order of pole (three term test) = 1.299e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.635
y[1] (closed_form) = 0.37407999700736002394111980847104
y[1] (numeric) = 0.37407999700735655447441474753381
absolute error = 3.46946670506093723e-15
relative error = 9.2746651326365239266667500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.635
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.635
Order of pole (three term test) = 4.410e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.636
y[1] (closed_form) = 0.37362282626239680537538632600235
y[1] (numeric) = 0.37362282626239333586956163086992
absolute error = 3.46950582469513243e-15
relative error = 9.2861184617732231683652800000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.636
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.636
Order of pole (three term test) = 8.983e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.637
y[1] (closed_form) = 0.37316649308205296799836105276238
y[1] (numeric) = 0.37316649308204949845360758172969
absolute error = 3.46954475347103269e-15
relative error = 9.2975784744643158006486100000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.637
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.637
Order of pole (three term test) = 1.372e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.638
y[1] (closed_form) = 0.37271099542161813224084286355349
y[1] (numeric) = 0.37271099542161466265735042799199
absolute error = 3.46958349243556150e-15
relative error = 9.3090451718782786692059999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.638
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.638
Order of pole (three term test) = 4.659e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.639
y[1] (closed_form) = 0.37225633124261769163104483790284
y[1] (numeric) = 0.37225633124261422200900220863741
absolute error = 3.46962204262926543e-15
relative error = 9.3205185551778909391830300000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.639
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.639
Order of pole (three term test) = 9.490e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.64
y[1] (closed_form) = 0.37180249851279000594883997620464
y[1] (numeric) = 0.3718024985127865362884348898478
absolute error = 3.46966040508635684e-15
relative error = 9.3319986255202653568640000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.64
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.64
Order of pole (three term test) = 9.666e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.641
y[1] (closed_form) = 0.37134949520606369163732077280801
y[1] (numeric) = 0.37134949520606022193873993805179
absolute error = 3.46969858083475622e-15
relative error = 9.3434853840568791644698199999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.641
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.641
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.642
y[1] (closed_form) = 0.3708973193025350089979689662795
y[1] (numeric) = 0.37089731930253153926139807014518
absolute error = 3.46973657089613432e-15
relative error = 9.3549788319336050927484800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.642
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.642
Order of pole (three term test) = 5.013e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.643
y[1] (closed_form) = 0.37044596878844534569832584353326
y[1] (numeric) = 0.37044596878844187592394955757935
absolute error = 3.46977437628595391e-15
relative error = 9.3664789702907419963955899999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.643
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.643
Order of pole (three term test) = 5.105e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.644
y[1] (closed_form) = 0.36999544165615879612363175685676
y[1] (numeric) = 0.36999544165615532631163374334555
absolute error = 3.46981199801351121e-15
relative error = 9.3779858002630452336705599999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.644
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.644
Order of pole (three term test) = 1.040e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.645
y[1] (closed_form) = 0.36954573590413983610646612651398
y[1] (numeric) = 0.36954573590413636625702904453687
absolute error = 3.46984943708197711e-15
relative error = 9.3894993229797571090877500000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.645
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.645
Order of pole (three term test) = 5.295e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.646
y[1] (closed_form) = 0.36909684953693109257096625126047
y[1] (numeric) = 0.36909684953692762268427176282244
absolute error = 3.46988669448843803e-15
relative error = 9.4010195395646369696874799999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.646
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.646
Order of pole (three term test) = 5.392e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.647
y[1] (closed_form) = 0.36864878056513120763073483867376
y[1] (numeric) = 0.36864878056512773770696361473733
absolute error = 3.46992377122393643e-15
relative error = 9.4125464511359909754458700000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.647
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.647
Order of pole (three term test) = 1.647e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.648
y[1] (closed_form) = 0.36820152700537279668206239984919
y[1] (numeric) = 0.36820152700536932672139412633801
absolute error = 3.46996066827351118e-15
relative error = 9.4240800588067021078067199999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.648
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.648
Order of pole (three term test) = 5.592e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.649
y[1] (closed_form) = 0.36775508688030050003659163114459
y[1] (numeric) = 0.36775508688029703003920501490714
absolute error = 3.46999738661623745e-15
relative error = 9.4356203636842594902774500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.649
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.649
Order of pole (three term test) = 5.695e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.65
y[1] (closed_form) = 0.36730945821854912764003673094582
y[1] (numeric) = 0.36730945821854565760610950567935
absolute error = 3.47003392722526647e-15
relative error = 9.4471673668707879645750000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.65
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.65
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.651
y[1] (closed_form) = 0.3668646390547218964260413727928
y[1] (numeric) = 0.3668646390547184263557503049279
absolute error = 3.47007029106786490e-15
relative error = 9.4587210694630772122849000000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.651
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.651
Order of pole (three term test) = 5.906e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=361.9MB, alloc=44.3MB, time=2.88
x[1] = -1.652
y[1] (closed_form) = 0.36642062742936875985671487785002
y[1] (numeric) = 0.36642062742936528975023577239605
absolute error = 3.47010647910545397e-15
relative error = 9.4702814725526108513428800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.652
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.652
Order of pole (three term test) = 1.804e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.653
y[1] (closed_form) = 0.36597742138896482920382709909095
y[1] (numeric) = 0.36597742138896135906133480544269
absolute error = 3.47014249229364826e-15
relative error = 9.4818485772255951484583400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.653
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.653
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.654
y[1] (closed_form) = 0.36553501898588888612706874543995
y[1] (numeric) = 0.36553501898588541594873716314562
absolute error = 3.47017833158229433e-15
relative error = 9.4934223845629879152902800000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.654
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.654
Order of pole (three term test) = 6.237e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.655
y[1] (closed_form) = 0.3650934182784019861081954345068
y[1] (numeric) = 0.36509341827839851589419751899785
absolute error = 3.47021399791550895e-15
relative error = 9.5050028956405269017737500000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.655
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.655
Order of pole (three term test) = 1.905e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.656
y[1] (closed_form) = 0.36465261733062615230227076477864
y[1] (numeric) = 0.36465261733062268205277853306154
absolute error = 3.47024949223171710e-15
relative error = 9.5165901115287581451456000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.656
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.656
Order of pole (three term test) = 6.467e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.657
y[1] (closed_form) = 0.3642126142125231593696062388164
y[1] (numeric) = 0.3642126142125196890847907751267
absolute error = 3.47028481546368970e-15
relative error = 9.5281840332930641611152999999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.657
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.657
Order of pole (three term test) = 1.317e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.658
y[1] (closed_form) = 0.36377340699987340685436404405441
y[1] (numeric) = 0.36377340699986993653439550547336
absolute error = 3.47031996853858105e-15
relative error = 9.5397846619936919175322000000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.658
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.658
Order of pole (three term test) = 2.012e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.659
y[1] (closed_form) = 0.36333499377425488167814260244503
y[1] (numeric) = 0.36333499377425141132319022447898
absolute error = 3.47035495237796605e-15
relative error = 9.5513919986857807780600499999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.659
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.659
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.66
y[1] (closed_form) = 0.36289737262302220931920452895921
y[1] (numeric) = 0.36289737262301873892943663108219
absolute error = 3.47038976789787702e-15
relative error = 9.5630060444193899163120000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.66
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.66
Order of pole (three term test) = 1.390e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.661
y[1] (closed_form) = 0.36246054163928579325033228570155
y[1] (numeric) = 0.36246054163928232282591627686108
absolute error = 3.47042441600884047e-15
relative error = 9.5746268002395261583328699999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.661
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.661
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.662
y[1] (closed_form) = 0.36202449892189104221060847629681
y[1] (numeric) = 0.36202449892188757175171086038345
absolute error = 3.47045889761591336e-15
relative error = 9.5862542671861709831798399999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.662
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.662
Order of pole (three term test) = 7.208e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.663
y[1] (closed_form) = 0.36158924257539768488871548675879
y[1] (numeric) = 0.36158924257539421439550186803947
absolute error = 3.47049321361871932e-15
relative error = 9.5978884462943079710930799999998e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.663
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.663
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.664
y[1] (closed_form) = 0.36115477071005917159763313609468
y[1] (numeric) = 0.36115477071005570107026822461026
absolute error = 3.47052736491148442e-15
relative error = 9.6095293385939495646003199999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.664
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.664
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.665
y[1] (closed_form) = 0.36072108144180216252288324360396
y[1] (numeric) = 0.36072108144179869196153086053113
absolute error = 3.47056135238307283e-15
relative error = 9.6211769451101640761467500000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.665
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.665
Order of pole (three term test) = 7.609e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.666
y[1] (closed_form) = 0.36028817289220610212872664071631
y[1] (numeric) = 0.36028817289220263153354972369414
absolute error = 3.47059517691702217e-15
relative error = 9.6328312668631023860765200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.666
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.666
Order of pole (three term test) = 7.747e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.667
y[1] (closed_form) = 0.3598560431884828793089612431443
y[1] (numeric) = 0.35985604318847940868012185156574
absolute error = 3.47062883939157856e-15
relative error = 9.6444923048680243530198399999998e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.667
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.667
Order of pole (three term test) = 7.888e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.668
y[1] (closed_form) = 0.35942469046345657287119944332304
y[1] (numeric) = 0.35942469046345310220885876359159
absolute error = 3.47066234067973145e-15
relative error = 9.6561600601353251537448000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.668
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.668
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.669
y[1] (closed_form) = 0.35899411285554328194571937214802
y[1] (numeric) = 0.35899411285553981125003772289973
absolute error = 3.47069568164924829e-15
relative error = 9.6678345336705617159406899999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.669
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.669
Order of pole (three term test) = 1.635e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.67
y[1] (closed_form) = 0.35856430850873104091218760084621
y[1] (numeric) = 0.35856430850872757018332443813743
absolute error = 3.47072886316270878e-15
relative error = 9.6795157264744785165420000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.67
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.67
Order of pole (three term test) = 8.325e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.671
y[1] (closed_form) = 0.35813527557255981843974069573507
y[1] (numeric) = 0.35813527557255634767785461819606
absolute error = 3.47076188607753901e-15
relative error = 9.6912036395430336028214100000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.671
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.671
Order of pole (three term test) = 8.476e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.672
y[1] (closed_form) = 0.35770701220210160023808978732172
y[1] (numeric) = 0.35770701220209812944333854127641
absolute error = 3.47079475124604531e-15
relative error = 9.7028982738674243319110400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.672
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.672
Order of pole (three term test) = 1.726e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.673
y[1] (closed_form) = 0.35727951655794055511947605673456
y[1] (numeric) = 0.35727951655793708429201654128673
absolute error = 3.47082745951544783e-15
relative error = 9.7145996304341128793740699999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.673
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.673
Order of pole (three term test) = 8.785e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.674
y[1] (closed_form) = 0.35685278680615328397345586230621
y[1] (numeric) = 0.35685278680614981311344413439227
absolute error = 3.47086001172791394e-15
relative error = 9.7263077102248517641274400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.674
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.674
Order of pole (three term test) = 1.789e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.675
y[1] (closed_form) = 0.35642682111828915125863221207396
y[1] (numeric) = 0.35642682111828568036622349148261
absolute error = 3.47089240872059135e-15
relative error = 9.7380225142167091063437500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.675
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.675
Order of pole (three term test) = 1.821e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.676
y[1] (closed_form) = 0.35600161767135069861757451825861
y[1] (numeric) = 0.35600161767134722769292319261764
absolute error = 3.47092465132564097e-15
relative error = 9.7497440433820936693467200000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.676
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.676
Order of pole (three term test) = 1.854e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.677
y[1] (closed_form) = 0.35557717464777414022328113104832
y[1] (numeric) = 0.35557717464777066926654076077871
absolute error = 3.47095674037026961e-15
relative error = 9.7614722986887799620216900000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.677
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.677
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.678
y[1] (closed_form) = 0.35515349023540993946763912427673
y[1] (numeric) = 0.35515349023540646847896244751434
absolute error = 3.47098867667676239e-15
relative error = 9.7732072810999330333247600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.678
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.678
Order of pole (three term test) = 9.608e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.679
y[1] (closed_form) = 0.35473056262750346660442327727763
y[1] (numeric) = 0.35473056262749999558396221476271
absolute error = 3.47102046106251492e-15
relative error = 9.7849489915741331225917199999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.679
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.679
Order of pole (three term test) = 9.781e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.68
y[1] (closed_form) = 0.35430839002267573696145124716554
y[1] (numeric) = 0.35430839002267226590935690710027
absolute error = 3.47105209434006527e-15
relative error = 9.7966974310654002180479999999998e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.68
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.68
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.681
y[1] (closed_form) = 0.35388697062490422933857463529293
y[1] (numeric) = 0.35388697062490075825499731816724
absolute error = 3.47108357731712569e-15
relative error = 9.8084526005232184069000900000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.681
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.681
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.682
y[1] (closed_form) = 0.35346630264350378421023610135152
y[1] (numeric) = 0.35346630264350031309532530473733
absolute error = 3.47111491079661419e-15
relative error = 9.8202145008925603236695599999998e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.682
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.682
Order of pole (three term test) = 1.032e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.683
y[1] (closed_form) = 0.35304638429310758135336094862152
y[1] (numeric) = 0.35304638429310411020726537193583
absolute error = 3.47114609557668569e-15
relative error = 9.8319831331139108733824099999998e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.683
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.683
Order of pole (three term test) = 1.051e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.684
y[1] (closed_form) = 0.35262721379364819652337777376567
y[1] (numeric) = 0.35262721379364472534624532300246
absolute error = 3.47117713245076321e-15
relative error = 9.8437584981232915536577599999998e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.684
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.684
Order of pole (three term test) = 1.069e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.685
y[1] (closed_form) = 0.35220878937033873680317692328012
y[1] (numeric) = 0.35220878937033526559515471571147
absolute error = 3.47120802220756865e-15
relative error = 9.8555405968522841002962500000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.685
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.685
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.686
y[1] (closed_form) = 0.35179110925365405425181770466151
y[1] (numeric) = 0.35179110925365058301305207350808
absolute error = 3.47123876563115343e-15
relative error = 9.8673294302280542155042800000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.686
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.686
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.687
y[1] (closed_form) = 0.35137417167931203748178564137557
y[1] (numeric) = 0.3513741716793085662124221404467
absolute error = 3.47126936350092887e-15
relative error = 9.8791249991733750352250300000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.687
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.687
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.688
y[1] (closed_form) = 0.35095797488825498079557961411469
y[1] (numeric) = 0.35095797488825150949576302241827
absolute error = 3.47129981659169642e-15
relative error = 9.8909273046066506441484799999999e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.688
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.688
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.689
y[1] (closed_form) = 0.3505425171266310305143755733561
y[1] (numeric) = 0.35054251712662755918424989967853
absolute error = 3.47133012567367757e-15
relative error = 9.9027363474419391511679700000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.689
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.689
Order of pole (three term test) = 1.169e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.69
y[1] (closed_form) = 0.35012779664577570813346871608137
y[1] (numeric) = 0.35012779664577223677317720353766
absolute error = 3.47136029151254371e-15
relative error = 9.9145521285889760901310000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.69
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.69
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.691
y[1] (closed_form) = 0.3497138117021935099411396683524
y[1] (numeric) = 0.34971381170219003855082479890684
absolute error = 3.47139031486944556e-15
relative error = 9.9263746489531970593543600000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.691
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.691
Order of pole (three term test) = 1.211e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.692
y[1] (closed_form) = 0.34930056055753958273952238038551
y[1] (numeric) = 0.34930056055753611131932587934289
absolute error = 3.47142019650104262e-15
relative error = 9.9382039094357608792636800000002e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.692
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.692
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.693
y[1] (closed_form) = 0.3488880414786014753079721964142
y[1] (numeric) = 0.34888804147859800385803503688194
absolute error = 3.47144993715953226e-15
relative error = 9.9500399109335721806927400000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.693
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.693
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.694
y[1] (closed_form) = 0.34847625273728096525134198204929
y[1] (numeric) = 0.34847625273727749377180438937068
absolute error = 3.47147953759267861e-15
relative error = 9.9618826543393038756859600000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.694
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.694
Order of pole (three term test) = 1.277e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.695
y[1] (closed_form) = 0.34806519261057596087747235057126
y[1] (numeric) = 0.34806519261057248936847380672991
absolute error = 3.47150899854384135e-15
relative error = 9.9737321405414197945837500000001e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.695
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.695
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.696
y[1] (closed_form) = 0.347654859380562477750088999644
y[1] (numeric) = 0.3476548593805590062117682476398
absolute error = 3.47153832075200420e-15
relative error = 9.9855883704241969129472000000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.696
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.696
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.697
y[1] (closed_form) = 0.34724525133437668956517602382658
y[1] (numeric) = 0.34724525133437321799767107202335
absolute error = 3.47156750495180323e-15
relative error = 9.9974513448677475079830700000000e-13 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.697
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.697
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.698
y[1] (closed_form) = 0.34683636676419705300075887797048
y[1] (numeric) = 0.34683636676419358140420700441547
absolute error = 3.47159655187355501e-15
relative error = 1.0009321064748041299052040000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.698
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.698
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.699
y[1] (closed_form) = 0.34642820396722650619188450360822
y[1] (numeric) = 0.34642820396722303456642226032373
absolute error = 3.47162546224328449e-15
relative error = 1.0021197530936927252118490000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.699
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.699
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.7
y[1] (closed_form) = 0.34602076124567474048442906574395
y[1] (numeric) = 0.34602076124567126883019228299118
absolute error = 3.47165423678275277e-15
relative error = 1.0033080744302155505300000000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.7
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.7
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.701
y[1] (closed_form) = 0.34561403690674054512319585152559
y[1] (numeric) = 0.34561403690673707344031964204103
absolute error = 3.47168287620948456e-15
relative error = 1.0044970705707398835388560000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.701
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.701
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.702
y[1] (closed_form) = 0.34520802926259422453158722509358
y[1] (numeric) = 0.34520802926259075282020598829795
absolute error = 3.47171138123679563e-15
relative error = 1.0056867416012274528166520000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.702
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.702
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.703
y[1] (closed_form) = 0.34480273663036008784194518395053
y[1] (numeric) = 0.34480273663035661610219261013069
absolute error = 3.47173975257381984e-15
relative error = 1.0068770876072365464346560000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.703
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.703
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.704
y[1] (closed_form) = 0.34439815733209901033745509048028
y[1] (numeric) = 0.34439815733209553856946416494414
absolute error = 3.47176799092553614e-15
relative error = 1.0080681086739241544682240000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.704
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.704
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.705
y[1] (closed_form) = 0.34399428969479106646829662627601
y[1] (numeric) = 0.34399428969478759467219963348066
absolute error = 3.47179609699279535e-15
relative error = 1.0092598048860480902333750000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.705
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.705
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.706
y[1] (closed_form) = 0.34359113205031823410650500474843
y[1] (numeric) = 0.34359113205031476228243353240176
absolute error = 3.47182407147234667e-15
relative error = 1.0104521763279690752848120000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.706
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.706
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.707
y[1] (closed_form) = 0.34318868273544716970577404663042
y[1] (numeric) = 0.34318868273544369785385898976625
absolute error = 3.47185191505686417e-15
relative error = 1.0116452230836528604890330000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.707
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.707
Order of pole (three term test) = 1.607e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.708
y[1] (closed_form) = 0.34278694009181205403419094055252
y[1] (numeric) = 0.34278694009180858215456250557961
absolute error = 3.47187962843497291e-15
relative error = 1.0128389452366722811318240000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.708
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.708
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.709
y[1] (closed_form) = 0.34238590246589750814964044344452
y[1] (numeric) = 0.34238590246589403624242815216954
absolute error = 3.47190721229127498e-15
relative error = 1.0140333428702093299861380000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.709
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.709
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.71
y[1] (closed_form) = 0.34198556820902157928935398926165
y[1] (numeric) = 0.34198556820901810735468668288629
absolute error = 3.47193466730637536e-15
relative error = 1.0152284160670572190176000000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.71
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.71
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.711
y[1] (closed_form) = 0.34158593567731879634680673511821
y[1] (numeric) = 0.34158593567731532438481257821066
absolute error = 3.47196199415690755e-15
relative error = 1.0164241649096224147683550000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.711
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.711
Order of pole (three term test) = 1.723e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.712
y[1] (closed_form) = 0.34118700323172329461088304655428
y[1] (numeric) = 0.34118700323171982262168953099523
absolute error = 3.47198919351555905e-15
relative error = 1.0176205894799266704243200000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.712
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.712
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.713
y[1] (closed_form) = 0.34078876923795200944393837312212
y[1] (numeric) = 0.34078876923794853742767232202543
absolute error = 3.47201626605109669e-15
relative error = 1.0188176898596090543138610000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.713
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.713
Order of pole (three term test) = 1.785e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.714
y[1] (closed_form) = 0.34039123206648793857708295606638
y[1] (numeric) = 0.34039123206648446653387052767467
absolute error = 3.47204321242839171e-15
relative error = 1.0200154661299279452071160000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.714
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.714
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.715
y[1] (closed_form) = 0.33999439009256347270270040544331
y[1] (numeric) = 0.33999439009256000063266709699859
absolute error = 3.47207003330844472e-15
relative error = 1.0212139183717630321582000000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.715
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.715
Order of pole (three term test) = 1.848e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.716
y[1] (closed_form) = 0.33959824169614379404589194798985
y[1] (numeric) = 0.33959824169614032194916259957937
absolute error = 3.47209672934841048e-15
relative error = 1.0224130466656173010394880000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.716
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.716
Order of pole (three term test) = 1.881e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.717
y[1] (closed_form) = 0.33920278526191034259820514238207
y[1] (numeric) = 0.33920278526190687047490394075956
absolute error = 3.47212330120162251e-15
relative error = 1.0236128510916190103883390000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.717
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.717
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.718
y[1] (closed_form) = 0.33880801917924434969866414774198
y[1] (numeric) = 0.3388080191792408775489146301245
absolute error = 3.47214974951761748e-15
relative error = 1.0248133317295236415039520000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.718
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.718
Order of pole (three term test) = 1.948e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.719
y[1] (closed_form) = 0.33841394184221043864876727645475
y[1] (numeric) = 0.33841394184220696647269233429523
absolute error = 3.47217607494215952e-15
relative error = 1.0260144886587158637378720000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.719
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.719
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.72
y[1] (closed_form) = 0.33802055164954029204975662520281
y[1] (numeric) = 0.33802055164953681984747850793856
absolute error = 3.47220227811726425e-15
relative error = 1.0272163219582114557200000000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.72
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.72
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.721
y[1] (closed_form) = 0.33762784700461638555209411983965
y[1] (numeric) = 0.3376278470046129133237344386169
absolute error = 3.47222835968122275e-15
relative error = 1.0284188317066592471082750000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.721
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.721
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.722
y[1] (closed_form) = 0.33723582631545578770869839111532
y[1] (numeric) = 0.33723582631545231545437812249003
absolute error = 3.47225432026862529e-15
relative error = 1.0296220179823430274432360000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.722
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.722
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.723
y[1] (closed_form) = 0.33684448799469402562510757970835
y[1] (numeric) = 0.33684448799469055334494706932344
absolute error = 3.47228016051038491e-15
relative error = 1.0308258808631834483479390000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.723
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.723
Order of pole (three term test) = 4.251e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.724
y[1] (closed_form) = 0.33645383045956901610133451047313
y[1] (numeric) = 0.33645383045956554379545347671224
absolute error = 3.47230588103376089e-15
relative error = 1.0320304204267399306996640000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.724
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.724
Order of pole (three term test) = 8.651e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.725
y[1] (closed_form) = 0.33606385213190506196177273681999
y[1] (numeric) = 0.33606385213190158963029027443803
absolute error = 3.47233148246238196e-15
relative error = 1.0332356367502125319725000000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.725
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.725
Order of pole (three term test) = 4.401e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.726
y[1] (closed_form) = 0.33567455143809691327109479583603
y[1] (numeric) = 0.33567455143809344091412937956659
absolute error = 3.47235696541626944e-15
relative error = 1.0344415299104438298237440000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.726
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.726
Order of pole (three term test) = 4.479e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.727
y[1] (closed_form) = 0.33528592680909389313565769184474
y[1] (numeric) = 0.33528592680909042075332717998462
absolute error = 3.47238233051186012e-15
relative error = 1.0356480999839207651843480000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.727
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.727
Order of pole (three term test) = 2.279e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.728
y[1] (closed_form) = 0.3348979766803840877914951989026
y[1] (numeric) = 0.33489797668038061538391683687346
absolute error = 3.47240757836202914e-15
relative error = 1.0368553470467765219573760000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.728
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.728
Order of pole (three term test) = 2.318e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.729
y[1] (closed_form) = 0.33451069949197860068153209914496
y[1] (numeric) = 0.33451069949197512824882252303241
absolute error = 3.47243270957611255e-15
relative error = 1.0380632711747923477584550000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.729
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.729
Order of pole (three term test) = 7.077e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.73
y[1] (closed_form) = 0.33412409368839587022620201142705
y[1] (numeric) = 0.33412409368839239776847725149729
absolute error = 3.47245772475992976e-15
relative error = 1.0392718724433993778704000000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.73
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.73
Order of pole (three term test) = 9.601e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.731
y[1] (closed_form) = 0.3337381577186460509931880704628
y[1] (numeric) = 0.33373815771864257851056355465692
absolute error = 3.47248262451580588e-15
relative error = 1.0404811509276804622402680000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.731
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.731
Order of pole (three term test) = 2.442e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.732
y[1] (closed_form) = 0.33335289003621545797353444735424
y[1] (numeric) = 0.33335289003621198546612500476032
absolute error = 3.47250740944259392e-15
relative error = 1.0416911067023719863470080000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.732
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.732
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.733
y[1] (closed_form) = 0.33296828909905107367289661434514
y[1] (numeric) = 0.33296828909904760114081647864842
absolute error = 3.47253208013569672e-15
relative error = 1.0429017398418656466512080000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.733
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.733
Order of pole (three term test) = 2.528e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.734
y[1] (closed_form) = 0.33258435336954511772820940575158
y[1] (numeric) = 0.33258435336954164517157221866276
absolute error = 3.47255663718708882e-15
relative error = 1.0441130504202102432067920000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.734
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.734
Order of pole (three term test) = 5.145e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.735
y[1] (closed_form) = 0.33220108131451967876155436885947
y[1] (numeric) = 0.33220108131451620618047318352127
absolute error = 3.47258108118533820e-15
relative error = 1.0453250385111134683095000000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.735
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.735
Order of pole (three term test) = 2.617e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.736
y[1] (closed_form) = 0.33181847140521140818450168829238
y[1] (numeric) = 0.33181847140520793557908897266459
absolute error = 3.47260541271562779e-15
relative error = 1.0465377041879436608211840000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.736
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.736
Order of pole (three term test) = 7.989e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.737
y[1] (closed_form) = 0.33143652211725627566768715971827
y[1] (numeric) = 0.33143652211725280303805479994136
absolute error = 3.47262963235977691e-15
relative error = 1.0477510475237315739767790000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.737
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.737
Order of pole (three term test) = 5.419e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.738
y[1] (closed_form) = 0.33105523193067438599186133817822
y[1] (numeric) = 0.33105523193067091333812064191575
absolute error = 3.47265374069626247e-15
relative error = 1.0489650685911721052430680000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.738
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.738
Order of pole (three term test) = 1.378e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.739
y[1] (closed_form) = 0.33067459932985485699811614680762
y[1] (numeric) = 0.33067459932985138432037784656748
absolute error = 3.47267773830024014e-15
relative error = 1.0501797674626260512416940000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.739
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.739
Order of pole (three term test) = 8.414e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.74
y[1] (closed_form) = 0.33029462280354075835645395692958
y[1] (numeric) = 0.3302946228035372856548282133643
absolute error = 3.47270162574356528e-15
relative error = 1.0513951442101218241728000000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.74
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.74
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.741
y[1] (closed_form) = 0.3299153008448141108733154937133
y[1] (numeric) = 0.32991530084481063814791189889953
absolute error = 3.47272540359481377e-15
relative error = 1.0526111989053571716785370000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.741
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.741
Order of pole (three term test) = 5.806e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.742
y[1] (closed_form) = 0.32953663195108094606012593571927
y[1] (numeric) = 0.3295366319510774733110535164166
absolute error = 3.47274907241930267e-15
relative error = 1.0538279316197008787485880000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.742
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.742
Order of pole (three term test) = 5.907e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.743
y[1] (closed_form) = 0.32915861462405642568635331424871
y[1] (numeric) = 0.32915861462405295291372053513795
absolute error = 3.47277263277911076e-15
relative error = 1.0550453424241944665307240000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.743
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.743
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.744
y[1] (closed_form) = 0.328781247369750021041999831664
y[1] (numeric) = 0.32878124736974654824591459856502
absolute error = 3.47279608523309898e-15
relative error = 1.0562634313895538939233280000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.744
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.744
Order of pole (three term test) = 3.057e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.745
y[1] (closed_form) = 0.32840452869845075163586505857916
y[1] (numeric) = 0.32840452869844727881643472164857
absolute error = 3.47281943033693059e-15
relative error = 1.0574821985861712069814750000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.745
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.745
Order of pole (three term test) = 3.110e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.746
y[1] (closed_form) = 0.3280284571247124830573301895086
y[1] (numeric) = 0.32802845712470901021466154641724
absolute error = 3.47284266864309136e-15
relative error = 1.0587016440841162300421760000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.746
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.746
Order of pole (three term test) = 6.328e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.747
y[1] (closed_form) = 0.32765303116733928373081468632629
y[1] (numeric) = 0.32765303116733581086501398541675
absolute error = 3.47286580070090954e-15
relative error = 1.0599217679531382224265860000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.747
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.747
Order of pole (three term test) = 9.656e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.748
y[1] (closed_form) = 0.32727824934937084029345076949662
y[1] (numeric) = 0.32727824934936736740462371292099
absolute error = 3.47288882705657563e-15
relative error = 1.0611425702626675063767520000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.748
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.748
Order of pole (three term test) = 3.274e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.749
y[1] (closed_form) = 0.32690411019806793132790737891226
y[1] (numeric) = 0.32690411019806445841615912575008
absolute error = 3.47291174825316218e-15
relative error = 1.0623640510818171361782180000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.749
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.749
Order of pole (three term test) = 6.662e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.75
y[1] (closed_form) = 0.32653061224489795918367346938775
y[1] (numeric) = 0.32653061224489448624910863874444
absolute error = 3.47293456483064331e-15
relative error = 1.0635862104793845136875000000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.75
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.75
Order of pole (three term test) = 1.017e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.751
y[1] (closed_form) = 0.32615775402552053962148088014322
y[1] (numeric) = 0.3261577540255170666642035542291
absolute error = 3.47295727732591412e-15
relative error = 1.0648090485238530017834120000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.751
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.751
Order of pole (three term test) = 6.894e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.752
y[1] (closed_form) = 0.32578553407977314901690957236088
y[1] (numeric) = 0.32578553407976967603702329955085
absolute error = 3.47297988627281003e-15
relative error = 1.0660325652833935478325120000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.752
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.752
Order of pole (three term test) = 7.014e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.753
y[1] (closed_form) = 0.3254139509516568288605728131613
y[1] (numeric) = 0.32541395095165335585818061103537
absolute error = 3.47300239220212593e-15
relative error = 1.0672567608258662802023370000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.753
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.753
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.754
y[1] (closed_form) = 0.32504300318932194729362694684507
y[1] (numeric) = 0.32504300318931847426883130520982
absolute error = 3.47302479564163525e-15
relative error = 1.0684816352188221112789000000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.754
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.754
Order of pole (three term test) = 3.629e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.755
y[1] (closed_form) = 0.32467268934505401741868978336215
y[1] (numeric) = 0.32467268934505054437159266725333
absolute error = 3.47304709711610882e-15
relative error = 1.0697071885295043068320500000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.755
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.755
Order of pole (three term test) = 7.383e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.756
y[1] (closed_form) = 0.32430300797525957212758339776153
y[1] (numeric) = 0.32430300797525609905828625042785
absolute error = 3.47306929714733368e-15
relative error = 1.0709334208248500706292480000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.756
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.756
Order of pole (three term test) = 7.510e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.757
y[1] (closed_form) = 0.32393395764045209518864132056213
y[1] (numeric) = 0.32393395764044862209724506643039
absolute error = 3.47309139625413174e-15
relative error = 1.0721603321714921133835260000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.757
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.757
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.758
y[1] (closed_form) = 0.32356553690523800833763675497418
y[1] (numeric) = 0.32356553690523453522424180259591
absolute error = 3.47311339495237827e-15
relative error = 1.0733879226357601995644280000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.758
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.758
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.759
y[1] (closed_form) = 0.3231977443383027141176976297647
y[1] (numeric) = 0.32319774433829924098240387474439
absolute error = 3.47313529375502031e-15
relative error = 1.0746161922836826995785110000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.759
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.759
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.76
y[1] (closed_form) = 0.32283057851239669421487603305785
y[1] (numeric) = 0.32283057851239322105778286096286
absolute error = 3.47315709317209499e-15
relative error = 1.0758451411809881441024000000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.76
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.76
Order of pole (three term test) = 1.608e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.761
y[1] (closed_form) = 0.32246403800432166303733391892802
y[1] (numeric) = 0.32246403800431818985854020818041
absolute error = 3.47317879371074761e-15
relative error = 1.0770747693931067339070810000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.761
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.761
Order of pole (three term test) = 8.179e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.762
y[1] (closed_form) = 0.32209812139491677628739398140334
y[1] (numeric) = 0.32209812139491330308699810615363
absolute error = 3.47320039587524971e-15
relative error = 1.0783050769851718760653240000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.762
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.762
Order of pole (three term test) = 8.319e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.763
y[1] (closed_form) = 0.3217328272690448942769842952555
y[1] (numeric) = 0.32173282726904142105508412823856
absolute error = 3.47322190016701694e-15
relative error = 1.0795360640220216875382860000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.763
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.763
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.764
y[1] (closed_form) = 0.32136815421557889973827777520683
y[1] (numeric) = 0.32136815421557542649497069057996
absolute error = 3.47324330708462687e-15
relative error = 1.0807677305682005092871520000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.764
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.764
Order of pole (three term test) = 8.607e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.765
y[1] (closed_form) = 0.32100410082738806988259275012239
y[1] (numeric) = 0.32100410082738459661797562628574
absolute error = 3.47326461712383665e-15
relative error = 1.0820000766879604027996250000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.765
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.765
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.766
y[1] (closed_form) = 0.32064066570132450246187903125477
y[1] (numeric) = 0.32064066570132102917604825365427
absolute error = 3.47328583077760050e-15
relative error = 1.0832331024452626224978000000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.766
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.766
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.767
y[1] (closed_form) = 0.32027784743820959558836481824713
y[1] (numeric) = 0.3202778474382061222814162821599
absolute error = 3.47330694853608723e-15
relative error = 1.0844668079037791261269470000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.767
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.767
Order of pole (three term test) = 9.058e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.768
y[1] (closed_form) = 0.31991564464282058106918367764788
y[1] (numeric) = 0.31991564464281710774121279095044
absolute error = 3.47332797088669744e-15
relative error = 1.0857011931268940138690560000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.768
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.768
Order of pole (three term test) = 1.382e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.769
y[1] (closed_form) = 0.31955405592387711101403769012268
y[1] (numeric) = 0.3195540559238736376651393760419
absolute error = 3.47334889831408078e-15
relative error = 1.0869362581777050143781580000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.769
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.769
Order of pole (three term test) = 9.370e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.77
y[1] (closed_form) = 0.31919307989402789747518273803824
y[1] (numeric) = 0.31919307989402442410545143788527
absolute error = 3.47336973130015297e-15
relative error = 1.0881720031190249239713000000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
memory used=405.7MB, alloc=44.3MB, time=3.22
Radius of convergence (given) for eq 1 = 1.77
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.77
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.771
y[1] (closed_form) = 0.31883271516983740488024483801863
y[1] (numeric) = 0.31883271516983393148977451390584
absolute error = 3.47339047032411279e-15
relative error = 1.0894084280133830643180390000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.771
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.771
Order of pole (three term test) = 4.847e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.772
y[1] (closed_form) = 0.31847296037177259501959245652207
y[1] (numeric) = 0.31847296037176912160847659406317
absolute error = 3.47341111586245890e-15
relative error = 1.0906455329230267146657600000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.772
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.772
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.773
y[1] (closed_form) = 0.31811381412418972435119892324836
y[1] (numeric) = 0.31811381412418625091953053424178
absolute error = 3.47343166838900658e-15
relative error = 1.0918833179099225465420820000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.773
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.773
Order of pole (three term test) = 5.014e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.774
y[1] (closed_form) = 0.3177552750553211933871314197687
y[1] (numeric) = 0.31775527505531771993500304486437
absolute error = 3.47345212837490433e-15
relative error = 1.0931217830357580419239080000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.774
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.774
Order of pole (three term test) = 5.099e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.775
y[1] (closed_form) = 0.31739734179726244792699861138663
y[1] (numeric) = 0.31739734179725897445450232273626
absolute error = 3.47347249628865037e-15
relative error = 1.0943609283619429071981250000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.775
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.775
Order of pole (three term test) = 5.186e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.776
y[1] (closed_form) = 0.3170400129859589319048778508238
y[1] (numeric) = 0.31704001298595545841210525471474
absolute error = 3.47349277259610906e-15
relative error = 1.0956007539496104890434560000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.776
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.776
Order of pole (three term test) = 5.274e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.777
y[1] (closed_form) = 0.31668328726119309161742505452495
y[1] (numeric) = 0.31668328726118961810446729399783
absolute error = 3.47351295776052712e-15
relative error = 1.0968412598596191542110480000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.777
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.777
Order of pole (three term test) = 5.364e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.778
y[1] (closed_form) = 0.31632716326657143110204587756114
y[1] (numeric) = 0.31632716326656795756899363501128
absolute error = 3.47353305224254986e-15
relative error = 1.0980824461525536991620240000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.778
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.778
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.779
y[1] (closed_form) = 0.31597163964951161843517573236696
y[1] (numeric) = 0.31597163964950814488211923212974
absolute error = 3.47355305650023722e-15
relative error = 1.0993243128887267263582020000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.779
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.779
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.78
y[1] (closed_form) = 0.31561671506122964272187855068804
y[1] (numeric) = 0.31561671506122616914890756160833
absolute error = 3.47357297098907971e-15
relative error = 1.1005668601281800153164000000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.78
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.78
Order of pole (three term test) = 5.643e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.781
y[1] (closed_form) = 0.31526238815672702154913001767676
y[1] (numeric) = 0.31526238815672354795633385566249
absolute error = 3.47359279616201427e-15
relative error = 1.1018100879306858945883470000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.781
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.781
Order of pole (three term test) = 5.739e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.782
y[1] (closed_form) = 0.3149086575947780586763003523198
y[1] (numeric) = 0.31490865759477458506376788287982
absolute error = 3.47361253246943998e-15
relative error = 1.1030539963557485923049520000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.782
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.782
Order of pole (three term test) = 1.167e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.783
y[1] (closed_form) = 0.31455552203791715173749460930474
y[1] (numeric) = 0.314555522037913678105314250071
absolute error = 3.47363218035923374e-15
relative error = 1.1042985854626056031262860000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.783
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.783
Order of pole (three term test) = 1.187e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.784
y[1] (closed_form) = 0.31420298015242614973154497375777
y[1] (numeric) = 0.31420298015242267607980469699201
absolute error = 3.47365174027676576e-15
relative error = 1.1055438553102290206658560000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.784
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.784
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.785
y[1] (closed_form) = 0.31385103060832176007657965146843
y[1] (numeric) = 0.31385103060831828640536698655343
absolute error = 3.47367121266491500e-15
relative error = 1.1067898059573268795875000000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.785
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.785
Order of pole (three term test) = 6.138e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.786
y[1] (closed_form) = 0.31349967207934300500721676245127
y[1] (numeric) = 0.31349967207933953131661879836677
absolute error = 3.47369059796408450e-15
relative error = 1.1080364374623444881762000000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.786
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.786
Order of pole (three term test) = 6.242e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.787
y[1] (closed_form) = 0.31314890324293872709354916390809
y[1] (numeric) = 0.31314890324293525338365255169153
absolute error = 3.47370989661221656e-15
relative error = 1.1092837498834657383990640000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.787
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.787
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.788
y[1] (closed_form) = 0.31279872278025514366219739851558
y[1] (numeric) = 0.31279872278025166993308835370769
absolute error = 3.47372910904480789e-15
relative error = 1.1105317432786144315088160000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.788
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.788
Order of pole (three term test) = 6.455e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.789
y[1] (closed_form) = 0.31244912937612344990081302387955
y[1] (numeric) = 0.31244912937611997615257732895492
absolute error = 3.47374823569492463e-15
relative error = 1.1117804177054555871732230000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.789
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.789
Order of pole (three term test) = 6.564e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.79
y[1] (closed_form) = 0.31210012171904747042851346712025
y[1] (numeric) = 0.31210012171904399666123647390303
absolute error = 3.47376727699321722e-15
relative error = 1.1130297732213967294602000000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.79
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.79
Order of pole (three term test) = 6.675e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.791
y[1] (closed_form) = 0.31175169850119135911582230277886
y[1] (numeric) = 0.31175169850118788532958893484359
absolute error = 3.47378623336793527e-15
relative error = 1.1142798098835891974808870000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.791
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.791
Order of pole (three term test) = 1.358e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.792
y[1] (closed_form) = 0.31140385841836734693877551020408
y[1] (numeric) = 0.31140385841836387313367026526185
absolute error = 3.47380510524494223e-15
relative error = 1.1155305277489294165278720000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.792
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.792
Order of pole (three term test) = 2.071e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.793
y[1] (closed_form) = 0.31105660017002353765293486568109
y[1] (numeric) = 0.31105660017002006382904181795107
absolute error = 3.47382389304773002e-15
relative error = 1.1167819268740601807066980000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.793
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.793
Order of pole (three term test) = 7.019e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.794
y[1] (closed_form) = 0.31070992245923175107412420194157
y[1] (numeric) = 0.31070992245922827723152700450799
absolute error = 3.47384259719743358e-15
relative error = 1.1180340073153719341480880000000e-12 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.794
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.794
Order of pole (three term test) = 7.138e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.795
y[1] (closed_form) = 0.31036382399267541375377286023541
y[1] (numeric) = 0.3103638239926719398925547473902
absolute error = 3.47386121811284521e-15
relative error = 1.1192867691290040087750250000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.795
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.795
Order of pole (three term test) = 7.258e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.796
y[1] (closed_form) = 0.3100183034806374968378133044975
y[1] (numeric) = 0.31001830348063402295805709406849
absolute error = 3.47387975621042901e-15
relative error = 1.1205402123708459181520160000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.796
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.796
Order of pole (three term test) = 7.380e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.797
y[1] (closed_form) = 0.309673359636988500899136599706
y[1] (numeric) = 0.30967335963698502700092469537098
absolute error = 3.47389821190433502e-15
relative error = 1.1217943370965385785599180000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.797
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.797
Order of pole (three term test) = 7.505e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.798
y[1] (closed_form) = 0.30932899117917448753466031346162
y[1] (numeric) = 0.30932899117917101361807470704824
absolute error = 3.47391658560641338e-15
relative error = 1.1230491433614755600517520000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.798
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.798
Order of pole (three term test) = 7.631e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.799
y[1] (closed_form) = 0.30898519682820515751910841703485
y[1] (numeric) = 0.30898519682820168358423069080643
absolute error = 3.47393487772622842e-15
relative error = 1.1243046312208043384716420000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.799
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.799
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.8
y[1] (closed_form) = 0.30864197530864197530864197530864
y[1] (numeric) = 0.30864197530863850135555330423614
absolute error = 3.47395308867107250e-15
relative error = 1.1255608007294274900000000000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.8
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.8
Order of pole (three term test) = 7.890e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.801
y[1] (closed_form) = 0.30829932534858633968851285962731
y[1] (numeric) = 0.30829932534858286571729401364732
absolute error = 3.47397121884597999e-15
relative error = 1.1268176519420039541543990000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.801
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.801
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.802
y[1] (closed_form) = 0.30795724567966780035994042875039
y[1] (numeric) = 0.30795724567966432637067177500946
absolute error = 3.47398926865374093e-15
relative error = 1.1280751849129502162859720000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.802
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.802
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.803
y[1] (closed_form) = 0.30761573503703232026243313587479
y[1] (numeric) = 0.30761573503702884625519464096001
absolute error = 3.47400723849491478e-15
relative error = 1.1293333996964415421057020000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.803
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.803
Order of pole (three term test) = 8.294e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.804
y[1] (closed_form) = 0.30727479215933058342879336876416
y[1] (numeric) = 0.30727479215932710940366460092022
absolute error = 3.47402512876784394e-15
relative error = 1.1305922963464131603839040000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.804
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.804
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.805
y[1] (closed_form) = 0.30693441578870634817105454991905
y[1] (numeric) = 0.30693441578870287412811468125176
absolute error = 3.47404293986866729e-15
relative error = 1.1318518749165614747502250000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.805
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.805
Order of pole (three term test) = 1.715e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.806
y[1] (closed_form) = 0.30659460467078484539660464871003
y[1] (numeric) = 0.3065946046707813713359324573765
absolute error = 3.47406067219133353e-15
relative error = 1.1331121354603452329455080000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.806
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.806
Order of pole (three term test) = 8.718e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.807
y[1] (closed_form) = 0.30625535755466122185474982152969
y[1] (numeric) = 0.30625535755465774777642369391511
absolute error = 3.47407832612761458e-15
relative error = 1.1343730780309867379730420000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.807
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.807
Order of pole (three term test) = 8.864e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.808
y[1] (closed_form) = 0.30591667319288902811496593311928
y[1] (numeric) = 0.30591667319288555401906386600056
absolute error = 3.47409590206711872e-15
relative error = 1.1356347026814729967534080000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.808
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.808
Order of pole (three term test) = 2.704e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.809
y[1] (closed_form) = 0.30557855034146875107907425589331
y[1] (numeric) = 0.30557855034146527696567385858956
absolute error = 3.47411340039730375e-15
relative error = 1.1368970094645568973103750000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.809
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.809
Order of pole (three term test) = 9.163e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.81
y[1] (closed_form) = 0.30524098775983639083056072769451
y[1] (numeric) = 0.30524098775983291669973922420442
absolute error = 3.47413082150349009e-15
relative error = 1.1381599984327583883849000000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.81
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.81
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.811
y[1] (closed_form) = 0.30490398421085208162523580511879
y[1] (numeric) = 0.30490398421084860747707003624511
absolute error = 3.47414816576887368e-15
relative error = 1.1394236696383656154643280000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.811
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.811
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.812
y[1] (closed_form) = 0.30456753846078875682840421229088
y[1] (numeric) = 0.30456753846078528266297063775202
absolute error = 3.47416543357453886e-15
relative error = 1.1406880231334360718747840000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.812
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.812
Order of pole (three term test) = 9.630e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.813
y[1] (closed_form) = 0.30423164927932085760468078646315
y[1] (numeric) = 0.30423164927931738342205548699193
absolute error = 3.47418262529947122e-15
relative error = 1.1419530589697977616532180000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.813
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.813
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.814
y[1] (closed_form) = 0.30389631543951308516755019455442
y[1] (numeric) = 0.30389631543950961096780887398418
absolute error = 3.47419974132057024e-15
relative error = 1.1432187771990503149463040000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.814
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.814
Order of pole (three term test) = 9.954e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.815
y[1] (closed_form) = 0.3035615357178091963967245710296
y[1] (numeric) = 0.30356153571780572217994255836764
absolute error = 3.47421678201266196e-15
relative error = 1.1444851778725661345181000000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.815
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.815
Order of pole (three term test) = 1.012e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.816
y[1] (closed_form) = 0.30322730889402084263230413941664
y[1] (numeric) = 0.30322730889401736839855639090513
absolute error = 3.47423374774851151e-15
relative error = 1.1457522610414915174322560000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.816
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.816
Order of pole (three term test) = 1.029e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.817
y[1] (closed_form) = 0.30289363375131645145569165912714
y[1] (numeric) = 0.3028936337513129772050527602916
absolute error = 3.47425063889883554e-15
relative error = 1.1470200267567477648119060000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.817
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.817
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.818
y[1] (closed_form) = 0.30256050907621015126815211774203
y[1] (numeric) = 0.30256050907620667700069628542739
absolute error = 3.47426745583231464e-15
relative error = 1.1482884750690323092215360000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.818
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.818
Order of pole (three term test) = 1.063e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.819
y[1] (closed_form) = 0.3022279336585507384788444979858
y[1] (numeric) = 0.30222793365854726419464558238021
absolute error = 3.47428419891560559e-15
relative error = 1.1495576060288198067573990000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.819
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.819
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.82
y[1] (closed_form) = 0.30189590629151068711508271947832
y[1] (numeric) = 0.3018959062915072128142142061247
absolute error = 3.47430086851335362e-15
relative error = 1.1508274196863632530888000000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.82
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.82
Order of pole (three term test) = 1.099e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.821
y[1] (closed_form) = 0.30156442577157520066850801905043
y[1] (numeric) = 0.30156442577157172635104303084591
absolute error = 3.47431746498820452e-15
relative error = 1.1520979160916950704705320000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.821
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.821
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.822
y[1] (closed_form) = 0.30123349089853130599177512076451
y[1] (numeric) = 0.30123349089852783165778641994785
absolute error = 3.47433398870081666e-15
relative error = 1.1533690952946281853135440000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.822
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.822
Order of pole (three term test) = 1.136e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.823
y[1] (closed_form) = 0.30090310047545698906126958841571
y[1] (numeric) = 0.3009031004754535147108295785427
absolute error = 3.47435044000987301e-15
relative error = 1.1546409573447571260450290000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.823
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.823
Order of pole (three term test) = 1.155e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.824
y[1] (closed_form) = 0.3005732533087103724222837796245
y[1] (numeric) = 0.30057325330870689805546450753145
absolute error = 3.47436681927209305e-15
relative error = 1.1559135022914591047116800000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.824
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.824
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.825
y[1] (closed_form) = 0.30024394820791893413398386188779
y[1] (numeric) = 0.30024394820791545975085701964327
absolute error = 3.47438312684224452e-15
relative error = 1.1571867301838950654425000000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.825
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.825
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.826
y[1] (closed_form) = 0.29991518398596876803240043715637
y[1] (numeric) = 0.29991518398596529363303736400117
absolute error = 3.47439936307315520e-15
relative error = 1.1584606410710107627635200000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.826
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.826
Order of pole (three term test) = 1.213e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.827
y[1] (closed_form) = 0.29958695945899388513057048247581
y[1] (numeric) = 0.2995869594589904107150421667512
absolute error = 3.47441552831572461e-15
relative error = 1.1597352350015378331732690000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.827
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.827
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.828
y[1] (closed_form) = 0.29925927344636555597584857959578
y[1] (numeric) = 0.29925927344636208154422566066027
absolute error = 3.47443162291893551e-15
relative error = 1.1610105120239948197247840000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.828
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.828
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.829
y[1] (closed_form) = 0.29893212477068169378529080565496
y[1] (numeric) = 0.29893212477067821933764357578946
absolute error = 3.47444764722986550e-15
relative error = 1.1622864721866882495085500000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.829
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.829
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.83
y[1] (closed_form) = 0.29860551225775627818089521932575
y[1] (numeric) = 0.29860551225775280371729362562738
absolute error = 3.47446360159369837e-15
relative error = 1.1635631155377136471293000000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.83
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.83
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.831
y[1] (closed_form) = 0.2982794347366088193473586312076
y[1] (numeric) = 0.29827943473660534486787227747208
absolute error = 3.47447948635373552e-15
relative error = 1.1648404421249565908666720000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.831
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.831
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.832
y[1] (closed_form) = 0.29795389103945386243588032264831
y[1] (numeric) = 0.29795389103945038794057847124106
absolute error = 3.47449530185140725e-15
relative error = 1.1661184519960937446224000000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.832
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.832
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.833
y[1] (closed_form) = 0.29762888000169053203840960222198
y[1] (numeric) = 0.29762888000168705752736117593807
absolute error = 3.47451104842628391e-15
relative error = 1.1673971451985938620085990000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.833
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.833
Order of pole (three term test) = 1.361e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.834
y[1] (closed_form) = 0.29730440046189211655759559228388
y[1] (numeric) = 0.29730440046188864203086917619677
absolute error = 3.47452672641608711e-15
relative error = 1.1686765217797188295363160000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.834
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.834
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.835
y[1] (closed_form) = 0.29698045126179569229855444765348
y[1] (numeric) = 0.29698045126179221775621829095275
absolute error = 3.47454233615670073e-15
relative error = 1.1699565817865246615574250000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.835
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.835
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.836
y[1] (closed_form) = 0.29665703124629178710942135266113
y[1] (numeric) = 0.29665703124628831255154337047916
absolute error = 3.47455787798218197e-15
relative error = 1.1712373252658625273945120000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.836
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.836
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.837
y[1] (closed_form) = 0.29633413926341408339850214945968
y[1] (numeric) = 0.29633413926341060882514992468746
absolute error = 3.47457335222477222e-15
relative error = 1.1725187522643797365673180000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.837
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.837
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.838
y[1] (closed_form) = 0.29601177416432916035668234739705
y[1] (numeric) = 0.29601177416432568576792313248913
absolute error = 3.47458875921490792e-15
relative error = 1.1738008628285207391292480000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.838
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.838
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.839
y[1] (closed_form) = 0.29568993480332627521458957793514
y[1] (numeric) = 0.29568993480332280061049029670377
absolute error = 3.47460409928123137e-15
relative error = 1.1750836570045281276061770000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.839
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.839
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.84
y[1] (closed_form) = 0.2953686200378071833648393194707
y[1] (numeric) = 0.29536862003780370874546656886926
absolute error = 3.47461937275060144e-15
relative error = 1.1763671348384436235264000000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.84
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.84
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.841
y[1] (closed_form) = 0.2950478287282759971805229486726
y[1] (numeric) = 0.29504782872827252254594300056845
absolute error = 3.47463457994810415e-15
relative error = 1.1776512963761090381616150000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.841
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.841
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.842
y[1] (closed_form) = 0.29472755973832908336192190662795
y[1] (numeric) = 0.29472755973832560871220070956465
absolute error = 3.47464972119706330e-15
relative error = 1.1789361416631672682621200000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.842
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.842
Order of pole (three term test) = 1.576e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.843
y[1] (closed_form) = 0.29440781193464499864425202604096
y[1] (numeric) = 0.29440781193464152397945520698998
absolute error = 3.47466479681905098e-15
relative error = 1.1802216707450632692166020000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.843
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.843
Order of pole (three term test) = 1.602e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.844
y[1] (closed_form) = 0.29408858418697446370005787663337
y[1] (numeric) = 0.29408858418697098902025074273542
absolute error = 3.47467980713389795e-15
relative error = 1.1815078836670450019711200000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.844
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.844
Order of pole (three term test) = 3.256e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.845
y[1] (closed_form) = 0.29376987536813037507068837626046
y[1] (numeric) = 0.29376987536812690037593591655641
absolute error = 3.47469475245970405e-15
relative error = 1.1827947804741644078801250000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.845
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.845
Order of pole (three term test) = 1.655e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.846
y[1] (closed_form) = 0.29345168435397785496209191141515
y[1] (numeric) = 0.29345168435397438025245879856668
absolute error = 3.47470963311284847e-15
relative error = 1.1840823612112783536794520000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.846
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.846
Order of pole (three term test) = 1.682e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.847
y[1] (closed_form) = 0.29313401002342433874097183890879
y[1] (numeric) = 0.29313401002342086401652243090877
absolute error = 3.47472444940800002e-15
relative error = 1.1853706259230495940228180000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.847
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.847
Order of pole (three term test) = 1.710e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.848
y[1] (closed_form) = 0.29281685125840969996814152658308
y[1] (numeric) = 0.29281685125840622522893986845582
absolute error = 3.47473920165812726e-15
relative error = 1.1866595746539477038135040000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.848
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.848
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.849
y[1] (closed_form) = 0.29250020694389641280671206074878
y[1] (numeric) = 0.29250020694389293805282188624016
absolute error = 3.47475389017450862e-15
relative error = 1.1879492074482500244564620000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.849
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.849
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.85
y[1] (closed_form) = 0.29218407596785975164353542731921
y[1] (numeric) = 0.29218407596785627687502016057678
absolute error = 3.47476851526674243e-15
relative error = 1.1892395243500425966675000000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.85
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.85
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.851
y[1] (closed_form) = 0.29186845722127802776311138780241
y[1] (numeric) = 0.29186845722127455298003414504554
absolute error = 3.47478307724275687e-15
relative error = 1.1905305254032210830750870000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.851
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.851
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.852
y[1] (closed_form) = 0.29155334959812286291394744575942
y[1] (numeric) = 0.29155334959811938811637103693951
absolute error = 3.47479757640881991e-15
relative error = 1.1918222106514917044588640000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.852
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.852
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.853
y[1] (closed_form) = 0.29123875199534949960813825919026
y[1] (numeric) = 0.29123875199534602479612518964113
absolute error = 3.47481201306954913e-15
relative error = 1.1931145801383721518710170000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.853
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.853
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.854
y[1] (closed_form) = 0.2909246633128871479957036245722
y[1] (numeric) = 0.2909246633128836731693160966507
absolute error = 3.47482638752792150e-15
relative error = 1.1944076339071925018694000000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.854
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.854
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.855
y[1] (closed_form) = 0.29061108245362936915599276378405
y[1] (numeric) = 0.29061108245362589431529267850095
absolute error = 3.47484070008528310e-15
relative error = 1.1957013720010961279177500000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.855
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.855
Order of pole (three term test) = 1.946e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.856
y[1] (closed_form) = 0.29029800832342449464922711058264
y[1] (numeric) = 0.29029800832342101979427606922388
absolute error = 3.47485495104135876e-15
relative error = 1.1969957944630406009487360000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.856
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.856
Order of pole (three term test) = 1.978e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.857
y[1] (closed_form) = 0.28998543983106608217201414316987
y[1] (numeric) = 0.2899854398310626073028734489082
absolute error = 3.47486914069426167e-15
relative error = 1.1982909013357985961649830000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.857
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.857
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.858
y[1] (closed_form) = 0.2896733758882834071614210680605
y[1] (numeric) = 0.28967337588827993227815172755761
absolute error = 3.47488326934050289e-15
relative error = 1.1995866926619587818753960000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.858
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.858
Order of pole (three term test) = 2.043e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.859
y[1] (closed_form) = 0.28936181540973199019294935213336
y[1] (numeric) = 0.28936181540972851529561207713256
absolute error = 3.47489733727500080e-15
relative error = 1.2008831684839267039704800000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.859
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.859
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.86
y[1] (closed_form) = 0.28905075731298416001849924846803
y[1] (numeric) = 0.28905075731298068510715445737747
absolute error = 3.47491134479109056e-15
relative error = 1.2021803288439256901376000000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.86
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.86
Order of pole (three term test) = 8.440e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.861
y[1] (closed_form) = 0.2887402005185196520911575912253
y[1] (numeric) = 0.28874020051851617716586541069191
absolute error = 3.47492529218053339e-15
relative error = 1.2034781737839977080788190000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.861
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.861
Order of pole (three term test) = 1.072e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.862
y[1] (closed_form) = 0.2884301439497162424243822691607
y[1] (numeric) = 0.2884301439497127674852025356348
absolute error = 3.47493917973352590e-15
relative error = 1.2047767033460042570439600000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.862
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.862
Order of pole (three term test) = 1.090e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.863
y[1] (closed_form) = 0.28812058653284041663389294994856
y[1] (numeric) = 0.28812058653283694168088521123925
absolute error = 3.47495300773870931e-15
relative error = 1.2060759175716272373159390000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.863
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.863
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.864
y[1] (closed_form) = 0.28781152719703807401130984177274
y[1] (numeric) = 0.28781152719703459904453335859416
absolute error = 3.47496677648317858e-15
relative error = 1.2073758165023698043495680000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.864
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.864
Order of pole (three term test) = 4.501e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.865
y[1] (closed_form) = 0.28750296487432526647931056789023
y[1] (numeric) = 0.28750296487432179149882431539869
absolute error = 3.47498048625249154e-15
relative error = 1.2086764001795572386716500000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.865
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.865
Order of pole (three term test) = 2.287e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.866
y[1] (closed_form) = 0.28719489849957897227879961722664
y[1] (numeric) = 0.28719489849957549728466228654866
absolute error = 3.47499413733067798e-15
relative error = 1.2099776686443378176528880000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.866
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.866
Order of pole (three term test) = 6.972e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.867
y[1] (closed_form) = 0.28688732701052790423930534250187
y[1] (numeric) = 0.28688732701052442923157534225331
absolute error = 3.47500773000024856e-15
relative error = 1.2112796219376836402857840000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.867
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.867
Order of pole (three term test) = 7.085e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.868
y[1] (closed_form) = 0.2865802493477433524845361297452
y[1] (numeric) = 0.28658024934773987746327158754141
absolute error = 3.47502126454220379e-15
relative error = 1.2125822601003914917716960000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.868
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.868
Order of pole (three term test) = 4.800e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.869
y[1] (closed_form) = 0.28627366445463006142574018202997
y[1] (numeric) = 0.28627366445462658639099894598707
absolute error = 3.47503474123604290e-15
relative error = 1.2138855831730836852606900000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.869
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.869
Order of pole (three term test) = 2.439e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.87
y[1] (closed_form) = 0.28596757127741714089622236838343
y[1] (numeric) = 0.28596757127741366584806200861076
absolute error = 3.47504816035977267e-15
relative error = 1.2151895911962089049723000000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.87
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.87
Order of pole (three term test) = 4.956e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.871
y[1] (closed_form) = 0.2856619687651490112810768085045
y[1] (numeric) = 0.28566196876514553621955461858836
absolute error = 3.47506152218991614e-15
relative error = 1.2164942842100430226245740000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.871
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.871
Order of pole (three term test) = 2.518e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.872
y[1] (closed_form) = 0.28535685586967638249689531740814
y[1] (numeric) = 0.28535685586967290742206831588675
absolute error = 3.47507482700152139e-15
relative error = 1.2177996622546899534773760000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.872
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.872
Order of pole (three term test) = 7.677e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.873
y[1] (closed_form) = 0.28505223154564726667690954352021
y[1] (numeric) = 0.28505223154564379158883447535008
absolute error = 3.47508807506817013e-15
relative error = 1.2191057253700824609986770000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.873
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.873
Order of pole (three term test) = 5.201e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.874
y[1] (closed_form) = 0.28474809475049802441771862104471
y[1] (numeric) = 0.28474809475049454931645195905839
absolute error = 3.47510126666198632e-15
relative error = 1.2204124735959829869536320000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.874
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.874
Order of pole (three term test) = 5.284e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.875
y[1] (closed_form) = 0.28444444444444444444444444444444
y[1] (numeric) = 0.28444444444444096933004239079973
absolute error = 3.47511440205364471e-15
relative error = 1.2217199069719844683593750000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.875
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.875
Order of pole (three term test) = 1.074e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.876
y[1] (closed_form) = 0.28414127959047285655184328130896
y[1] (numeric) = 0.28414127959046938142436176892962
absolute error = 3.47512748151237934e-15
relative error = 1.2230280255375111552091840000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.876
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.876
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.877
y[1] (closed_form) = 0.28383859915433127767958539128144
y[1] (numeric) = 0.28383859915432780253908008528953
absolute error = 3.47514050530599191e-15
relative error = 1.2243368293318193971886390000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.877
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.877
Order of pole (three term test) = 2.772e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.878
y[1] (closed_form) = 0.28353640210452059098059363449436
y[1] (numeric) = 0.28353640210451711582711993363412
absolute error = 3.47515347370086024e-15
relative error = 1.2256463183939984766692160000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.878
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.878
Order of pole (three term test) = 8.450e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.879
y[1] (closed_form) = 0.28323468741228575774200775439927
y[1] (numeric) = 0.28323468741228228257562079245275
absolute error = 3.47516638696194652e-15
relative error = 1.2269564927629713823319320000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.879
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.879
Order of pole (three term test) = 1.145e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.88
y[1] (closed_form) = 0.28293345405160706201901312811227
y[1] (numeric) = 0.28293345405160358683976777530662
absolute error = 3.47517924535280565e-15
relative error = 1.2282673524774956289360000000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.88
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.88
Order of pole (three term test) = 5.816e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.881
y[1] (closed_form) = 0.28263270099919138784244131343938
y[1] (numeric) = 0.282632700999187912650392177846
absolute error = 3.47519204913559338e-15
relative error = 1.2295788975761640208974180000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.881
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.881
Order of pole (three term test) = 5.910e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.882
y[1] (closed_form) = 0.28233242723446352886171470647027
y[1] (numeric) = 0.2823324272344600536569161353957
absolute error = 3.47520479857107457e-15
relative error = 1.2308911280974054725272680000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.882
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.882
Order of pole (three term test) = 3.002e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.883
y[1] (closed_form) = 0.28203263173955753028536907777304
y[1] (numeric) = 0.28203263173955405506787515914183
absolute error = 3.47521749391863121e-15
relative error = 1.2322040440794857576353690000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.883
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.883
Order of pole (three term test) = 9.152e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.884
y[1] (closed_form) = 0.28173331349930806298204569939731
y[1] (numeric) = 0.28173331349930458775191026312679
absolute error = 3.47523013543627052e-15
relative error = 1.2335176455605083014837120000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.884
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.884
Order of pole (three term test) = 9.299e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.885
y[1] (closed_form) = 0.28143447150124182960549922957314
y[1] (numeric) = 0.28143447150123835436277584894012
absolute error = 3.47524272338063302e-15
relative error = 1.2348319325784149762489500000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.885
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.885
Order of pole (three term test) = 1.575e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.886
y[1] (closed_form) = 0.28113610473556900260781850752714
y[1] (numeric) = 0.28113610473556552735256050052678
absolute error = 3.47525525800700036e-15
relative error = 1.2361469051709868252518560000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.886
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.886
Order of pole (three term test) = 1.920e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.887
y[1] (closed_form) = 0.28083821219517469400570494744253
y[1] (numeric) = 0.28083821219517121873796537813918
absolute error = 3.47526773956930335e-15
relative error = 1.2374625633758448720276150000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.887
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.887
Order of pole (three term test) = 3.251e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.888
y[1] (closed_form) = 0.28054079287561045676529732835392
y[1] (numeric) = 0.28054079287560698148512900822414
absolute error = 3.47528016832012978e-15
relative error = 1.2387789072304508686520320000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.888
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.888
Order of pole (three term test) = 9.910e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=449.5MB, alloc=44.3MB, time=3.56
x[1] = -1.889
y[1] (closed_form) = 0.28024384577508581767167247565452
y[1] (numeric) = 0.28024384577508234237912796492232
absolute error = 3.47529254451073220e-15
relative error = 1.2400959367721080434636200000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.889
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.889
Order of pole (three term test) = 1.678e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.89
y[1] (closed_form) = 0.27994736989445984154978863973573
y[1] (numeric) = 0.27994736989445636624492024870003
absolute error = 3.47530486839103570e-15
relative error = 1.2414136520379618623970000000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.89
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.89
Order of pole (three term test) = 1.364e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.891
y[1] (closed_form) = 0.27965136423723272670427231778686
y[1] (numeric) = 0.27965136423722925138713210814122
absolute error = 3.47531714020964564e-15
relative error = 1.2427320530650007860808840000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.891
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.891
Order of pole (three term test) = 3.464e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.892
y[1] (closed_form) = 0.27935582780953743144607985553951
y[1] (numeric) = 0.27935582780953395611671964168423
absolute error = 3.47532936021385528e-15
relative error = 1.2440511398900570047025920000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.892
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.892
Order of pole (three term test) = 3.520e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.893
y[1] (closed_form) = 0.27906075962013133157469242620726
y[1] (numeric) = 0.27906075962012785623316377655383
absolute error = 3.47534152864965343e-15
relative error = 1.2453709125498071934080070000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.893
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.893
Order of pole (three term test) = 1.430e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.894
y[1] (closed_form) = 0.27876615868038790868512693338269
y[1] (numeric) = 0.27876615868038443333148117165071
absolute error = 3.47535364576173198e-15
relative error = 1.2466913710807732381007280000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.894
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.894
Order of pole (three term test) = 1.090e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.895
y[1] (closed_form) = 0.27847202400428846916966604242521
y[1] (numeric) = 0.27847202400428499380395424893179
absolute error = 3.47536571179349342e-15
relative error = 1.2480125155193229708555500000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.895
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.895
Order of pole (three term test) = 1.476e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.896
y[1] (closed_form) = 0.27817835460841389378482792999697
y[1] (numeric) = 0.27817835460841041840710094293863
absolute error = 3.47537772698705834e-15
relative error = 1.2493343459016709113565440000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.896
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.896
Order of pole (three term test) = 1.125e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.897
y[1] (closed_form) = 0.27788514951193641765471047285215
y[1] (numeric) = 0.27788514951193294226501888957932
absolute error = 3.47538969158327283e-15
relative error = 1.2506568622638789855493470000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.897
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.897
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.898
y[1] (closed_form) = 0.27759240773661144058245549360927
y[1] (numeric) = 0.27759240773660796518084967189342
absolute error = 3.47540160582171585e-15
relative error = 1.2519800646418572464903400000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.898
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.898
Order of pole (three term test) = 1.161e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.899
y[1] (closed_form) = 0.27730012830676936754218636176963
y[1] (numeric) = 0.27730012830676589212871642106306
absolute error = 3.47541346994070657e-15
relative error = 1.2533039530713645973440570000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.899
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.899
Order of pole (three term test) = 7.864e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.9
y[1] (closed_form) = 0.27700831024930747922437673130194
y[1] (numeric) = 0.27700831024930400379909255399028
absolute error = 3.47542528417731166e-15
relative error = 1.2546285275880095092600000000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.9
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.9
Order of pole (three term test) = 3.995e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.901
y[1] (closed_form) = 0.27671695259368183250820950019107
y[1] (numeric) = 0.27671695259367835707116073283856
absolute error = 3.47543704876735251e-15
relative error = 1.2559537882272507267990510000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.901
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.901
Order of pole (three term test) = 4.058e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.902
y[1] (closed_form) = 0.27642605437189919073508322082793
y[1] (numeric) = 0.27642605437189571528631927541548
absolute error = 3.47544876394541245e-15
relative error = 1.2572797350243979860769800000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.902
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.902
Order of pole (three term test) = 1.237e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.903
y[1] (closed_form) = 0.27613561461850898365801819126202
y[1] (numeric) = 0.27613561461850550819758824641817
absolute error = 3.47546042994484385e-15
relative error = 1.2586063680146127021984650000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.903
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.903
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.904
y[1] (closed_form) = 0.27584563237059529694230633429842
y[1] (numeric) = 0.27584563237059182147025933652316
absolute error = 3.47547204699777526e-15
relative error = 1.2599336872329086836956160000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.904
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.904
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.905
y[1] (closed_form) = 0.27555610666776889109333774223104
y[1] (numeric) = 0.27555610666776541560972240711257
absolute error = 3.47548361533511847e-15
relative error = 1.2612616927141528305591750000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.905
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.905
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.906
y[1] (closed_form) = 0.27526703655215924968812244758641
y[1] (numeric) = 0.27526703655215577419298726101092
absolute error = 3.47549513518657549e-15
relative error = 1.2625903844930658156789640000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.906
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.906
Order of pole (three term test) = 1.756e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.907
y[1] (closed_form) = 0.27497842106840665678760859241571
y[1] (numeric) = 0.2749784210684031812810018117702
absolute error = 3.47550660678064551e-15
relative error = 1.2639197626042227713295990000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.907
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.907
Order of pole (three term test) = 4.461e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.908
y[1] (closed_form) = 0.27469025926365430340747772811378
y[1] (numeric) = 0.27469025926365082788944738348188
absolute error = 3.47551803034463190e-15
relative error = 1.2652498270820540025201600000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.908
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.908
Order of pole (three term test) = 9.063e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.909
y[1] (closed_form) = 0.27440255018754042292567450204855
y[1] (numeric) = 0.27440255018753694739626839739954
absolute error = 3.47552940610464901e-15
relative error = 1.2665805779608456398811810000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.909
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.909
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.91
y[1] (closed_form) = 0.27411529289219045530550149392835
y[1] (numeric) = 0.27411529289218697976476720829929
absolute error = 3.47554073428562906e-15
relative error = 1.2679120152747403373786000000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.91
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.91
Order of pole (three term test) = 4.676e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.911
y[1] (closed_form) = 0.27382848643220924001368047118215
y[1] (numeric) = 0.27382848643220576446166535985328
absolute error = 3.47555201511132887e-15
relative error = 1.2692441390577379238259270000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.911
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.911
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.912
y[1] (closed_form) = 0.2735421298646732375133488559374
y[1] (numeric) = 0.27354212986466976195010005160069
absolute error = 3.47556324880433671e-15
relative error = 1.2705769493436961101562240000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.912
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.912
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.913
y[1] (closed_form) = 0.27325622224912277921252475359803
y[1] (numeric) = 0.27325622224911930363808916751913
absolute error = 3.47557443558607890e-15
relative error = 1.2719104461663311173994100000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.913
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.913
Order of pole (three term test) = 9.803e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.914
y[1] (closed_form) = 0.2729707626475543457491355015947
y[1] (numeric) = 0.2729707626475508701635598247681
absolute error = 3.47558557567682660e-15
relative error = 1.2732446295592183859133600000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.914
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.914
Order of pole (three term test) = 9.958e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.915
y[1] (closed_form) = 0.27268575012441287349426337353176
y[1] (numeric) = 0.27268575012440939789759407782946
absolute error = 3.47559666929570230e-15
relative error = 1.2745794995557931867117500000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.915
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.915
Order of pole (three term test) = 1.012e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.916
y[1] (closed_form) = 0.27240118374658408915581783552199
y[1] (numeric) = 0.27240118374658061354810117483547
absolute error = 3.47560771666068652e-15
relative error = 1.2759150561893513213365120000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.916
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.916
Order of pole (three term test) = 1.541e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.917
y[1] (closed_form) = 0.27211706258338687236539661470047
y[1] (numeric) = 0.27211706258338339674667862607618
absolute error = 3.47561871798862429e-15
relative error = 1.2772512994930497528453810000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.917
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.917
Order of pole (three term test) = 1.566e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.918
y[1] (closed_form) = 0.27183338570656564613164782136414
y[1] (numeric) = 0.27183338570656217050197432613246
absolute error = 3.47562967349523168e-15
relative error = 1.2785882294999072666776320000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.918
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.918
Order of pole (three term test) = 5.301e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.919
y[1] (closed_form) = 0.27155015219028279504399248240559
y[1] (numeric) = 0.27155015219027931940340908730333
absolute error = 3.47564058339510226e-15
relative error = 1.2799258462428051173687860000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.919
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.919
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.92
y[1] (closed_form) = 0.27126736111111111111111111111111
y[1] (numeric) = 0.27126736111110763545966320939763
absolute error = 3.47565144790171348e-15
relative error = 1.2812641497544876572672000000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.92
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.92
Order of pole (three term test) = 5.469e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.921
y[1] (closed_form) = 0.27098501154802626711913937328212
y[1] (numeric) = 0.27098501154802279145687214584899
absolute error = 3.47566226722743313e-15
relative error = 1.2826031400675630061084330000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.921
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.921
Order of pole (three term test) = 2.222e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.922
y[1] (closed_form) = 0.27070310258239931739505652822188
y[1] (numeric) = 0.27070310258239584172201494469625
absolute error = 3.47567304158352563e-15
relative error = 1.2839428172145036693372920000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.922
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.922
Order of pole (three term test) = 1.129e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.923
y[1] (closed_form) = 0.27042163329798922586128614151327
y[1] (numeric) = 0.27042163329798575017751496135494
absolute error = 3.47568377118015833e-15
relative error = 1.2852831812276471713098570000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.923
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.923
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.924
y[1] (closed_form) = 0.27014060278093542126806160070193
y[1] (numeric) = 0.27014060278093194557360537429417
absolute error = 3.47569445622640776e-15
relative error = 1.2866242321391966812181760000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.924
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.924
Order of pole (three term test) = 1.746e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.925
y[1] (closed_form) = 0.26986001011975037949063923089897
y[1] (numeric) = 0.26986001011974690378554230063303
absolute error = 3.47570509693026594e-15
relative error = 1.2879659699812216723912500000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.925
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.925
Order of pole (three term test) = 1.774e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.926
y[1] (closed_form) = 0.26957985440531223277896932073425
y[1] (numeric) = 0.26957985440530875706327582208779
absolute error = 3.47571569349864646e-15
relative error = 1.2893083947856585075854960000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.926
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.926
Order of pole (three term test) = 1.802e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.927
y[1] (closed_form) = 0.26930013473085740584796014573446
y[1] (numeric) = 0.26930013473085393012171400834378
absolute error = 3.47572624613739068e-15
relative error = 1.2906515065843110796373720000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.927
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.927
Order of pole (three term test) = 6.100e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.928
y[1] (closed_form) = 0.26902085019197327869699213167817
y[1] (numeric) = 0.26902085019196980296023708040434
absolute error = 3.47573675505127383e-15
relative error = 1.2919953054088514260494720000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.928
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.928
Order of pole (three term test) = 1.859e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.929
y[1] (closed_form) = 0.2687419998865908760478586503078
y[1] (numeric) = 0.2687419998865874003006382062967
absolute error = 3.47574722044401110e-15
relative error = 1.2933397912908203507555100000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.929
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.929
Order of pole (three term test) = 6.293e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.93
y[1] (closed_form) = 0.26846358291497758329082659937179
y[1] (numeric) = 0.26846358291497410753318408110816
absolute error = 3.47575764251826363e-15
relative error = 1.2946849642616280195387000000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.93
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.93
Order of pole (three term test) = 6.391e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.931
y[1] (closed_form) = 0.26818559837972988882902390365057
y[1] (numeric) = 0.26818559837972641306100242800602
absolute error = 3.47576802147564455e-15
relative error = 1.2960308243525545847902550000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.931
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.931
Order of pole (three term test) = 1.298e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.932
y[1] (closed_form) = 0.26790804538576615271187239861288
y[1] (numeric) = 0.26790804538576267693351488188798
absolute error = 3.47577835751672490e-15
relative error = 1.2973773715947507763137600000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.932
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.932
Order of pole (three term test) = 6.593e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.933
y[1] (closed_form) = 0.26763092304031940144879323878647
y[1] (numeric) = 0.26763092304031592566014239774688
absolute error = 3.47578865084103959e-15
relative error = 1.2987246060192385176599510000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.933
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.933
Order of pole (three term test) = 1.339e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.934
y[1] (closed_form) = 0.26735423045293014889491802384586
y[1] (numeric) = 0.26735423045292667309601637675261
absolute error = 3.47579890164709325e-15
relative error = 1.3000725276569115120197000000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.934
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.934
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.935
y[1] (closed_form) = 0.26707796673543924310104227176518
y[1] (numeric) = 0.26707796673543576729193213939908
absolute error = 3.47580911013236610e-15
relative error = 1.3014211365385358460772500000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.935
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.935
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.936
y[1] (closed_form) = 0.26680213100198073902055870500649
y[1] (numeric) = 0.26680213100197726320128221168671
absolute error = 3.47581927649331978e-15
relative error = 1.3027704326947505894138880000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.936
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.936
Order of pole (three term test) = 1.403e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.937
y[1] (closed_form) = 0.26652672236897479696660606737422
y[1] (numeric) = 0.26652672236897132113720514197117
absolute error = 3.47582940092540305e-15
relative error = 1.3041204161560683556105450000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.937
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.937
Order of pole (three term test) = 7.125e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.938
y[1] (closed_form) = 0.26625173995512060671316487053243
y[1] (numeric) = 0.26625173995511713087368124747479
absolute error = 3.47583948362305764e-15
relative error = 1.3054710869528759298848160000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.938
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.938
Order of pole (three term test) = 7.236e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.939
y[1] (closed_form) = 0.26597718288138933713432459483031
y[1] (numeric) = 0.26597718288138586128479981510645
absolute error = 3.47584952477972386e-15
relative error = 1.3068224451154348170643060000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.939
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.939
Order of pole (three term test) = 1.470e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.94
y[1] (closed_form) = 0.26570305027101711127643745350196
y[1] (numeric) = 0.26570305027101363541691286565565
absolute error = 3.47585952458784631e-15
relative error = 1.3081744906738818372316000000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.94
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.94
Order of pole (three term test) = 7.463e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.941
y[1] (closed_form) = 0.26542934124949800675836188689472
y[1] (numeric) = 0.26542934124949453088887864801516
absolute error = 3.47586948323887956e-15
relative error = 1.3095272236582297203588360000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.941
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.941
Order of pole (three term test) = 1.516e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.942
y[1] (closed_form) = 0.26515605494457708139548449844671
y[1] (numeric) = 0.26515605494457360551608357515307
absolute error = 3.47587940092329364e-15
relative error = 1.3108806440983676395324960000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.942
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.942
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.943
y[1] (closed_form) = 0.2648831904862434239436921908992
y[1] (numeric) = 0.26488319048623994805441436031947
absolute error = 3.47588927783057973e-15
relative error = 1.3122347520240618295102770000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.943
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.943
Order of pole (three term test) = 2.345e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.944
y[1] (closed_form) = 0.26461074700672322985994682382428
y[1] (numeric) = 0.26461074700671975396083267456871
absolute error = 3.47589911414925557e-15
relative error = 1.3135895474649561097787520000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.944
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.944
Order of pole (three term test) = 1.588e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.945
y[1] (closed_form) = 0.26433872364047290197659280602163
y[1] (numeric) = 0.26433872364046942606768273915056
absolute error = 3.47590891006687107e-15
relative error = 1.3149450304505724929586750000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.945
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.945
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.946
y[1] (closed_form) = 0.2640671195241721759870036726455
y[1] (numeric) = 0.2640671195241687000683379026318
absolute error = 3.47591866577001370e-15
relative error = 1.3163012010103117200749200000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.946
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.946
Order of pole (three term test) = 8.188e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.947
y[1] (closed_form) = 0.26379593379671727064064689094069
y[1] (numeric) = 0.26379593379671379471226544662676
absolute error = 3.47592838144431393e-15
relative error = 1.3176580591734538244669370000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.947
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.947
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.948
y[1] (closed_form) = 0.26352516559921406254611690397986
y[1] (numeric) = 0.2635251655992105866080596295292
absolute error = 3.47593805727445066e-15
relative error = 1.3190156049691587017304640000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.948
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.948
Order of pole (three term test) = 1.689e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.949
y[1] (closed_form) = 0.26325481407497128548115477250703
y[1] (numeric) = 0.26325481407496780953346132835049
absolute error = 3.47594769344415654e-15
relative error = 1.3203738384264666477000540000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.949
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.949
Order of pole (three term test) = 2.573e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.95
y[1] (closed_form) = 0.26298487836949375410913872452334
y[1] (numeric) = 0.26298487836949027815184858829999
absolute error = 3.47595729013622335e-15
relative error = 1.3217327595742989288375000000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.95
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.95
Order of pole (three term test) = 2.612e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.951
y[1] (closed_form) = 0.2627153576304756120019934841337
y[1] (numeric) = 0.26271535763047213603514595162647
absolute error = 3.47596684753250723e-15
relative error = 1.3230923684414583052779230000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.951
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.951
Order of pole (three term test) = 8.843e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.952
y[1] (closed_form) = 0.26244625100779360386992743886052
y[1] (numeric) = 0.26244625100779012789356162492651
absolute error = 3.47597636581393401e-15
relative error = 1.3244526650566296014039040000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.952
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.952
Order of pole (three term test) = 8.980e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.953
y[1] (closed_form) = 0.26217755765350037189886553149028
y[1] (numeric) = 0.26217755765349689591302037098587
absolute error = 3.47598584516050441e-15
relative error = 1.3258136494483802365161690000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.953
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.953
Order of pole (three term test) = 9.119e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.954
y[1] (closed_form) = 0.26190927672181777609690224183864
y[1] (numeric) = 0.2619092767218143001016164905394
absolute error = 3.47599528575129924e-15
relative error = 1.3271753216451607649031840000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.954
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.954
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.955
y[1] (closed_form) = 0.2616414073691302385515531688045
y[1] (numeric) = 0.26164140736912676254686540431989
absolute error = 3.47600468776448461e-15
relative error = 1.3285376816753054291535250000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.955
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.955
Order of pole (three term test) = 9.403e-30
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.956
y[1] (closed_form) = 0.26137394875397811150003554685703
y[1] (numeric) = 0.26137394875397463548598416954006
absolute error = 3.47601405137731697e-15
relative error = 1.3299007295670326578933920000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.956
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.956
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.957
y[1] (closed_form) = 0.26110690003705106911525754670746
y[1] (numeric) = 0.26110690003704759309188078055913
absolute error = 3.47602337676614833e-15
relative error = 1.3312644653484456415502170000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.957
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.957
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.958
y[1] (closed_form) = 0.2608402603811815229106434303207
y[1] (numeric) = 0.26084026038117804687797932388944
absolute error = 3.47603266410643126e-15
relative error = 1.3326288890475328333062640000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.958
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.958
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.959
y[1] (closed_form) = 0.26057402895133806066736656850843
y[1] (numeric) = 0.26057402895133458462545299578447
absolute error = 3.47604191357272396e-15
relative error = 1.3339940006921684859536760000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.959
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.959
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.96
y[1] (closed_form) = 0.26030820491461890878800499791754
y[1] (numeric) = 0.26030820491461543273687965922226
absolute error = 3.47605112533869528e-15
relative error = 1.3353598003101131787648000000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.96
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.96
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.961
y[1] (closed_form) = 0.26004278744024541798107460601568
y[1] (numeric) = 0.26004278744024194192077502888602
absolute error = 3.47606029957712966e-15
relative error = 1.3367262879290143227252860000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.961
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.961
Order of pole (three term test) = 1.031e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.962
y[1] (closed_form) = 0.25977777569955557218133320032711
y[1] (numeric) = 0.25977777569955209611189674039498
absolute error = 3.47606943645993213e-15
relative error = 1.3380934635764066978235720000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.962
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.962
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.963
y[1] (closed_form) = 0.25951316886599752061118465425969
y[1] (numeric) = 0.25951316886599404453264849612646
absolute error = 3.47607853615813323e-15
relative error = 1.3394613272797129686351870000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.963
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.963
Order of pole (three term test) = 1.063e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.964
y[1] (closed_form) = 0.2592489661151231328889460388832
y[1] (numeric) = 0.25924896611511965680134719698935
absolute error = 3.47608759884189385e-15
relative error = 1.3408298790662441780029600000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.964
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.964
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.965
y[1] (closed_form) = 0.25898516662458157709017216038951
y[1] (numeric) = 0.25898516662457810099354747987937
absolute error = 3.47609662468051014e-15
relative error = 1.3421991189632002765321500000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.965
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.965
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.966
y[1] (closed_form) = 0.2587217695741129206686612390289
y[1] (numeric) = 0.25872176957410944456304739661055
absolute error = 3.47610561384241835e-15
relative error = 1.3435690469976706340012600000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.966
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.966
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.967
y[1] (closed_form) = 0.25845877414554175414419259934315
y[1] (numeric) = 0.25845877414553827802962610414358
absolute error = 3.47611456649519957e-15
relative error = 1.3449396631966345209091730000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.967
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.967
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.968
y[1] (closed_form) = 0.25819617952277083746447220569767
y[1] (numeric) = 0.25819617952276736134098940011311
absolute error = 3.47612348280558456e-15
relative error = 1.3463109675869616334909440000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.968
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.968
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.969
y[1] (closed_form) = 0.25793398489177476894918468357046
y[1] (numeric) = 0.25793398489177129281682174411199
absolute error = 3.47613236293945847e-15
relative error = 1.3476829601954125849309670000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.969
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.969
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.97
y[1] (closed_form) = 0.25767218944059367672447112783117
y[1] (numeric) = 0.25767218944059020058326406596561
absolute error = 3.47614120706186556e-15
relative error = 1.3490556410486394051804000000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.97
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.97
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.971
y[1] (closed_form) = 0.25741079235932693255657052630983
y[1] (numeric) = 0.25741079235932345640655518929592
absolute error = 3.47615001533701391e-15
relative error = 1.3504290101731860455138310000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.971
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.971
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.972
y[1] (closed_form) = 0.25714979284012688799377903221161
y[1] (numeric) = 0.25714979284012341183499110393159
absolute error = 3.47615878792828002e-15
relative error = 1.3518030675954888489295680000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.972
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.972
Order of pole (three term test) = 1.219e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.973
y[1] (closed_form) = 0.25688919007719263272629561420793
y[1] (numeric) = 0.25688919007718915655877061599442
absolute error = 3.47616752499821351e-15
relative error = 1.3531778133418770678568790000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.973
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.973
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.974
y[1] (closed_form) = 0.25662898326676377507393481007915
y[1] (numeric) = 0.2566289832667602988977081015375
absolute error = 3.47617622670854165e-15
relative error = 1.3545532474385733242555400000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.974
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.974
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.975
y[1] (closed_form) = 0.25636917160711424451209742028521
y[1] (numeric) = 0.2563691716071107683272042001112
absolute error = 3.47618489322017401e-15
relative error = 1.3559293699116941247756250000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.975
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.975
Order of pole (three term test) = 1.276e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.976
y[1] (closed_form) = 0.25610975429854611614679801340786
y[1] (numeric) = 0.25610975429854263995327332020093
absolute error = 3.47619352469320693e-15
relative error = 1.3573061807872503141911680000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.976
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.976
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.977
y[1] (closed_form) = 0.2558507305433834570499540875864
y[1] (numeric) = 0.25585073054337998084783280065831
absolute error = 3.47620212128692809e-15
relative error = 1.3586836800911475760679610000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.977
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.977
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.978
y[1] (closed_form) = 0.25559209954596619436654565232727
y[1] (numeric) = 0.25559209954596271815586249250627
absolute error = 3.47621068315982100e-15
relative error = 1.3600618678491869105364000000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.978
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.978
Order of pole (three term test) = 1.336e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.979
y[1] (closed_form) = 0.25533386051264400510565587481083
y[1] (numeric) = 0.25533386051264052888644540524141
absolute error = 3.47621921046956942e-15
relative error = 1.3614407440870650928834220000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.979
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.979
Order of pole (three term test) = 1.356e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.98
y[1] (closed_form) = 0.25507601265177022752780328537904
y[1] (numeric) = 0.2550760126517667513000999123172
absolute error = 3.47622770337306184e-15
relative error = 1.3628203088303751637536000000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.98
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.98
Order of pole (three term test) = 1.377e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.981
y[1] (closed_form) = 0.25481855517369579404137386952933
y[1] (numeric) = 0.25481855517369231780521184313344
absolute error = 3.47623616202639589e-15
relative error = 1.3642005621046069001276290000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.981
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.981
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.982
y[1] (closed_form) = 0.25456148729076318552135719966072
y[1] (numeric) = 0.25456148729075970927677061477804
absolute error = 3.47624458658488268e-15
relative error = 1.3655815039351472669028320000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.982
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.982
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.983
y[1] (closed_form) = 0.25430480821730040696398459014584
y[1] (numeric) = 0.25430480821729693071100738709463
absolute error = 3.47625297720305121e-15
relative error = 1.3669631343472809039519690000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.983
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.983
Order of pole (three term test) = 1.441e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.984
y[1] (closed_form) = 0.25404851716961498439125910509886
y[1] (numeric) = 0.25404851716961150812992507044619
absolute error = 3.47626133403465267e-15
relative error = 1.3683454533661905780203520000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.984
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.984
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.985
y[1] (closed_form) = 0.25379261336598798291975712046901
y[1] (numeric) = 0.25379261336598450665009988780427
absolute error = 3.47626965723266474e-15
relative error = 1.3697284610169576425166500000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.985
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.985
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.986
y[1] (closed_form) = 0.25353709602666804590846905174084
y[1] (numeric) = 0.25353709602666456963052210244495
absolute error = 3.47627794694929589e-15
relative error = 1.3711121573245625052154440000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.986
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.986
Order of pole (three term test) = 1.508e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.987
y[1] (closed_form) = 0.25328196437386545510083281642706
y[1] (numeric) = 0.25328196437386197881462948043744
absolute error = 3.47628620333598962e-15
relative error = 1.3724965423138850802005780000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.987
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.987
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.988
y[1] (closed_form) = 0.25302721763174621167649761749572
y[1] (numeric) = 0.25302721763174273538207107406703
absolute error = 3.47629442654342869e-15
relative error = 1.3738816160097052436611360000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.988
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.988
Order of pole (three term test) = 1.554e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.989
y[1] (closed_form) = 0.25277285502642613812873772061067
y[1] (numeric) = 0.25277285502642266182612099907135
absolute error = 3.47630261672153932e-15
relative error = 1.3752673784367032856177720000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.989
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.989
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.99
y[1] (closed_form) = 0.25251887578596500088381606525088
y[1] (numeric) = 0.25251887578596152457304204575552
absolute error = 3.47631077401949536e-15
relative error = 1.3766538296194603575136000000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.99
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.99
Order of pole (three term test) = 1.601e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.991
y[1] (closed_form) = 0.25226527914036065357897580801199
y[1] (numeric) = 0.25226527914035717726007722228955
absolute error = 3.47631889858572244e-15
relative error = 1.3780409695824589195677640000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.991
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.991
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.992
y[1] (closed_form) = 0.25201206432154320091611425622167
y[1] (numeric) = 0.25201206432153972458912368831954
absolute error = 3.47632699056790213e-15
relative error = 1.3794287983500831997576320000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.992
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.992
Order of pole (three term test) = 1.650e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.993
y[1] (closed_form) = 0.25175923056336918300856812189376
y[1] (numeric) = 0.25175923056336570667351800891777
absolute error = 3.47633505011297599e-15
relative error = 1.3808173159466196168103510000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.993
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.993
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.994
y[1] (closed_form) = 0.25150677710161578013881162041792
y[1] (numeric) = 0.25150677710161230379573425326824
absolute error = 3.47634307736714968e-15
relative error = 1.3822065223962572345068480000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.994
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.994
Order of pole (three term test) = 1.701e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.995
y[1] (closed_form) = 0.25125470317397503784523966557999
y[1] (numeric) = 0.25125470317397156149416718968299
absolute error = 3.47635107247589700e-15
relative error = 1.3835964177230881957425000000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.995
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.995
Order of pole (three term test) = 1.727e-29
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.996
y[1] (closed_form) = 0.25100300802004811225657728282216
y[1] (numeric) = 0.25100300802004463589754169885824
absolute error = 3.47635903558396392e-15
relative error = 1.3849870019511081600702720000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.996
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.996
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.997
y[1] (closed_form) = 0.2507516908813395355928233863063
y[1] (numeric) = 0.25075169088133605922585655093371
absolute error = 3.47636696683537259e-15
relative error = 1.3863782751042167407273310000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.997
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.997
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.998
y[1] (closed_form) = 0.25050075100125150175200225250275
y[1] (numeric) = 0.25050075100124802537713587907744
absolute error = 3.47637486637342531e-15
relative error = 1.3877702372062179331221240000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.998
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.998
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = -1.999
y[1] (closed_form) = 0.25025018762507817190235938379395
y[1] (numeric) = 0.25025018762507469551962504308545
absolute error = 3.47638273434070850e-15
relative error = 1.3891628882808205506708500000000e-12 %
Desired digits = 12
Estimated correct digits = 11
Correct digits = 14
h = -0.001
Radius of convergence (given) for eq 1 = 1.999
Order of pole (given) = 2
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.999
Order of pole (three term test) = 1.833e-29
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff ( y , x , 1 ) = neg ( 2.0 ) / x / x / x ;
Iterations = 1300
Total Elapsed Time = 3 Seconds
Elapsed Time(since restart) = 3 Seconds
Expected Time Remaining = 0 Seconds
Optimized Time Remaining = 0 Seconds
Expected Total Time = 3 Seconds
Time to Timeout = 2 Minutes 56 Seconds
Percent Done = 0 %
> quit
memory used=490.3MB, alloc=44.3MB, time=3.88