|\^/| 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(6.0) ) / ( c(x) - c(6.0) ));
> end;
exact_soln_y :=
proc(x) return c(1.0)/((c(x) - c(6.0))*(c(x) - c(6.0))) 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,
> array_const_6D0,
#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_tmp6,
> array_tmp7,
> array_tmp8,
> 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_const_6D0, 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_tmp6,
array_tmp7, array_tmp8, 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,
> array_const_6D0,
#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_tmp6,
> array_tmp7,
> array_tmp8,
> 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_const_6D0, 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_tmp6,
array_tmp7, array_tmp8, 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,
> array_const_6D0,
#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_tmp6,
> array_tmp7,
> array_tmp8,
> 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_const_6D0, 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_tmp6,
array_tmp7, array_tmp8, 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,
> array_const_6D0,
#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_tmp6,
> array_tmp7,
> array_tmp8,
> 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_const_6D0, 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_tmp6,
array_tmp7, array_tmp8, 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,
> array_const_6D0,
#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_tmp6,
> array_tmp7,
> array_tmp8,
> 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)*35*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_const_6D0, 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_tmp6,
array_tmp7, array_tmp8, 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)*35*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,
> array_const_6D0,
#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_tmp6,
> array_tmp7,
> array_tmp8,
> 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_const_6D0, 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_tmp6,
array_tmp7, array_tmp8, 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,
> array_const_6D0,
#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_tmp6,
> array_tmp7,
> array_tmp8,
> 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_const_6D0, 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_tmp6,
array_tmp7, array_tmp8, 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,
> array_const_6D0,
#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_tmp6,
> array_tmp7,
> array_tmp8,
> 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 sub LINEAR - CONST $eq_no = 1 i = 1
> array_tmp2[1] := array_x[1] - array_const_6D0[1];
> #emit pre div CONST - LINEAR $eq_no = 1 i = 1
> array_tmp3[1] := array_tmp1[1] / array_tmp2[1];
> #emit pre sub LINEAR - CONST $eq_no = 1 i = 1
> array_tmp4[1] := array_x[1] - array_const_6D0[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 1
> array_tmp5[1] := array_tmp3[1] / array_tmp4[1];
> #emit pre sub LINEAR - CONST $eq_no = 1 i = 1
> array_tmp6[1] := array_x[1] - array_const_6D0[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 1
> array_tmp7[1] := array_tmp5[1] / array_tmp6[1];
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp8[1] := array_const_0D0[1] + array_tmp7[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_tmp8[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 sub LINEAR - CONST $eq_no = 1 i = 2
> array_tmp2[2] := array_x[2];
> #emit pre div CONST - LINEAR $eq_no = 1 i = 2
> array_tmp3[2] := neg(array_tmp3[1])* array_tmp2[2] / array_tmp2[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 sub LINEAR - CONST $eq_no = 1 i = 2
> array_tmp4[2] := array_x[2];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 2
> array_tmp5[2] := (array_tmp3[2] - array_tmp5[1] * array_tmp4[2]) / array_tmp4[1];
> #emit pre sub LINEAR - CONST $eq_no = 1 i = 2
> array_tmp6[2] := array_x[2];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 2
> array_tmp7[2] := (array_tmp5[2] - array_tmp7[1] * array_tmp6[2]) / array_tmp6[1];
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp8[2] := array_tmp7[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_tmp8[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_tmp3[3] := neg(array_tmp3[2])* array_tmp2[2] / array_tmp2[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 3
> array_tmp5[3] := (array_tmp3[3] - array_tmp5[2] * array_tmp4[2]) / array_tmp4[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 3
> array_tmp7[3] := (array_tmp5[3] - array_tmp7[2] * array_tmp6[2]) / array_tmp6[1];
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp8[3] := array_tmp7[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_tmp8[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_tmp3[4] := neg(array_tmp3[3])* array_tmp2[2] / array_tmp2[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 4
> array_tmp5[4] := (array_tmp3[4] - array_tmp5[3] * array_tmp4[2]) / array_tmp4[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 4
> array_tmp7[4] := (array_tmp5[4] - array_tmp7[3] * array_tmp6[2]) / array_tmp6[1];
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp8[4] := array_tmp7[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_tmp8[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_tmp3[5] := neg(array_tmp3[4])* array_tmp2[2] / array_tmp2[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 5
> array_tmp5[5] := (array_tmp3[5] - array_tmp5[4] * array_tmp4[2]) / array_tmp4[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 5
> array_tmp7[5] := (array_tmp5[5] - array_tmp7[4] * array_tmp6[2]) / array_tmp6[1];
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp8[5] := array_tmp7[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_tmp8[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_tmp3[kkk] := array_tmp1[1] * array_tmp2[kkk];
> #emit div FULL LINEAR $eq_no = 1 i = 1
> array_tmp5[kkk] := neg(ats(kkk,array_tmp4,array_tmp5,2)) / array_tmp4[1];
> #emit div FULL LINEAR $eq_no = 1 i = 1
> array_tmp7[kkk] := neg(ats(kkk,array_tmp6,array_tmp7,2)) / array_tmp6[1];
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp8[kkk] := array_tmp7[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_tmp8[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_const_6D0, 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_tmp6,
array_tmp7, array_tmp8, 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_x[1] - array_const_6D0[1];
array_tmp3[1] := array_tmp1[1]/array_tmp2[1];
array_tmp4[1] := array_x[1] - array_const_6D0[1];
array_tmp5[1] := array_tmp3[1]/array_tmp4[1];
array_tmp6[1] := array_x[1] - array_const_6D0[1];
array_tmp7[1] := array_tmp5[1]/array_tmp6[1];
array_tmp8[1] := array_const_0D0[1] + array_tmp7[1];
if not array_y_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp8[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] := array_x[2];
array_tmp3[2] := neg(array_tmp3[1])*array_tmp2[2]/array_tmp2[1];
array_tmp4[2] := array_x[2];
array_tmp5[2] :=
(-array_tmp4[2]*array_tmp5[1] + array_tmp3[2])/array_tmp4[1];
array_tmp6[2] := array_x[2];
array_tmp7[2] :=
(-array_tmp6[2]*array_tmp7[1] + array_tmp5[2])/array_tmp6[1];
array_tmp8[2] := array_tmp7[2];
if not array_y_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp8[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_tmp3[3] := neg(array_tmp3[2])*array_tmp2[2]/array_tmp2[1];
array_tmp5[3] :=
(-array_tmp4[2]*array_tmp5[2] + array_tmp3[3])/array_tmp4[1];
array_tmp7[3] :=
(-array_tmp6[2]*array_tmp7[2] + array_tmp5[3])/array_tmp6[1];
array_tmp8[3] := array_tmp7[3];
if not array_y_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp8[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_tmp3[4] := neg(array_tmp3[3])*array_tmp2[2]/array_tmp2[1];
array_tmp5[4] :=
(-array_tmp4[2]*array_tmp5[3] + array_tmp3[4])/array_tmp4[1];
array_tmp7[4] :=
(-array_tmp6[2]*array_tmp7[3] + array_tmp5[4])/array_tmp6[1];
array_tmp8[4] := array_tmp7[4];
if not array_y_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp8[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_tmp3[5] := neg(array_tmp3[4])*array_tmp2[2]/array_tmp2[1];
array_tmp5[5] :=
(-array_tmp4[2]*array_tmp5[4] + array_tmp3[5])/array_tmp4[1];
array_tmp7[5] :=
(-array_tmp6[2]*array_tmp7[4] + array_tmp5[5])/array_tmp6[1];
array_tmp8[5] := array_tmp7[5];
if not array_y_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp8[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_tmp3[kkk] := array_tmp1[1]*array_tmp2[kkk];
array_tmp5[kkk] :=
neg(ats(kkk, array_tmp4, array_tmp5, 2))/array_tmp4[1];
array_tmp7[kkk] :=
neg(ats(kkk, array_tmp6, array_tmp7, 2))/array_tmp6[1];
array_tmp8[kkk] := array_tmp7[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_tmp8[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,
> array_const_6D0,
> #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_tmp6,
> array_tmp7,
> array_tmp8,
> 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:=30;
> 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_tmp6:= Array(0..(20),[]);
> array_tmp7:= Array(0..(20),[]);
> array_tmp8:= 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_tmp6[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp7[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp8[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_tmp6);
> zero_ats_ar(array_tmp7);
> zero_ats_ar(array_tmp8);
> 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_const_6D0);
> array_const_6D0[1] := c(6.0);
> 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/sing6_backpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = neg ( 2.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=30;");
> 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(3.0);");
> omniout_str(ALWAYS,"x_end := c(2.0);");
> omniout_str(ALWAYS,"");
> 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,"glob_type_given_pole := 1;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_rad_poles[1,1] := c(6.0);");
> 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(3.0);");
> 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,"");
> omniout_str(ALWAYS,"return(c(1.0)/ ( c(x) - c(6.0) ) / ( c(x) - c(6.0) ));");
> 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(3.0);
> 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(6.0);
> array_given_rad_poles[1,2] := c(0.0);
> array_given_ord_poles[1,1] := c(3.0);
> 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 - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; ");
> 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,"2020-05-26T00:33:21-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"sing6_back")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = neg ( 2.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; ")
> ;
> 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,"sing6_back diffeq.mxt")
> ;
> logitem_str(html_log_file,"sing6_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_const_6D0, 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_tmp6,
array_tmp7, array_tmp8, 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 := 30;
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_tmp6 := Array(0 .. 20, []);
array_tmp7 := Array(0 .. 20, []);
array_tmp8 := 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_tmp6[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_tmp7[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_tmp8[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_tmp6);
zero_ats_ar(array_tmp7);
zero_ats_ar(array_tmp8);
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_const_6D0);
array_const_6D0[1] := c(6.0);
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/sing6_backpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = neg ( 2.0 ) / \
( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; \
");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=30;");
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(3.0);");
omniout_str(ALWAYS, "x_end := c(2.0);");
omniout_str(ALWAYS, "");
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, "glob_type_given_pole := 1;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_rad_poles[1,1] := c(6.0);");
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(3.0);");
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, "");
omniout_str(ALWAYS,
"return(c(1.0)/ ( c(x) - c(6.0) ) / ( c(x) - c(6.0) ));");
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(3.0);
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(6.0);
array_given_rad_poles[1, 2] := c(0.);
array_given_ord_poles[1, 1] := c(3.0);
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 - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 \
) ; ");
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, "2020-05-26T00:33:21-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"sing6_back");
logitem_str(html_log_file, "diff ( y , x , 1 ) = ne\
g ( 2.0 ) / ( x - 6.0 ) / ( x - 6.0 ) \
/ ( x - 6.0 ) ; ");
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, "sing6_back diffeq.mxt");
logitem_str(html_log_file, "sing6_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/sing6_backpostode.ode#################
diff ( y , x , 1 ) = neg ( 2.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=30;
max_terms:=20;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := c(3.0);
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(6.0);
array_given_rad_poles[1,2] := c(0.0);
array_given_ord_poles[1,1] := c(3.0);
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(6.0) ) / ( c(x) - c(6.0) ));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
TOP MAIN SOLVE Loop
x[1] = 2.999
y[1] (closed_form) = 0.111037074057620024692424528934
y[1] (numeric) = 0.111037074057620024692119885969
absolute error = 3.04642965e-22
relative error = 2.74361484743296499999999999999e-19 %
Desired digits = 12
Estimated correct digits = 14
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.001
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.001
Order of pole (three term test) = 7.209e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.998
y[1] (closed_form) = 0.110963110979533519958490919445
y[1] (numeric) = 0.110963110979533519957882444617
absolute error = 6.08474828e-22
relative error = 5.48357758383531199999999999999e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.002
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.002
Order of pole (three term test) = 1.456e-27
NO COMPLEX POLE (six term test) for Equation 1
memory used=4.3MB, alloc=40.3MB, time=0.08
TOP MAIN SOLVE Loop
x[1] = 2.997
y[1] (closed_form) = 0.110889221778332667443556554446
y[1] (numeric) = 0.110889221778332667442645056428
absolute error = 9.11498018e-22
relative error = 8.21989732980616199999999999998e-19 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.003
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.003
Order of pole (three term test) = 7.355e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.996
y[1] (closed_form) = 0.110815406355662489960124184177
y[1] (numeric) = 0.110815406355662489958910469221
absolute error = 1.213714956e-21
relative error = 1.09525831823832960000000000000e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.004
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.004
Order of pole (three term test) = 7.429e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.995
y[1] (closed_form) = 0.110741664613331635294475928915
y[1] (numeric) = 0.110741664613331635292960800861
absolute error = 1.515128054e-21
relative error = 1.36816442058213500000000000000e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.005
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.005
Order of pole (three term test) = 7.503e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.994
y[1] (closed_form) = 0.11066799645331204966425543236
y[1] (numeric) = 0.110667996453312049662439692643
absolute error = 1.815739717e-21
relative error = 1.64070894494418120000000000000e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.006
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.006
Order of pole (three term test) = 7.578e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.993
y[1] (closed_form) = 0.110594401777738651936082186681
y[1] (numeric) = 0.11059440177773865193396663434
absolute error = 2.115552341e-21
relative error = 1.91289279293867090000000000001e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.007
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.007
Order of pole (three term test) = 7.654e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.992
y[1] (closed_form) = 0.110520880488909008601177003169
y[1] (numeric) = 0.110520880488909008598762434853
absolute error = 2.414568316e-21
relative error = 2.18471686555402240000000000000e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.008
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.008
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.991
y[1] (closed_form) = 0.11044743248928300950698364638
y[1] (numeric) = 0.110447432489283009504270856359
absolute error = 2.712790021e-21
relative error = 2.45618205861257010000000000000e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.009
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.009
Order of pole (three term test) = 3.904e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.99
y[1] (closed_form) = 0.110374057681482544342777673536
y[1] (numeric) = 0.110374057681482544339767453706
absolute error = 3.010219830e-21
relative error = 2.72728926817829999999999999999e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.01
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.01
Order of pole (three term test) = 7.887e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.989
y[1] (closed_form) = 0.110300755968291179877259524773
y[1] (numeric) = 0.110300755968291179873952664667
absolute error = 3.306860106e-21
relative error = 2.99803938510688260000000000002e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.011
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.011
Order of pole (three term test) = 3.983e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.988
y[1] (closed_form) = 0.110227527252653837946134893802
y[1] (numeric) = 0.110227527252653837942532180593
absolute error = 3.602713209e-21
relative error = 3.26843330227500960000000000001e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.012
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.012
Order of pole (three term test) = 8.046e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.987
y[1] (closed_form) = 0.110154371437676474187691372567
y[1] (numeric) = 0.11015437143767647418379359108
absolute error = 3.897781487e-21
relative error = 3.53847190640573029999999999998e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.013
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.013
Order of pole (three term test) = 8.126e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.986
y[1] (closed_form) = 0.110081288426625757524386307825
y[1] (numeric) = 0.110081288426625757520194240546
absolute error = 4.192067279e-21
relative error = 3.80815608076226840000000000001e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.014
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.014
Order of pole (three term test) = 4.104e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.985
y[1] (closed_form) = 0.110008278122928750388466732122
y[1] (numeric) = 0.1100082781229287503839811592
absolute error = 4.485572922e-21
relative error = 4.07748671148874499999999999998e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.015
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.015
Order of pole (three term test) = 4.145e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.984
y[1] (closed_form) = 0.109935340430172589689648136552
y[1] (numeric) = 0.109935340430172589684869835812
absolute error = 4.778300740e-21
relative error = 4.34646467760294400000000000000e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.016
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.016
Order of pole (three term test) = 8.372e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.983
y[1] (closed_form) = 0.109862475252104168522884738114
y[1] (numeric) = 0.109862475252104168517814485062
absolute error = 5.070253052e-21
relative error = 4.61509085824360279999999999999e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.017
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.017
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.982
y[1] (closed_form) = 0.109789682492629818614269760276
y[1] (numeric) = 0.109789682492629818608908328109
absolute error = 5.361432167e-21
relative error = 4.88336612810581080000000000002e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.018
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.018
Order of pole (three term test) = 8.541e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.981
y[1] (closed_form) = 0.109716962055814993503110091865
y[1] (numeric) = 0.109716962055814993497458251474
absolute error = 5.651840391e-21
relative error = 5.15129136379551510000000000000e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.019
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.019
Order of pole (three term test) = 4.313e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.98
y[1] (closed_form) = 0.109644313845883952458225516425
y[1] (numeric) = 0.109644313845883952452284036408
absolute error = 5.941480017e-21
relative error = 5.41886743470467999999999999999e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.02
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.02
Order of pole (three term test) = 8.712e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.979
y[1] (closed_form) = 0.109571737767219445126528512045
y[1] (numeric) = 0.109571737767219445120298158713
absolute error = 6.230353332e-21
relative error = 5.68609520936514120000000000002e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.021
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.021
Order of pole (three term test) = 4.400e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.978
y[1] (closed_form) = 0.109499233724362396911946410199
y[1] (numeric) = 0.109499233724362396905427947581
absolute error = 6.518462618e-21
relative error = 5.95297555634831120000000000000e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.022
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.022
Order of pole (three term test) = 4.443e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.977
y[1] (closed_form) = 0.109426801622011595082753471593
y[1] (numeric) = 0.109426801622011595075947661446
absolute error = 6.805810147e-21
relative error = 6.21950933968537629999999999998e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.023
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.023
Order of pole (three term test) = 4.488e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.976
y[1] (closed_form) = 0.109354441365023375605386187397
y[1] (numeric) = 0.109354441365023375598293789213
absolute error = 7.092398184e-21
relative error = 6.48569742158499839999999999999e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.024
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.024
Order of pole (three term test) = 4.532e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.975
y[1] (closed_form) = 0.109282152858411310702820845571
y[1] (numeric) = 0.109282152858411310695442616584
absolute error = 7.378228987e-21
relative error = 6.75154066241668749999999999998e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.025
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.025
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.974
y[1] (closed_form) = 0.109209936007345897135598114425
y[1] (numeric) = 0.10920993600734589712793480962
absolute error = 7.663304805e-21
relative error = 7.01703991886281800000000000000e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.026
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.026
Order of pole (three term test) = 9.247e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.973
y[1] (closed_form) = 0.109137790717154245203585089115
y[1] (numeric) = 0.109137790717154245195637461233
absolute error = 7.947627882e-21
relative error = 7.28219604756099779999999999999e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.027
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.027
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.972
y[1] (closed_form) = 0.109065716893319768466570921509
y[1] (numeric) = 0.109065716893319768458339721057
absolute error = 8.231200452e-21
relative error = 7.54700990050903680000000000002e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.028
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.028
Order of pole (three term test) = 9.432e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.971
y[1] (closed_form) = 0.108993714441481874181797809902
y[1] (numeric) = 0.108993714441481874173283785158
absolute error = 8.514024744e-21
relative error = 7.81148232962657040000000000001e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.029
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.029
Order of pole (three term test) = 1.905e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.97
y[1] (closed_form) = 0.108921783267435654456534762387
y[1] (numeric) = 0.108921783267435654447738659409
absolute error = 8.796102978e-21
relative error = 8.07561418307202000000000000001e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.03
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.03
Order of pole (three term test) = 4.810e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.969
y[1] (closed_form) = 0.108849923277131578113807166483
y[1] (numeric) = 0.108849923277131578104729729115
absolute error = 9.077437368e-21
relative error = 8.33940630797586480000000000000e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.031
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.031
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.968
y[1] (closed_form) = 0.108778134376675183269400797822
y[1] (numeric) = 0.108778134376675183260042767703
absolute error = 9.358030119e-21
relative error = 8.60285954766898560000000000003e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.032
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.032
Order of pole (three term test) = 4.906e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.967
y[1] (closed_form) = 0.108706416472326770618264482494
y[1] (numeric) = 0.108706416472326770608626599063
absolute error = 9.637883431e-21
relative error = 8.86597474533943589999999999999e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.033
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.033
Order of pole (three term test) = 9.910e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.966
y[1] (closed_form) = 0.108634769470501097428441191002
y[1] (numeric) = 0.108634769470501097418524191507
absolute error = 9.916999495e-21
relative error = 9.12875274033962200000000000001e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.034
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.034
Order of pole (three term test) = 2.002e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.965
y[1] (closed_form) = 0.108563193277767072240662886858
y[1] (numeric) = 0.108563193277767072230467506363
absolute error = 1.0195380495e-20
relative error = 9.39119437000563750000000000001e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.035
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.035
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.964
y[1] (closed_form) = 0.108491687800847450271749979603
y[1] (numeric) = 0.108491687800847450261276950995
absolute error = 1.0473028608e-20
relative error = 9.65330046964039680000000000005e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.036
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.036
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.963
y[1] (closed_form) = 0.108420252946618529519961740661
y[1] (numeric) = 0.108420252946618529509211794656
absolute error = 1.0749946005e-20
relative error = 9.91507187341908450000000000001e-18 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.037
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.037
Order of pole (three term test) = 5.155e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.962
y[1] (closed_form) = 0.108348888622109847570449530871
y[1] (numeric) = 0.108348888622109847559423396024
absolute error = 1.1026134847e-20
relative error = 1.01765094106835068000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.038
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.038
Order of pole (three term test) = 2.603e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.961
y[1] (closed_form) = 0.108277594734503879098970160969
y[1] (numeric) = 0.108277594734503879087668563678
absolute error = 1.1301597291e-20
relative error = 1.04376139114573611000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.039
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.039
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.96
y[1] (closed_form) = 0.108206371191135734072022160665
y[1] (numeric) = 0.10820637119113573406044582518
absolute error = 1.1576335485e-20
relative error = 1.06983862018176000000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.04
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.04
Order of pole (three term test) = 5.310e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.959
y[1] (closed_form) = 0.108135217899492856641573168451
y[1] (numeric) = 0.108135217899492856629722816881
absolute error = 1.1850351570e-20
relative error = 1.09588271057209170000000000001e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.041
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.041
Order of pole (three term test) = 2.145e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.958
y[1] (closed_form) = 0.108064134767214724732552072865
y[1] (numeric) = 0.108064134767214724720428425182
absolute error = 1.2123647683e-20
relative error = 1.12189374477628812000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.042
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.042
Order of pole (three term test) = 5.416e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.957
y[1] (closed_form) = 0.10799312170209255032128493672
y[1] (numeric) = 0.107993121702092550308888710772
absolute error = 1.2396225948e-20
relative error = 1.14787180448361852000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.043
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.043
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.956
y[1] (closed_form) = 0.107922178612068980403059118906
y[1] (numeric) = 0.107922178612068980390391030419
absolute error = 1.2668088487e-20
relative error = 1.17381697162878832000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.044
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.044
Order of pole (three term test) = 1.105e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.955
y[1] (closed_form) = 0.107851305405237798647005373691
y[1] (numeric) = 0.107851305405237798634066136277
absolute error = 1.2939237414e-20
relative error = 1.19972932783543350000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.045
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.045
Order of pole (three term test) = 5.578e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.954
y[1] (closed_form) = 0.107780501989843627736493055271
y[1] (numeric) = 0.107780501989843627723283380435
absolute error = 1.3209674836e-20
relative error = 1.22560895450688976000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.046
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.046
Order of pole (three term test) = 2.253e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.953
y[1] (closed_form) = 0.10770976827428163239323888551
y[1] (numeric) = 0.107709768274281632379759482658
absolute error = 1.3479402852e-20
relative error = 1.25145593273164068000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.047
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.047
Order of pole (three term test) = 5.689e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.952
y[1] (closed_form) = 0.107639104167097223083335055559
y[1] (numeric) = 0.107639104167097223069586632005
absolute error = 1.3748423554e-20
relative error = 1.27727034337420416000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.048
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.048
Order of pole (three term test) = 1.149e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.951
y[1] (closed_form) = 0.107568509576985760403407727356
y[1] (numeric) = 0.107568509576985760389390988327
absolute error = 1.4016739029e-20
relative error = 1.30305226725934629000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.049
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.049
Order of pole (three term test) = 5.802e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.95
y[1] (closed_form) = 0.107497984412792260145122278957
y[1] (numeric) = 0.107497984412792260130837927601
absolute error = 1.4284351356e-20
relative error = 1.32880178489190000000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.05
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.05
Order of pole (three term test) = 1.172e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.949
y[1] (closed_form) = 0.107427528583511099036256898324
y[1] (numeric) = 0.107427528583511099021705635717
absolute error = 1.4551262607e-20
relative error = 1.35451897654782807000000000001e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.051
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.051
Order of pole (three term test) = 1.184e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.948
y[1] (closed_form) = 0.107357141998285721156571373605
y[1] (numeric) = 0.107357141998285721141753898756
absolute error = 1.4817474849e-20
relative error = 1.38020392245879695999999999999e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.052
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.052
Order of pole (three term test) = 1.793e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.947
y[1] (closed_form) = 0.1072868245664083450267031542
y[1] (numeric) = 0.107286824566408345011620164062
absolute error = 1.5082990138e-20
relative error = 1.40585670225181642000000000001e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.053
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.053
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.946
y[1] (closed_form) = 0.107216576197319671368327966071
y[1] (numeric) = 0.107216576197319671352980155543
absolute error = 1.5347810528e-20
relative error = 1.43147739578571648000000000001e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.054
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.054
Order of pole (three term test) = 1.219e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.945
y[1] (closed_form) = 0.1071463968006085915338274568
y[1] (numeric) = 0.107146396800608591518215518735
absolute error = 1.5611938065e-20
relative error = 1.45706608259096625000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.055
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.055
Order of pole (three term test) = 6.155e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.944
y[1] (closed_form) = 0.107076286286011896603711521066
y[1] (numeric) = 0.10707628628601189658783614628
absolute error = 1.5875374786e-20
relative error = 1.48262284177424896000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.056
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.056
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.943
y[1] (closed_form) = 0.107006244563413987150048115358
y[1] (numeric) = 0.107006244563413987133909992634
absolute error = 1.6138122724e-20
relative error = 1.50814775248338276000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.057
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.057
Order of pole (three term test) = 6.277e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.942
y[1] (closed_form) = 0.106936271542846583664158512063
y[1] (numeric) = 0.10693627154284658364775832816
absolute error = 1.6400183903e-20
relative error = 1.53364089343893692000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.058
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.058
Order of pole (three term test) = 6.339e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.941
y[1] (closed_form) = 0.106866367134488437646841067591
y[1] (numeric) = 0.106866367134488437630179507247
absolute error = 1.6661560344e-20
relative error = 1.55910234349333464000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.059
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.059
Order of pole (three term test) = 6.401e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.94
y[1] (closed_form) = 0.106796531248665043359391686958
y[1] (numeric) = 0.106796531248665043342469432901
absolute error = 1.6922254057e-20
relative error = 1.58453218088125200000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.06
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.06
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.939
y[1] (closed_form) = 0.106726763795848350233694258346
y[1] (numeric) = 0.106726763795848350216511991297
absolute error = 1.7182267049e-20
relative error = 1.60993048396623328999999999999e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.061
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.061
Order of pole (three term test) = 1.958e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.938
y[1] (closed_form) = 0.106657064686656475939659405596
y[1] (numeric) = 0.106657064686656475922217804278
absolute error = 1.7441601318e-20
relative error = 1.63529733067762392000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.062
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.062
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.937
y[1] (closed_form) = 0.106587433831853420108294964522
y[1] (numeric) = 0.106587433831853420090594705665
absolute error = 1.7700258857e-20
relative error = 1.66063279888349433000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.063
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.063
Order of pole (three term test) = 1.331e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.936
y[1] (closed_form) = 0.106517871142348778708696630286
y[1] (numeric) = 0.106517871142348778690738388634
absolute error = 1.7958241652e-20
relative error = 1.68593696620174592000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.064
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.064
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.935
y[1] (closed_form) = 0.106448376529197459077252248057
y[1] (numeric) = 0.106448376529197459059036696374
absolute error = 1.8215551683e-20
relative error = 1.71120991009230674999999999999e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.065
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.065
Order of pole (three term test) = 6.789e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.934
y[1] (closed_form) = 0.10637894990359939559735822771
y[1] (numeric) = 0.106378949903599395578886036788
absolute error = 1.8472190922e-20
relative error = 1.73645170766768231999999999999e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.066
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.066
Order of pole (three term test) = 1.371e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.933
y[1] (closed_form) = 0.10630959117689926602795155557
y[1] (numeric) = 0.106309591176899266009223394234
absolute error = 1.8728161336e-20
relative error = 1.76166243597309304000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.067
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.067
Order of pole (three term test) = 1.385e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.932
y[1] (closed_form) = 0.106240300260586208479165852158
y[1] (numeric) = 0.106240300260586208460182387272
absolute error = 1.8983464886e-20
relative error = 1.78684217189120863999999999999e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.068
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.068
Order of pole (three term test) = 1.398e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.931
y[1] (closed_form) = 0.106171077066293539033424884653
y[1] (numeric) = 0.106171077066293539014186781128
absolute error = 1.9238103525e-20
relative error = 1.81199099195232525000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.069
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.069
Order of pole (three term test) = 1.412e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.93
y[1] (closed_form) = 0.106101921505798470010291886386
y[1] (numeric) = 0.106101921505798469990799807185
absolute error = 1.9492079201e-20
relative error = 1.83710897261504900000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.07
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.07
Order of pole (three term test) = 7.129e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.929
y[1] (closed_form) = 0.106032833491021828873397963173
y[1] (numeric) = 0.106032833491021828853652569318
absolute error = 1.9745393855e-20
relative error = 1.86219619007653055000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.071
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.071
Order of pole (three term test) = 1.440e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.928
y[1] (closed_form) = 0.105963812934027777777777777778
y[1] (numeric) = 0.105963812934027777757779728356
absolute error = 1.9998049422e-20
relative error = 1.88725272036507648000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.072
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.072
Order of pole (three term test) = 1.454e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.927
y[1] (closed_form) = 0.105894859747023533755945599269
y[1] (numeric) = 0.105894859747023533735695551439
absolute error = 2.0250047830e-20
relative error = 1.91227863924426070000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.073
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.073
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.926
y[1] (closed_form) = 0.105825973842359089541049683601
y[1] (numeric) = 0.105825973842359089520548292599
absolute error = 2.0501391002e-20
relative error = 1.93727402240014952000000000001e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.074
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.074
Order of pole (three term test) = 1.483e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.925
y[1] (closed_form) = 0.105757155132526935025447815454
y[1] (numeric) = 0.105757155132526935004695734599
absolute error = 2.0752080855e-20
relative error = 1.96223894534559375000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.075
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.075
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.924
y[1] (closed_form) = 0.105688403530161779353051689239
y[1] (numeric) = 0.105688403530161779332049569942
absolute error = 2.1002119297e-20
relative error = 1.98717348313491472000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.076
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.076
Order of pole (three term test) = 1.512e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.923
y[1] (closed_form) = 0.105619718948040273643792639341
y[1] (numeric) = 0.105619718948040273622541131108
absolute error = 2.1251508233e-20
relative error = 2.01207771092959456999999999999e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.077
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.077
Order of pole (three term test) = 1.527e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.922
y[1] (closed_form) = 0.105551101299080734348566046069
y[1] (numeric) = 0.105551101299080734327065796509
absolute error = 2.1500249560e-20
relative error = 2.03695170352403039999999999999e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.078
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.078
Order of pole (three term test) = 1.542e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.921
y[1] (closed_form) = 0.105482550496342867233016544622
y[1] (numeric) = 0.105482550496342867211268199454
absolute error = 2.1748345168e-20
relative error = 2.06179553543825487999999999999e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.079
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.079
Order of pole (three term test) = 7.783e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.92
y[1] (closed_form) = 0.10541406645302749198853094957
y[1] (numeric) = 0.105414066453027491966535152627
absolute error = 2.1995796943e-20
relative error = 2.08660928120075200000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.08
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.08
Order of pole (three term test) = 7.860e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.919
y[1] (closed_form) = 0.10534564908247626746881057704
y[1] (numeric) = 0.105345649082476267446567970275
absolute error = 2.2242606765e-20
relative error = 2.11139301515775165000000000001e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.081
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.081
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.918
y[1] (closed_form) = 0.105277298298171417550399401014
y[1] (numeric) = 0.105277298298171417527910624508
absolute error = 2.2488776506e-20
relative error = 2.13614681128178344000000000001e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.082
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.082
Order of pole (three term test) = 8.014e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.917
y[1] (closed_form) = 0.105209014013735457615549218934
y[1] (numeric) = 0.1052090140137354575928149109
absolute error = 2.2734308034e-20
relative error = 2.16087074354978225999999999999e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.083
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.083
Order of pole (three term test) = 1.619e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.916
y[1] (closed_form) = 0.105140796142930921655807725241
y[1] (numeric) = 0.105140796142930921632828522033
absolute error = 2.2979203208e-20
relative error = 2.18556488546667648000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.084
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.084
Order of pole (three term test) = 8.172e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.915
y[1] (closed_form) = 0.105072644599660089994720099609
y[1] (numeric) = 0.105072644599660089971496635724
absolute error = 2.3223463885e-20
relative error = 2.21022931072919125000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.085
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.085
Order of pole (three term test) = 2.475e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.914
y[1] (closed_form) = 0.105004559297964717628039409471
y[1] (numeric) = 0.105004559297964717604572317559
absolute error = 2.3467091912e-20
relative error = 2.23486409246373152000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.086
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.086
Order of pole (three term test) = 8.332e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.913
y[1] (closed_form) = 0.104936540152025763179845804149
y[1] (numeric) = 0.104936540152025763156135715016
absolute error = 2.3710089133e-20
relative error = 2.25946930389073677000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.087
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.087
Order of pole (three term test) = 1.683e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.912
y[1] (closed_form) = 0.10486858707616311847297914038
y[1] (numeric) = 0.104868587076163118449026682995
absolute error = 2.3952457385e-20
relative error = 2.28404501794269439999999999999e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.088
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.088
Order of pole (three term test) = 1.699e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.911
y[1] (closed_form) = 0.104800699984835338712194326488
y[1] (numeric) = 0.104800699984835338688000127992
absolute error = 2.4194198496e-20
relative error = 2.30859130707150816000000000001e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.089
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.089
Order of pole (three term test) = 8.579e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.91
y[1] (closed_form) = 0.104732878792639373278453304846
y[1] (numeric) = 0.104732878792639373254017990551
absolute error = 2.4435314295e-20
relative error = 2.33310824420089500000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.09
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.09
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.909
y[1] (closed_form) = 0.104665123414310297132772209651
y[1] (numeric) = 0.104665123414310297108096403053
absolute error = 2.4675806598e-20
relative error = 2.35759590138946038000000000001e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.091
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.091
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.908
y[1] (closed_form) = 0.104597433764721042828046839568
y[1] (numeric) = 0.104597433764721042803131162347
absolute error = 2.4915677221e-20
relative error = 2.38205435106990543999999999999e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.092
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.092
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.907
y[1] (closed_form) = 0.104529809758882133127284172337
y[1] (numeric) = 0.104529809758882133102129244368
absolute error = 2.5154927969e-20
relative error = 2.40648366499705880999999999999e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.093
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.093
Order of pole (three term test) = 8.918e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.906
y[1] (closed_form) = 0.104462251311941414226672221273
y[1] (numeric) = 0.104462251311941414201278660628
absolute error = 2.5393560645e-20
relative error = 2.43088391510639219999999999999e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.094
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.094
Order of pole (three term test) = 1.801e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.905
y[1] (closed_form) = 0.104394758339183789581925091541
y[1] (numeric) = 0.104394758339183789556293514497
absolute error = 2.5631577044e-20
relative error = 2.45525517293902100000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.095
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.095
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.904
y[1] (closed_form) = 0.104327330756030954336344637408
y[1] (numeric) = 0.104327330756030954310475658452
absolute error = 2.5868978956e-20
relative error = 2.47959750992714496000000000001e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.096
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.096
Order of pole (three term test) = 1.836e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.903
y[1] (closed_form) = 0.10425996847804113034904465027
y[1] (numeric) = 0.104259968478041130322938882104
absolute error = 2.6105768166e-20
relative error = 2.50391099739285894000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.097
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.097
Order of pole (three term test) = 9.271e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.902
y[1] (closed_form) = 0.10419267142090880182178802126
y[1] (numeric) = 0.104192671420908801795446074809
absolute error = 2.6341946451e-20
relative error = 2.52819570625903404000000000001e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.098
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.098
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.901
y[1] (closed_form) = 0.104125439500464451522891821686
y[1] (numeric) = 0.104125439500464451496314306101
absolute error = 2.6577515585e-20
relative error = 2.55245170752738585000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.099
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.099
Order of pole (three term test) = 9.452e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.9
y[1] (closed_form) = 0.104058272632674297606659729448
y[1] (numeric) = 0.104058272632674297579847252115
absolute error = 2.6812477333e-20
relative error = 2.57667907170130000000000000001e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.1
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.1
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.899
y[1] (closed_form) = 0.103991170733640031026805700089
y[1] (numeric) = 0.10399117073364003099975886663
absolute error = 2.7046833459e-20
relative error = 2.60087786955269259000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.101
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.101
Order of pole (three term test) = 9.637e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.898
y[1] (closed_form) = 0.10392413371959855354233723714
y[1] (numeric) = 0.103924133719598553515056651423
absolute error = 2.7280585717e-20
relative error = 2.62504817125603667999999999999e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.102
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.102
Order of pole (three term test) = 9.731e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.897
y[1] (closed_form) = 0.103857161506921716314371058166
y[1] (numeric) = 0.10385716150692171628685732231
absolute error = 2.7513735856e-20
relative error = 2.64919004686704304000000000001e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.103
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.103
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.896
y[1] (closed_form) = 0.103790254012116059092358380274
y[1] (numeric) = 0.103790254012116059064612094652
absolute error = 2.7746285622e-20
relative error = 2.67330356651415552000000000001e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.104
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.104
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.895
y[1] (closed_form) = 0.103723411151822549988201461981
y[1] (numeric) = 0.103723411151822549960223225228
absolute error = 2.7978236753e-20
relative error = 2.69738879991591825000000000001e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.105
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.105
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.894
y[1] (closed_form) = 0.103656632842816325836747437297
y[1] (numeric) = 0.103656632842816325808537846315
absolute error = 2.8209590982e-20
relative error = 2.72144581666825752000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.106
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.106
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.893
y[1] (closed_form) = 0.103589919002006433141149862603
y[1] (numeric) = 0.103589919002006433112709512567
absolute error = 2.8440350036e-20
relative error = 2.74547468614674164000000000001e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.107
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.107
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.892
y[1] (closed_form) = 0.103523269546435569601592767616
y[1] (numeric) = 0.103523269546435569572922251977
absolute error = 2.8670515639e-20
relative error = 2.76947547779485296000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.108
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.108
Order of pole (three term test) = 1.031e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.891
y[1] (closed_form) = 0.103456684393279826225876358296
y[1] (numeric) = 0.10345668439327982619697626879
absolute error = 2.8900089506e-20
relative error = 2.79344826054344785999999999999e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.109
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.109
Order of pole (three term test) = 1.041e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.89
y[1] (closed_form) = 0.103390163459848430020367862202
y[1] (numeric) = 0.103390163459848429991238788855
absolute error = 2.9129073347e-20
relative error = 2.81739310319518699999999999999e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.11
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.11
Order of pole (three term test) = 1.051e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.889
y[1] (closed_form) = 0.103323706663583487259825335407
y[1] (numeric) = 0.103323706663583487230467866539
absolute error = 2.9357468868e-20
relative error = 2.84131007452010628000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.111
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.111
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.888
y[1] (closed_form) = 0.103257313922059727334606564852
y[1] (numeric) = 0.103257313922059727305021287082
absolute error = 2.9585277770e-20
relative error = 2.86519924315786880000000000001e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.112
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.112
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.887
y[1] (closed_form) = 0.103190985152984247173779500884
y[1] (numeric) = 0.103190985152984247143966999137
absolute error = 2.9812501747e-20
relative error = 2.88906067742273442999999999999e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.113
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.113
Order of pole (three term test) = 1.082e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.886
y[1] (closed_form) = 0.103124720274196256242654941798
y[1] (numeric) = 0.103124720274196256212615799311
absolute error = 3.0039142487e-20
relative error = 2.91289444539869052000000000001e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.114
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.114
Order of pole (three term test) = 1.093e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.885
y[1] (closed_form) = 0.103058519203666822113266465531
y[1] (numeric) = 0.103058519203666822083001263855
absolute error = 3.0265201676e-20
relative error = 2.93670061532605099999999999999e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.115
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.115
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.884
y[1] (closed_form) = 0.102992381859498616606326863215
y[1] (numeric) = 0.102992381859498616575836182225
absolute error = 3.0490680990e-20
relative error = 2.96047925482441439999999999999e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.116
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.116
Order of pole (three term test) = 1.114e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.883
y[1] (closed_form) = 0.102926308159925662503194575289
y[1] (numeric) = 0.102926308159925662472478993188
absolute error = 3.0715582101e-20
relative error = 2.98423043147282589000000000001e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.117
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.117
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.882
y[1] (closed_form) = 0.102860298023313080826387863143
y[1] (numeric) = 0.102860298023313080795447956463
absolute error = 3.0939906680e-20
relative error = 3.00795421310052320000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.118
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.118
Order of pole (three term test) = 1.135e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.881
y[1] (closed_form) = 0.102794351368156838687188668033
y[1] (numeric) = 0.102794351368156838656025011646
absolute error = 3.1163656387e-20
relative error = 3.03165066681414307000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.119
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.119
Order of pole (three term test) = 1.146e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.88
y[1] (closed_form) = 0.102728468113083497698882314267
y[1] (numeric) = 0.102728468113083497667495481388
absolute error = 3.1386832879e-20
relative error = 3.05531985977337600000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.12
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.12
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.879
y[1] (closed_form) = 0.102662648176849962954183405384
y[1] (numeric) = 0.102662648176849962922573967576
absolute error = 3.1609437808e-20
relative error = 3.07896185899554927999999999999e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.121
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.121
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.878
y[1] (closed_form) = 0.102596891478343232565402440411
y[1] (numeric) = 0.102596891478343232533570967592
absolute error = 3.1831472819e-20
relative error = 3.10257673115945995999999999999e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.122
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.122
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.877
y[1] (closed_form) = 0.10253119793658014776591184224
y[1] (numeric) = 0.102531197936580147733858902687
absolute error = 3.2052939553e-20
relative error = 3.12616454289611337000000000002e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.123
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.123
Order of pole (three term test) = 1.191e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.876
y[1] (closed_form) = 0.102465567470707143571474241796
y[1] (numeric) = 0.102465567470707143539200402148
absolute error = 3.2273839648e-20
relative error = 3.14972536088539647999999999999e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.124
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.124
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.875
y[1] (closed_form) = 0.1024
y[1] (numeric) = 0.102399999999999999967505825268
absolute error = 3.2494174732e-20
relative error = 3.17325925117187500000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.125
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.125
Order of pole (three term test) = 1.214e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.874
y[1] (closed_form) = 0.102334495443863593848305074686
y[1] (numeric) = 0.102334495443863593815591128254
absolute error = 3.2713946432e-20
relative error = 3.19676628004146431999999999999e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
memory used=55.1MB, alloc=44.3MB, time=0.44
Radius of convergence (given) for eq 1 = 3.126
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.126
Order of pole (three term test) = 1.226e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.873
y[1] (closed_form) = 0.10226905372183165102444445149
y[1] (numeric) = 0.102269053721831650991511295123
absolute error = 3.2933156367e-20
relative error = 3.22024651333697342999999999999e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.127
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.127
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.872
y[1] (closed_form) = 0.102203674753566499434200456564
y[1] (numeric) = 0.102203674753566499401048650412
absolute error = 3.3151806152e-20
relative error = 3.24370001684730368000000000001e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.128
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.128
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.871
y[1] (closed_form) = 0.102138358458858822420309354617
y[1] (numeric) = 0.102138358458858822386939457219
absolute error = 3.3369897398e-20
relative error = 3.26712685630652118000000000001e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.129
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.129
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.87
y[1] (closed_form) = 0.102073104757627412753013708418
y[1] (numeric) = 0.102073104757627412719426276709
absolute error = 3.3587431709e-20
relative error = 3.29052709709902100000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.13
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.13
Order of pole (three term test) = 1.274e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.869
y[1] (closed_form) = 0.102007913569918927170532035534
y[1] (numeric) = 0.102007913569918927136727624851
absolute error = 3.3804410683e-20
relative error = 3.31390080435568963000000000001e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.131
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.131
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.868
y[1] (closed_form) = 0.101942784815907641468041344731
y[1] (numeric) = 0.101942784815907641434020508815
absolute error = 3.4020835916e-20
relative error = 3.33724804334472384000000000001e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.132
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.132
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.867
y[1] (closed_form) = 0.101877718415895206133772168209
y[1] (numeric) = 0.101877718415895206099535459212
absolute error = 3.4236708997e-20
relative error = 3.36056887898053933000000000002e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.133
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.133
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.866
y[1] (closed_form) = 0.101812714290310402530819726743
y[1] (numeric) = 0.101812714290310402496367695232
absolute error = 3.4452031511e-20
relative error = 3.38386337611655515999999999999e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.134
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.134
Order of pole (three term test) = 1.324e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.865
y[1] (closed_form) = 0.101747772359708899623278872838
y[1] (numeric) = 0.101747772359708899588612067803
absolute error = 3.4666805035e-20
relative error = 3.40713159915112875000000000001e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.135
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.135
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.864
y[1] (closed_form) = 0.101682892544773011245314452312
y[1] (numeric) = 0.101682892544773011210433421166
absolute error = 3.4881031146e-20
relative error = 3.43037361281212415999999999998e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.136
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.136
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.863
y[1] (closed_form) = 0.101618074766311453911782707225
y[1] (numeric) = 0.101618074766311453876687995815
absolute error = 3.5094711410e-20
relative error = 3.45358948107474290000000000001e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.137
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.137
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.862
y[1] (closed_form) = 0.101553318945259105169023312986
y[1] (numeric) = 0.101553318945259105133715465592
absolute error = 3.5307847394e-20
relative error = 3.47677926834003336000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.138
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.138
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.861
y[1] (closed_form) = 0.10148862500267676248444559961
y[1] (numeric) = 0.101488625002676762448925158954
absolute error = 3.5520440656e-20
relative error = 3.49994303845018576000000000002e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.139
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.139
Order of pole (three term test) = 1.389e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.86
y[1] (closed_form) = 0.101423992859750902673536451783
y[1] (numeric) = 0.101423992859750902637803959032
absolute error = 3.5732492751e-20
relative error = 3.52308085527759600000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.14
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.14
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.859
y[1] (closed_form) = 0.101359422437793441862921314376
y[1] (numeric) = 0.10135942243779344182697730915
absolute error = 3.5944005226e-20
relative error = 3.54619278223094106000000000001e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.141
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.141
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.858
y[1] (closed_form) = 0.101294913658241495988113649652
y[1] (numeric) = 0.101294913658241495951958670024
absolute error = 3.6154979628e-20
relative error = 3.56927888304274991999999999999e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.142
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.142
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.857
y[1] (closed_form) = 0.101230466442657141824592099428
y[1] (numeric) = 0.101230466442657141788226681933
absolute error = 3.6365417495e-20
relative error = 3.59233922088065254999999999999e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.143
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.143
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.856
y[1] (closed_form) = 0.101166080712727178550848500152
y[1] (numeric) = 0.101166080712727178514273179791
absolute error = 3.6575320361e-20
relative error = 3.61537385883909696000000000001e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.144
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.144
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.855
y[1] (closed_form) = 0.101101756390262889842053781079
y[1] (numeric) = 0.101101756390262889805269091322
absolute error = 3.6784689757e-20
relative error = 3.63838286003730925000000000001e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.145
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.145
Order of pole (three term test) = 1.471e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.854
y[1] (closed_form) = 0.101037493397199806492992645683
y[1] (numeric) = 0.101037493397199806455999118475
absolute error = 3.6993527208e-20
relative error = 3.66136628732173728000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.146
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.146
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.853
y[1] (closed_form) = 0.100973291655597469568921794065
y[1] (numeric) = 0.100973291655597469531719959832
absolute error = 3.7201834233e-20
relative error = 3.68432420326446897000000000001e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.147
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.147
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.852
y[1] (closed_form) = 0.100909151087639194083010289504
y[1] (numeric) = 0.100909151087639194045600677157
absolute error = 3.7409612347e-20
relative error = 3.70725667035984688000000000001e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.148
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.148
Order of pole (three term test) = 1.513e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.851
y[1] (closed_form) = 0.100845071615631833199024505453
y[1] (numeric) = 0.100845071615631833161407642391
absolute error = 3.7616863062e-20
relative error = 3.73016375112267462000000000001e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.149
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.149
Order of pole (three term test) = 1.528e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.85
y[1] (closed_form) = 0.100781053162005542957923910305
y[1] (numeric) = 0.100781053162005542920100322423
absolute error = 3.7823587882e-20
relative error = 3.75304550759144999999999999999e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.15
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.15
Order of pole (three term test) = 1.542e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.849
y[1] (closed_form) = 0.10071709564931354752703775612
y[1] (numeric) = 0.100717095649313547489007967812
absolute error = 3.8029788308e-20
relative error = 3.77590200182258707999999999999e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.151
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.151
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.848
y[1] (closed_form) = 0.100653199000231904970496534309
y[1] (numeric) = 0.100653199000231904932261068473
absolute error = 3.8235465836e-20
relative error = 3.79873329569106944000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.152
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.152
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.847
y[1] (closed_form) = 0.100589363137559273539595846022
y[1] (numeric) = 0.100589363137559273501155224064
absolute error = 3.8440621958e-20
relative error = 3.82153945098858821999999999998e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.153
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.153
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.846
y[1] (closed_form) = 0.100525587984216678481774107745
y[1] (numeric) = 0.100525587984216678443128849586
absolute error = 3.8645258159e-20
relative error = 3.84432052912414844000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.154
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.154
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.845
y[1] (closed_form) = 0.100461873463247279366889273435
y[1] (numeric) = 0.100461873463247279328039897512
absolute error = 3.8849375923e-20
relative error = 3.86707659171940074999999999999e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.155
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.155
Order of pole (three term test) = 1.618e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.844
y[1] (closed_form) = 0.100398219497816137929483503368
y[1] (numeric) = 0.100398219497816137890430526643
absolute error = 3.9052976725e-20
relative error = 3.88980769981179599999999999999e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.156
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.156
Order of pole (three term test) = 1.633e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.843
y[1] (closed_form) = 0.100334626011209986425728446943
y[1] (numeric) = 0.100334626011209986386472384905
absolute error = 3.9256062038e-20
relative error = 3.91251391454970662000000000002e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.157
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.157
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.842
y[1] (closed_form) = 0.100271092926836996503747531827
y[1] (numeric) = 0.100271092926836996464288898495
absolute error = 3.9458633332e-20
relative error = 3.93519529709236048000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.158
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.158
Order of pole (three term test) = 1.664e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.841
y[1] (closed_form) = 0.100207620168226548586015365235
y[1] (numeric) = 0.100207620168226548546354673167
absolute error = 3.9660692068e-20
relative error = 3.95785190801043108000000000001e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.159
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.159
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.84
y[1] (closed_form) = 0.100144207659029001762538054799
y[1] (numeric) = 0.100144207659029001722675815094
absolute error = 3.9862239705e-20
relative error = 3.98048380798248000000000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.16
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.16
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.839
y[1] (closed_form) = 0.100080855323015464193521946381
y[1] (numeric) = 0.100080855323015464153458668684
absolute error = 4.0063277697e-20
relative error = 4.00309105749485936999999999998e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.161
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.161
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.838
y[1] (closed_form) = 0.100017563084077564020241954487
y[1] (numeric) = 0.100017563084077563979978146995
absolute error = 4.0263807492e-20
relative error = 4.02567371674044048000000000001e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.162
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.162
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.837
y[1] (closed_form) = 0.0999543308662272207828243275647
y[1] (numeric) = 0.0999543308662272207423604970272
absolute error = 4.04638305375e-20
relative error = 4.04823184616725837500000000000e-17 %
Desired digits = 12
Estimated correct digits = 13
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.163
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.163
Order of pole (three term test) = 1.745e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.836
y[1] (closed_form) = 0.0998911585935964173436623455082
y[1] (numeric) = 0.0998911585935964173029989972361
absolute error = 4.06633482721e-20
relative error = 4.07076550563772801600000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.164
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.164
Order of pole (three term test) = 1.762e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.835
y[1] (closed_form) = 0.099828046190436972315187090237
y[1] (numeric) = 0.0998280461904369722743247281052
absolute error = 4.08623621318e-20
relative error = 4.09327475505720255000000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.165
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.165
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.834
y[1] (closed_form) = 0.0997649935811203129907190621772
y[1] (numeric) = 0.0997649935811203129496581886295
absolute error = 4.10608735477e-20
relative error = 4.11575965414289621200000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.166
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.166
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.833
y[1] (closed_form) = 0.0997020006901372487771300360354
y[1] (numeric) = 0.0997020006901372487358711520892
absolute error = 4.12588839462e-20
relative error = 4.13822026244267971800000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.167
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.167
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.832
y[1] (closed_form) = 0.0996390674420977451280481583513
y[1] (numeric) = 0.0996390674420977450865917636017
absolute error = 4.14563947496e-20
relative error = 4.16065663939409510400000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.168
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.168
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.831
y[1] (closed_form) = 0.0995761937617306979763428870385
y[1] (numeric) = 0.0995761937617306979346894796631
absolute error = 4.16534073754e-20
relative error = 4.18306884425304399400000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.169
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.169
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.83
y[1] (closed_form) = 0.0995133795738837086646299594981
y[1] (numeric) = 0.0995133795738837086227800362612
absolute error = 4.18499232369e-20
relative error = 4.20545693615284410000000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.17
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.17
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.829
y[1] (closed_form) = 0.0994506248035228593725401509521
y[1] (numeric) = 0.0994506248035228593304942072094
absolute error = 4.20459437427e-20
relative error = 4.22782097405290490700000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.171
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.171
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.828
y[1] (closed_form) = 0.0993879293757324890394991484442
y[1] (numeric) = 0.099387929375732488997257678147
absolute error = 4.22414702972e-20
relative error = 4.25016101678782764800000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.172
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.172
Order of pole (three term test) = 1.901e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.827
y[1] (closed_form) = 0.0993252932157149697817694185169
y[1] (numeric) = 0.0993252932157149697393329142167
absolute error = 4.24365043002e-20
relative error = 4.27247712302608285800000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.173
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.173
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.826
y[1] (closed_form) = 0.0992627162487904838025084879549
y[1] (numeric) = 0.0992627162487904837598774408077
absolute error = 4.26310471472e-20
relative error = 4.29476935129905427200000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.174
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.174
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.825
y[1] (closed_form) = 0.0992001984003968007936015872031
y[1] (numeric) = 0.0992001984003968007507764869741
absolute error = 4.28251002290e-20
relative error = 4.31703775995963125000000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.175
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.175
Order of pole (three term test) = 1.955e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.824
y[1] (closed_form) = 0.0991377395960890558280301251832
y[1] (numeric) = 0.0991377395960890557850114602505
absolute error = 4.30186649327e-20
relative error = 4.33928240728186515200000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.176
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.176
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.823
y[1] (closed_form) = 0.09907533976153952774154097226
y[1] (numeric) = 0.0990753397615395276983292296197
absolute error = 4.32117426403e-20
relative error = 4.36150335131876558700000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.177
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.177
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.822
y[1] (closed_form) = 0.0990129988225374180023850251155
y[1] (numeric) = 0.0990129988225374179589806903858
absolute error = 4.34043347297e-20
relative error = 4.38370065000195414800000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.178
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.178
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.821
y[1] (closed_form) = 0.0989507167049886300678970132815
y[1] (numeric) = 0.0989507167049886300243005707064
absolute error = 4.35964425751e-20
relative error = 4.40587436118106179100000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.179
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.179
Order of pole (three term test) = 2.030e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.82
y[1] (closed_form) = 0.0988884933349155492266919821211
y[1] (numeric) = 0.0988884933349155491829039145758
absolute error = 4.37880675453e-20
relative error = 4.42802454245091719999999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.18
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.18
Order of pole (three term test) = 2.050e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.819
y[1] (closed_form) = 0.0988263286384568229252573511716
y[1] (numeric) = 0.0988263286384568228812781401665
absolute error = 4.39792110051e-20
relative error = 4.45015125129176681100000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.181
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.181
Order of pole (three term test) = 2.069e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.818
y[1] (closed_form) = 0.0987642225418671415777228999862
y[1] (numeric) = 0.0987642225418671415335530256702
absolute error = 4.41698743160e-20
relative error = 4.47225454513915184000000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.182
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.182
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.817
y[1] (closed_form) = 0.0987021749715170198575944759947
y[1] (numeric) = 0.0987021749715170198132344171606
absolute error = 4.43600588341e-20
relative error = 4.49433448117036974900000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.183
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.183
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.816
y[1] (closed_form) = 0.0986401858538925784702406504887
y[1] (numeric) = 0.0986401858538925784256908845773
absolute error = 4.45497659114e-20
relative error = 4.51639111643481958400000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.184
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.184
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.815
y[1] (closed_form) = 0.0985782551155953264049249696254
y[1] (numeric) = 0.0985782551155953263601859727296
absolute error = 4.47389968958e-20
relative error = 4.53842450785296755000000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.185
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.185
Order of pole (three term test) = 2.149e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.814
y[1] (closed_form) = 0.0985163826833419436651798574193
y[1] (numeric) = 0.0985163826833419436202521042875
absolute error = 4.49277531318e-20
relative error = 4.56043471228636552800000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.186
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.186
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.813
y[1] (closed_form) = 0.0984545684839640644763216270524
y[1] (numeric) = 0.0984545684839640644312055910942
absolute error = 4.51160359582e-20
relative error = 4.58242178630322695800000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.187
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.187
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.812
y[1] (closed_form) = 0.0983928124444080609689094455527
y[1] (numeric) = 0.0983928124444080609236055988421
absolute error = 4.53038467106e-20
relative error = 4.60438578643096246399999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.188
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.188
Order of pole (three term test) = 4.420e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.811
y[1] (closed_form) = 0.0983311144917348273369544749555
y[1] (numeric) = 0.0983311144917348272914632882357
absolute error = 4.54911867198e-20
relative error = 4.62632676899271175800000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.189
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.189
Order of pole (three term test) = 4.462e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.81
y[1] (closed_form) = 0.098269474553119564469688780574
y[1] (numeric) = 0.0982694745531195644240107232607
absolute error = 4.56780573133e-20
relative error = 4.64824479025872130000000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.19
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.19
Order of pole (three term test) = 4.504e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.809
y[1] (closed_form) = 0.0982078925558515650557069539339
y[1] (numeric) = 0.0982078925558515650098424941202
absolute error = 4.58644598137e-20
relative error = 4.67013990628263789700000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.191
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.191
Order of pole (three term test) = 9.094e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.808
y[1] (closed_form) = 0.0981463684273339991582967443672
y[1] (numeric) = 0.0981463684273339991122463488275
absolute error = 4.60503955397e-20
relative error = 4.69201217300209900800000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.192
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.192
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.807
y[1] (closed_form) = 0.0980849020950837002607783292001
y[1] (numeric) = 0.0980849020950837002145424633944
absolute error = 4.62358658057e-20
relative error = 4.71386164619697119300000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.193
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.193
Order of pole (three term test) = 6.950e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.806
y[1] (closed_form) = 0.0980234934867309517806751779812
y[1] (numeric) = 0.0980234934867309517342543060588
absolute error = 4.64208719224e-20
relative error = 4.73568838154945046400000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.194
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.194
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.805
y[1] (closed_form) = 0.097962142530019274051542781292
y[1] (numeric) = 0.0979621425300192740049373660961
absolute error = 4.66054151959e-20
relative error = 4.75749243455127097500000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.195
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.195
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.804
y[1] (closed_form) = 0.0979008491528052117712848194161
y[1] (numeric) = 0.0979008491528052117244953224872
absolute error = 4.67894969289e-20
relative error = 4.77927386062507022400000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.196
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.196
Order of pole (three term test) = 2.383e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.803
y[1] (closed_form) = 0.0978396132830581219157896405264
y[1] (numeric) = 0.0978396132830581218688165221076
absolute error = 4.69731184188e-20
relative error = 4.80103271492936809200000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.197
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.197
Order of pole (three term test) = 4.811e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.802
y[1] (closed_form) = 0.0977784348488599621167232021576
y[1] (numeric) = 0.0977784348488599620695669211972
absolute error = 4.71562809604e-20
relative error = 4.82276905263326721600000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.198
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.198
Order of pole (three term test) = 2.428e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.801
y[1] (closed_form) = 0.0977173137784050795023179035414
y[1] (numeric) = 0.0977173137784050794549789176978
absolute error = 4.73389858436e-20
relative error = 4.84448292868050803600000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.199
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.199
Order of pole (three term test) = 2.451e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.8
y[1] (closed_form) = 0.09765625
y[1] (numeric) = 0.0976562499999999999524787656454
absolute error = 4.75212343546e-20
relative error = 4.86617439791104000000000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.2
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.2
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.799
y[1] (closed_form) = 0.0975952434420632180997015439859
y[1] (numeric) = 0.0975952434420632180519985162108
absolute error = 4.77030277751e-20
relative error = 4.88784351497812415100000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.201
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.201
Order of pole (three term test) = 2.497e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.798
y[1] (closed_form) = 0.0975342940331249870767060406109
y[1] (numeric) = 0.0975342940331249870288216732273
absolute error = 4.78843673836e-20
relative error = 4.90949033448043614400000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.202
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.202
Order of pole (three term test) = 2.521e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.797
y[1] (closed_form) = 0.0974734017018271096728802386225
y[1] (numeric) = 0.0974734017018271096248149841688
absolute error = 4.80652544537e-20
relative error = 4.93111491078689123300000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.203
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.203
Order of pole (three term test) = 2.544e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.796
y[1] (closed_form) = 0.0974125663769227292351477008296
y[1] (numeric) = 0.0974125663769227291869020105736
absolute error = 4.82456902560e-20
relative error = 4.95271729823037696000000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.204
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.204
Order of pole (three term test) = 1.027e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.795
y[1] (closed_form) = 0.0973517879872761213100630109448
y[1] (numeric) = 0.0973517879872761212616373348885
absolute error = 4.84256760563e-20
relative error = 4.97429755092215007500000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.205
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.205
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.794
y[1] (closed_form) = 0.0972910664618624856933486767832
y[1] (numeric) = 0.0972910664618624856447434636664
absolute error = 4.86052131168e-20
relative error = 4.99585572287389324800000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.206
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.206
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.793
y[1] (closed_form) = 0.0972304017297677389332599827181
y[1] (numeric) = 0.0972304017297677388844756800226
absolute error = 4.87843026955e-20
relative error = 5.01739186793510479500000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.207
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.207
Order of pole (three term test) = 2.642e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.792
y[1] (closed_form) = 0.0971697937201883072866462273245
y[1] (numeric) = 0.097169793720188307237683281277
absolute error = 4.89629460475e-20
relative error = 5.03890603992579040000000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.208
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.208
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.791
y[1] (closed_form) = 0.0971092423624309201265799552347
y[1] (numeric) = 0.0971092423624309200774388108121
absolute error = 4.91411444226e-20
relative error = 5.06039829238863990599999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.209
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.209
Order of pole (three term test) = 5.383e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.79
y[1] (closed_form) = 0.0970487475859124038004289554642
y[1] (numeric) = 0.097048747585912403751110056397
absolute error = 4.93188990672e-20
relative error = 5.08186867878335520000000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.21
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.21
Order of pole (three term test) = 2.717e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.789
y[1] (closed_form) = 0.0969883093201594759372489518231
y[1] (numeric) = 0.0969883093201594758877527405985
absolute error = 4.94962112246e-20
relative error = 5.10331725251674016600000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.211
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.211
Order of pole (three term test) = 2.742e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.788
y[1] (closed_form) = 0.0969279274948085402033780545866
y[1] (numeric) = 0.0969279274948085401537049724536
absolute error = 4.96730821330e-20
relative error = 5.12474406673561552000000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.212
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.212
Order of pole (three term test) = 2.768e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.787
y[1] (closed_form) = 0.0968676020396054815051171763791
y[1] (numeric) = 0.0968676020396054814552676633514
absolute error = 4.98495130277e-20
relative error = 5.14614917455254321300000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.213
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.213
Order of pole (three term test) = 8.382e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.786
y[1] (closed_form) = 0.0968073328844054616373837392337
y[1] (numeric) = 0.0968073328844054615873582340939
absolute error = 5.00255051398e-20
relative error = 5.16753262891085480799999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.214
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.214
Order of pole (three term test) = 8.460e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.785
y[1] (closed_form) = 0.0967471199591727153772291141107
y[1] (numeric) = 0.0967471199591727153270280544146
absolute error = 5.02010596961e-20
relative error = 5.18889448257321222500000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.215
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.215
Order of pole (three term test) = 2.847e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.784
y[1] (closed_form) = 0.0966869631939803470211133387786
y[1] (numeric) = 0.096686963193980346970737160858
absolute error = 5.03761779206e-20
relative error = 5.21023478827561113600000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.216
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.216
Order of pole (three term test) = 5.746e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.783
y[1] (closed_form) = 0.0966268625190101273648337549325
y[1] (numeric) = 0.0966268625190101273142828938995
absolute error = 5.05508610330e-20
relative error = 5.23155359857148937000000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.217
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.217
Order of pole (three term test) = 8.700e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.782
y[1] (closed_form) = 0.0965668178645522911250072907949
y[1] (numeric) = 0.096566817864552291074282180546
absolute error = 5.07251102489e-20
relative error = 5.25285096585129923599999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.218
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.218
Order of pole (three term test) = 2.927e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.781
y[1] (closed_form) = 0.096506829161005334801009191214
y[1] (numeric) = 0.0965068291610053347501102644337
absolute error = 5.08989267803e-20
relative error = 5.27412694239324168299999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.219
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.219
Order of pole (three term test) = 2.955e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.78
y[1] (closed_form) = 0.0964468963388758149762740635006
y[1] (numeric) = 0.096446896338875814925201751665
absolute error = 5.10723118356e-20
relative error = 5.29538158036235040000000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.22
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.22
Order of pole (three term test) = 8.947e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.779
y[1] (closed_form) = 0.0963870193287781470578681639556
y[1] (numeric) = 0.0963870193287781470066228973358
absolute error = 5.12452666198e-20
relative error = 5.31661493183032451799999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.221
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.221
Order of pole (three term test) = 6.021e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.778
y[1] (closed_form) = 0.0963271980614344044532448972595
y[1] (numeric) = 0.0963271980614344044018271049262
absolute error = 5.14177923333e-20
relative error = 5.33782704865009957199999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.222
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.222
Order of pole (three term test) = 3.038e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.777
y[1] (closed_form) = 0.0962674324676741181830985386699
y[1] (numeric) = 0.0962674324676741181315086484968
absolute error = 5.15898901731e-20
relative error = 5.35901798257925889900000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.223
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.223
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.776
y[1] (closed_form) = 0.0962077224784340769292342173154
y[1] (numeric) = 0.0962077224784340768774726559823
absolute error = 5.17615613331e-20
relative error = 5.38018778531036025600000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.224
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.224
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.775
y[1] (closed_form) = 0.0961480680247581275163752178353
y[1] (numeric) = 0.0961480680247581274644424108324
absolute error = 5.19328070029e-20
relative error = 5.40133650834536812500000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.225
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.225
Order of pole (three term test) = 3.124e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.774
y[1] (closed_form) = 0.0960884690377969758268316672232
y[1] (numeric) = 0.0960884690377969757747280388547
absolute error = 5.21036283685e-20
relative error = 5.42246420306735506000000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.226
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.226
Order of pole (three term test) = 6.307e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.773
y[1] (closed_form) = 0.0960289254488079881469576740028
y[1] (numeric) = 0.0960289254488079880946836473904
absolute error = 5.22740266124e-20
relative error = 5.44357092074999159600000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.227
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.227
Order of pole (three term test) = 6.366e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.772
y[1] (closed_form) = 0.0959694371891549929443269778535
y[1] (numeric) = 0.0959694371891549928918829749404
absolute error = 5.24440029131e-20
relative error = 5.46465671250455390399999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.228
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.228
Order of pole (three term test) = 1.285e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.771
y[1] (closed_form) = 0.0959100041903080830745601495274
y[1] (numeric) = 0.0959100041903080830219465910821
absolute error = 5.26135584453e-20
relative error = 5.48572162929972177300000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.229
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.229
Order of pole (three term test) = 3.243e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.77
y[1] (closed_form) = 0.0958506263838434184167393533916
y[1] (numeric) = 0.0958506263838434183639566590104
absolute error = 5.27826943812e-20
relative error = 5.50676572209621480000000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.23
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.23
Order of pole (three term test) = 3.273e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.769
y[1] (closed_form) = 0.0957913037014430289363496482207
y[1] (numeric) = 0.0957913037014430288833982363325
absolute error = 5.29514118882e-20
relative error = 5.52778904160611440200000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.231
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.231
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.768
y[1] (closed_form) = 0.0957320360748946181746887560043
y[1] (numeric) = 0.0957320360748946181215690438737
absolute error = 5.31197121306e-20
relative error = 5.54879163846912614400000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.232
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.232
Order of pole (three term test) = 1.667e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.767
y[1] (closed_form) = 0.0956728234360913671636901735113
y[1] (numeric) = 0.0956728234360913671104025772424
absolute error = 5.32875962689e-20
relative error = 5.56977356317864512100000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.233
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.233
Order of pole (three term test) = 6.731e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.766
y[1] (closed_form) = 0.0956136657170317387651074372517
y[1] (numeric) = 0.0956136657170317387116523717915
absolute error = 5.34550654602e-20
relative error = 5.59073486612259511200000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.234
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.234
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.765
y[1] (closed_form) = 0.0955545628498192824330102792822
y[1] (numeric) = 0.0955545628498192823793881584244
absolute error = 5.36221208578e-20
relative error = 5.61167559754070004999999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.235
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.235
Order of pole (three term test) = 6.857e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.764
y[1] (closed_form) = 0.095495514766662439398546329076
y[1] (numeric) = 0.0954955147666624393447575654644
absolute error = 5.37887636116e-20
relative error = 5.63259580756537273600000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.236
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.236
Order of pole (three term test) = 3.460e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.763
y[1] (closed_form) = 0.0954365213998743482759249254331
y[1] (numeric) = 0.095436521399874348221969930565
absolute error = 5.39549948681e-20
relative error = 5.65349554622084508900000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.237
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.237
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.762
y[1] (closed_form) = 0.0953775826818726510885825021813
y[1] (numeric) = 0.0953775826818726510344616864114
absolute error = 5.41208157699e-20
relative error = 5.67437486336987415600000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.238
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.238
Order of pole (three term test) = 1.410e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.761
y[1] (closed_form) = 0.0953186985451792997144919022476
y[1] (numeric) = 0.0953186985451792996602056747912
absolute error = 5.42862274564e-20
relative error = 5.69523380878614624400000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.239
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.239
Order of pole (three term test) = 1.067e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.76
y[1] (closed_form) = 0.0952598689224203627495808565769
y[1] (numeric) = 0.0952598689224203626951296255134
absolute error = 5.44512310635e-20
relative error = 5.71607243212197599999999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.24
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.24
Order of pole (three term test) = 1.077e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.759
y[1] (closed_form) = 0.0952010937463258327882277373909
y[1] (numeric) = 0.095201093746325832733611909668
absolute error = 5.46158277229e-20
relative error = 5.73689078283387154900000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.241
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.241
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.758
y[1] (closed_form) = 0.0951423729497294341198055594352
y[1] (numeric) = 0.0951423729497294340650255408715
absolute error = 5.47800185637e-20
relative error = 5.75768891034956926800000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.242
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.242
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.757
y[1] (closed_form) = 0.0950837064655684308402480581767
y[1] (numeric) = 0.0950837064655684307853042534654
absolute error = 5.49438047113e-20
relative error = 5.77846686395172953700000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.243
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.243
Order of pole (three term test) = 3.692e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.756
y[1] (closed_form) = 0.0950250942268834353776145204427
y[1] (numeric) = 0.095025094226883435322507333155
absolute error = 5.51071872877e-20
relative error = 5.79922469280853307199999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.244
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.244
Order of pole (three term test) = 7.453e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.755
y[1] (closed_form) = 0.0949665361668182174306328807387
y[1] (numeric) = 0.0949665361668182173753627133281
absolute error = 5.52701674106e-20
relative error = 5.81996244587803265000000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.245
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.245
Order of pole (three term test) = 3.761e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.754
y[1] (closed_form) = 0.0949080322186195133192034254966
y[1] (numeric) = 0.0949080322186195132637706793013
absolute error = 5.54327461953e-20
relative error = 5.84068017210717574800000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.246
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.246
Order of pole (three term test) = 7.592e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.753
y[1] (closed_form) = 0.0948495823156368357458482677952
y[1] (numeric) = 0.0948495823156368356902533430419
absolute error = 5.55949247533e-20
relative error = 5.86137792028364679700000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.247
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.247
Order of pole (three term test) = 3.831e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.752
y[1] (closed_form) = 0.0947911863913222839670945667208
y[1] (numeric) = 0.0947911863913222839113378625281
absolute error = 5.57567041927e-20
relative error = 5.88205573907705420800000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.248
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.248
Order of pole (three term test) = 3.867e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.751
y[1] (closed_form) = 0.0947328443792303543737822684934
y[1] (numeric) = 0.0947328443792303543178641828754
absolute error = 5.59180856180e-20
relative error = 5.90271367701693618000000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
memory used=98.8MB, alloc=44.3MB, time=0.78
Radius of convergence (given) for eq 1 = 3.249
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.249
Order of pole (three term test) = 1.171e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.75
y[1] (closed_form) = 0.0946745562130177514792899408283
y[1] (numeric) = 0.0946745562130177514232108706976
absolute error = 5.60790701307e-20
relative error = 5.92335178255518750000000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.25
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.25
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.749
y[1] (closed_form) = 0.0946163218264431993146750577468
y[1] (numeric) = 0.0946163218264431992584353989181
absolute error = 5.62396588287e-20
relative error = 5.94397010400189128699999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.251
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.251
Order of pole (three term test) = 1.590e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.748
y[1] (closed_form) = 0.0945581411533672532297278692343
y[1] (numeric) = 0.0945581411533672531733280164283
absolute error = 5.63998528060e-20
relative error = 5.96456868949264224000000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.252
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.252
Order of pole (three term test) = 1.605e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.747
y[1] (closed_form) = 0.0945000141277521120989407587916
y[1] (numeric) = 0.0945000141277521120423811056372
absolute error = 5.65596531544e-20
relative error = 5.98514758716739189600000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.253
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.253
Order of pole (three term test) = 4.050e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.746
y[1] (closed_form) = 0.094441940683661430931397752055
y[1] (numeric) = 0.0944419406836614308746786910938
absolute error = 5.67190609612e-20
relative error = 6.00570684492641579200000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.254
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.254
Order of pole (three term test) = 8.174e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.745
y[1] (closed_form) = 0.0943839207552601338835915913364
y[1] (numeric) = 0.0943839207552601338267135140252
absolute error = 5.68780773112e-20
relative error = 6.02624651064096780000000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.255
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.255
Order of pole (three term test) = 4.125e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.744
y[1] (closed_form) = 0.0943259542768142276741785341293
y[1] (numeric) = 0.0943259542768142276171418308439
absolute error = 5.70367032854e-20
relative error = 6.04676663201486374400000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.256
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.256
Order of pole (three term test) = 4.163e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.743
y[1] (closed_form) = 0.0942680411826906153996837684289
y[1] (numeric) = 0.0942680411826906153424888284674
absolute error = 5.71949399615e-20
relative error = 6.06726725663650113500000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.257
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.257
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.742
y[1] (closed_form) = 0.0942101814073569107501730641031
y[1] (numeric) = 0.0942101814073569106928202756889
absolute error = 5.73527884142e-20
relative error = 6.08774843200984408800000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.258
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.258
Order of pole (three term test) = 4.240e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.741
y[1] (closed_form) = 0.094152374885381252623908997587
y[1] (numeric) = 0.0941523748853812525663987478722
absolute error = 5.75102497148e-20
relative error = 6.10821020551117698800000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.259
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.259
Order of pole (three term test) = 4.280e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.74
y[1] (closed_form) = 0.0940946215514321201400127968684
y[1] (numeric) = 0.0940946215514321200823454719377
absolute error = 5.76673249307e-20
relative error = 6.12865262433507320000000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.26
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.26
Order of pole (three term test) = 8.639e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.739
y[1] (closed_form) = 0.094036921340278148048155555123
y[1] (numeric) = 0.0940369213402781479903315399958
absolute error = 5.78240151272e-20
relative error = 6.14907573568475191200000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.261
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.261
Order of pole (three term test) = 4.359e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.738
y[1] (closed_form) = 0.0939792741867879425343052544565
y[1] (numeric) = 0.0939792741867879424763249330911
absolute error = 5.79803213654e-20
relative error = 6.16947958654815317599999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.262
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.262
Order of pole (three term test) = 4.399e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.737
y[1] (closed_form) = 0.0939216800259298974215587260803
y[1] (numeric) = 0.0939216800259298973634224813769
absolute error = 5.81362447034e-20
relative error = 6.18986422382454674599999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.263
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.263
Order of pole (three term test) = 4.440e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.736
y[1] (closed_form) = 0.0938641387927720107650903498655
y[1] (numeric) = 0.0938641387927720107067985636695
absolute error = 5.82917861960e-20
relative error = 6.21022969429180416000000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.264
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.264
Order of pole (three term test) = 4.481e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.735
y[1] (closed_form) = 0.0938066504224817018402519646631
y[1] (numeric) = 0.0938066504224817017818050177679
absolute error = 5.84469468952e-20
relative error = 6.23057604465883420000000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.265
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.265
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.734
y[1] (closed_form) = 0.093749214850325628522861121038
y[1] (numeric) = 0.0937492148503256284642593931889
absolute error = 5.86017278491e-20
relative error = 6.25090332144754519600000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.266
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.266
Order of pole (three term test) = 9.128e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.733
y[1] (closed_form) = 0.0936918320116695050607174601944
y[1] (numeric) = 0.0936918320116695050019613300909
absolute error = 5.87561301035e-20
relative error = 6.27121157116255411499999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.267
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.267
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.732
y[1] (closed_form) = 0.0936345018419779202353896468706
y[1] (numeric) = 0.0936345018419779201764794921707
absolute error = 5.89101546999e-20
relative error = 6.29150084007704817600000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.268
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.268
Order of pole (three term test) = 4.649e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.731
y[1] (closed_form) = 0.0935772242768141559133179199168
y[1] (numeric) = 0.0935772242768141558542541172394
absolute error = 5.90638026774e-20
relative error = 6.31177117443462941400000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.269
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.269
Order of pole (three term test) = 4.692e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.73
y[1] (closed_form) = 0.0935199992518400059852799521177
y[1] (numeric) = 0.093519999251840005926062877046
absolute error = 5.92170750717e-20
relative error = 6.33202262034180930000000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.27
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.27
Order of pole (three term test) = 4.735e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.729
y[1] (closed_form) = 0.0934628267028155956932703306649
y[1] (numeric) = 0.0934628267028155956339003577495
absolute error = 5.93699729154e-20
relative error = 6.35225522379920291400000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.271
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.271
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.728
y[1] (closed_form) = 0.0934057065655992013438465815006
y[1] (numeric) = 0.0934057065655992012843240842628
absolute error = 5.95224972378e-20
relative error = 6.37246903067930995200000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.272
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.272
Order of pole (three term test) = 9.645e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.727
y[1] (closed_form) = 0.0933486387761470704069972646049
y[1] (numeric) = 0.0933486387761470703473226155397
absolute error = 5.96746490652e-20
relative error = 6.39266408675777890800000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.273
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.273
Order of pole (three term test) = 4.867e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.726
y[1] (closed_form) = 0.0932916232705132419995902631906
y[1] (numeric) = 0.0932916232705132419397638337701
absolute error = 5.98264294205e-20
relative error = 6.41284043766975458000000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.274
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.274
Order of pole (three term test) = 1.965e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.725
y[1] (closed_form) = 0.0932346599848493677524619777402
y[1] (numeric) = 0.0932346599848493676924841384163
absolute error = 5.99778393239e-20
relative error = 6.43299812898404937500000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.275
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.275
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.724
y[1] (closed_form) = 0.0931777488554045330602107158883
y[1] (numeric) = 0.0931777488554045330000818360961
absolute error = 6.01288797922e-20
relative error = 6.45313720612733827200000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.276
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.276
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.723
y[1] (closed_form) = 0.0931208898185250787127601413537
y[1] (numeric) = 0.0931208898185250786524805895145
absolute error = 6.02795518392e-20
relative error = 6.47325771442620376800000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.277
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.277
Order of pole (three term test) = 1.010e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.722
y[1] (closed_form) = 0.0930640828106544229077612094756
y[1] (numeric) = 0.093064082810654422847331353
absolute error = 6.04298564756e-20
relative error = 6.49335969909561070400000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.278
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.278
Order of pole (three term test) = 5.095e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.721
y[1] (closed_form) = 0.0930073277683328836429035734437
y[1] (numeric) = 0.0930073277683328835823237787347
absolute error = 6.05797947090e-20
relative error = 6.51344320523809269000000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.279
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.279
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.72
y[1] (closed_form) = 0.0929506246281975014872099940512
y[1] (numeric) = 0.0929506246281975014264806265071
absolute error = 6.07293675441e-20
relative error = 6.53350827786445440000000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.28
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.28
Order of pole (three term test) = 5.189e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.719
y[1] (closed_form) = 0.0928939733269818627303898267723
y[1] (numeric) = 0.0928939733269818626695112507902
absolute error = 6.08785759821e-20
relative error = 6.55355496182843198100000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.281
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.281
Order of pole (three term test) = 5.237e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.718
y[1] (closed_form) = 0.092837373801515922909330193202
y[1] (numeric) = 0.0928373738015159228483027721805
absolute error = 6.10274210215e-20
relative error = 6.57358330191191766000000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.282
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.282
Order of pole (three term test) = 1.057e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.717
y[1] (closed_form) = 0.0927808259887258307108059694069
y[1] (numeric) = 0.0927808259887258306496300657493
absolute error = 6.11759036576e-20
relative error = 6.59359334277038326400000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.283
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.283
Order of pole (three term test) = 1.067e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.716
y[1] (closed_form) = 0.0927243298256337522494922415697
y[1] (numeric) = 0.0927243298256337521881682166867
absolute error = 6.13240248830e-20
relative error = 6.61358512898595248000000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.284
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.284
Order of pole (three term test) = 5.382e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.715
y[1] (closed_form) = 0.0926678852493576957203653894715
y[1] (numeric) = 0.0926678852493576956588936037844
absolute error = 6.14717856871e-20
relative error = 6.63355870501275697500000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.285
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.285
Order of pole (three term test) = 1.086e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.714
y[1] (closed_form) = 0.0926114921971113364245814608834
y[1] (numeric) = 0.0926114921971113363629622738274
absolute error = 6.16191870560e-20
relative error = 6.65351411516528575999999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.286
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.286
Order of pole (three term test) = 1.096e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.713
y[1] (closed_form) = 0.0925551506062038421679229948552
y[1] (numeric) = 0.0925551506062038421061567648822
absolute error = 6.17662299730e-20
relative error = 6.67345140367152037000000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.287
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.287
Order of pole (three term test) = 1.106e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.712
y[1] (closed_form) = 0.0924988604140396990309079392141
y[1] (numeric) = 0.0924988604140396989689950237957
absolute error = 6.19129154184e-20
relative error = 6.69337061465058969600000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.288
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.288
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.711
y[1] (closed_form) = 0.0924426215581185375096567873545
y[1] (numeric) = 0.0924426215581185374475975429845
absolute error = 6.20592443700e-20
relative error = 6.71327179216606770000000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.289
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.289
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.71
y[1] (closed_form) = 0.0923864339760349590266165316286
y[1] (numeric) = 0.0923864339760349589644113138267
absolute error = 6.22052178019e-20
relative error = 6.73315498009545789999999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.29
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.29
Order of pole (three term test) = 1.137e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.709
y[1] (closed_form) = 0.0923302976054783628102424953704
y[1] (numeric) = 0.0923302976054783627478916586849
absolute error = 6.23508366855e-20
relative error = 6.75302022223747825499999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.291
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.291
Order of pole (three term test) = 1.721e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.708
y[1] (closed_form) = 0.092274212384232773142741562815
y[1] (numeric) = 0.0922742123842327730802454608258
absolute error = 6.24961019892e-20
relative error = 6.77286756227885548800000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.292
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.292
Order of pole (three term test) = 5.790e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.707
y[1] (closed_form) = 0.0922181782501766669749827759499
y[1] (numeric) = 0.0922181782501766669123417612708
absolute error = 6.26410146791e-20
relative error = 6.79269704386943855899999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.293
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.293
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.706
y[1] (closed_form) = 0.0921621951412828019076837096685
y[1] (numeric) = 0.0921621951412828018448981339514
absolute error = 6.27855757171e-20
relative error = 6.81250871041547655600000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.294
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.294
Order of pole (three term test) = 5.896e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.705
y[1] (closed_form) = 0.0921062629956180445379834715311
y[1] (numeric) = 0.0921062629956180444750536854678
absolute error = 6.29297860633e-20
relative error = 6.83230260533899682500000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.295
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.295
Order of pole (three term test) = 5.950e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.704
y[1] (closed_form) = 0.0920503817513431991705155999624
y[1] (numeric) = 0.0920503817513431991074419532878
absolute error = 6.30736466746e-20
relative error = 6.85207877192531353599999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.296
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.296
Order of pole (three term test) = 6.005e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.703
y[1] (closed_form) = 0.0919945513467128368920965549054
y[1] (numeric) = 0.0919945513467128368288793964007
absolute error = 6.32171585047e-20
relative error = 6.87183725332216482299999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.297
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.297
Order of pole (three term test) = 6.060e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.702
y[1] (closed_form) = 0.0919387717200751250091479077862
y[1] (numeric) = 0.0919387717200751249457875852816
absolute error = 6.33603225046e-20
relative error = 6.89157809259323298400000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.298
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.298
Order of pole (three term test) = 1.835e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.701
y[1] (closed_form) = 0.091883042809871656846972743171
y[1] (numeric) = 0.0918830428098716567834696035485
absolute error = 6.35031396225e-20
relative error = 6.91130133270656122500000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.299
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.299
Order of pole (three term test) = 6.171e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.7
y[1] (closed_form) = 0.0918273645546372819100091827364
y[1] (numeric) = 0.0918273645546372818463635719327
absolute error = 6.36456108037e-20
relative error = 6.93100701652293000000000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.3
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.3
Order of pole (three term test) = 1.245e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.699
y[1] (closed_form) = 0.0917717368929999364021863331512
y[1] (numeric) = 0.0917717368929999363383985961604
absolute error = 6.37877369908e-20
relative error = 6.95069518681688270799999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.301
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.301
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.698
y[1] (closed_form) = 0.0917161597636804741065103431981
y[1] (numeric) = 0.0917161597636804740425808240755
absolute error = 6.39295191226e-20
relative error = 6.97036588615608810400000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.302
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.302
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.697
y[1] (closed_form) = 0.0916606331054924976230106319918
y[1] (numeric) = 0.0916606331054924975589396738552
absolute error = 6.40709581366e-20
relative error = 6.99001915717301909400000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.303
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.303
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.696
y[1] (closed_form) = 0.0916051568573421899641787194625
y[1] (numeric) = 0.0916051568573421898999666644962
absolute error = 6.42120549663e-20
relative error = 7.00965504226996780800000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.304
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.304
Order of pole (three term test) = 6.458e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.695
y[1] (closed_form) = 0.0915497309582281465070344524526
y[1] (numeric) = 0.0915497309582281464426816419096
absolute error = 6.43528105430e-20
relative error = 7.02927358381452574999999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.305
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.305
Order of pole (three term test) = 1.303e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.694
y[1] (closed_form) = 0.0914943553472412073009567747728
y[1] (numeric) = 0.0914943553472412072364635489782
absolute error = 6.44932257946e-20
relative error = 7.04887482400788765600000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.306
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.306
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.693
y[1] (closed_form) = 0.0914390299635642897304185374711
y[1] (numeric) = 0.0914390299635642896657852358245
absolute error = 6.46333016466e-20
relative error = 7.06845880499327603400000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.307
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.307
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.692
y[1] (closed_form) = 0.09138375474647222153176718636
y[1] (numeric) = 0.0913837547464722214669941473382
absolute error = 6.47730390218e-20
relative error = 7.08802556882250435200000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.308
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.308
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.691
y[1] (closed_form) = 0.0913285296353315741631954975766
y[1] (numeric) = 0.0913285296353315740982830587366
absolute error = 6.49124388400e-20
relative error = 7.10757515742242040000000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.309
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.309
Order of pole (three term test) = 6.757e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.69
y[1] (closed_form) = 0.0912733545696004965270488586266
y[1] (numeric) = 0.0912733545696004964619973566085
absolute error = 6.50515020181e-20
relative error = 7.12710761260505410000000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.31
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.31
Order of pole (three term test) = 2.046e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.689
y[1] (closed_form) = 0.091218229488828549043617912013
y[1] (numeric) = 0.0912182294888285489784276825422
absolute error = 6.51902294708e-20
relative error = 7.14662297614358046799999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.311
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.311
Order of pole (three term test) = 6.881e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.688
y[1] (closed_form) = 0.0911631543326565380755676911947
y[1] (numeric) = 0.0911631543326565380102390690855
absolute error = 6.53286221092e-20
relative error = 7.16612128961820364800000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.312
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.312
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.687
y[1] (closed_form) = 0.0911081290408163507021566842982
y[1] (numeric) = 0.0911081290408163506366900034559
absolute error = 6.54666808423e-20
relative error = 7.18560259457978688700000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.313
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.313
Order of pole (three term test) = 7.007e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.686
y[1] (closed_form) = 0.091053153553130789842401559704
y[1] (numeric) = 0.0910531535531307897767971531279
absolute error = 6.56044065761e-20
relative error = 7.20506693245049555600000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.314
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.314
Order of pole (three term test) = 7.071e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.685
y[1] (closed_form) = 0.0909982278095134097263455794199
y[1] (numeric) = 0.0909982278095134096606037792057
absolute error = 6.57418002142e-20
relative error = 7.22451434458891995000000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.315
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.315
Order of pole (three term test) = 7.135e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.684
y[1] (closed_form) = 0.0909433517499683517135910110136
y[1] (numeric) = 0.0909433517499683516477121483569
absolute error = 6.58788626567e-20
relative error = 7.24394487216850635200000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.316
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.316
Order of pole (three term test) = 7.200e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.683
y[1] (closed_form) = 0.0908885253145901804582581268655
y[1] (numeric) = 0.0908885253145901803922425320638
absolute error = 6.60155948017e-20
relative error = 7.26335855634161431300000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.317
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.317
Order of pole (three term test) = 7.265e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.682
y[1] (closed_form) = 0.0908337484435637204195356506112
y[1] (numeric) = 0.0908337484435637203533836530665
absolute error = 6.61519975447e-20
relative error = 7.28275543817297842800000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.318
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.318
Order of pole (three term test) = 7.331e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.681
y[1] (closed_form) = 0.0907790210771638927169897749235
y[1] (numeric) = 0.0907790210771638926507017031455
absolute error = 6.62880717780e-20
relative error = 7.30213555857293057999999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.319
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.319
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.68
y[1] (closed_form) = 0.0907243431557555523298011322398
y[1] (numeric) = 0.0907243431557555522633773138487
absolute error = 6.64238183911e-20
relative error = 7.32149895834060640000000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.32
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.32
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.679
y[1] (closed_form) = 0.0906697146197933256391013506977
y[1] (numeric) = 0.0906697146197933255725421124262
absolute error = 6.65592382715e-20
relative error = 7.34084567825142631500000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.321
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.321
Order of pole (three term test) = 7.533e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.678
y[1] (closed_form) = 0.0906151354098214483125830714253
y[1] (numeric) = 0.0906151354098214482458887391219
absolute error = 6.66943323034e-20
relative error = 7.36017575891314525600000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.322
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.322
Order of pole (three term test) = 2.280e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.677
y[1] (closed_form) = 0.0905606054664736035305595404737
y[1] (numeric) = 0.0905606054664736034637304391049
absolute error = 6.68291013688e-20
relative error = 7.37948924088639935200000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.323
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.323
Order of pole (three term test) = 1.534e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.676
y[1] (closed_form) = 0.0905061247304727605526521190743
y[1] (numeric) = 0.0905061247304727604856885727274
absolute error = 6.69635463469e-20
relative error = 7.39878616461785774399999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.324
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.324
Order of pole (three term test) = 1.548e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.675
y[1] (closed_form) = 0.0904516931426310136242862796087
y[1] (numeric) = 0.0904516931426310135571886114949
absolute error = 6.70976681138e-20
relative error = 7.41806657040630125000000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.325
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.325
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.674
y[1] (closed_form) = 0.0903973106438494212221788716897
y[1] (numeric) = 0.0903973106438494211549474041458
absolute error = 6.72314675439e-20
relative error = 7.43733049855663916400000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.326
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.326
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.673
y[1] (closed_form) = 0.0903429771751178456380016530959
y[1] (numeric) = 0.0903429771751178455706367075876
absolute error = 6.73649455083e-20
relative error = 7.45657798920241610699999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.327
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.327
Order of pole (three term test) = 7.952e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.672
y[1] (closed_form) = 0.0902886926775147928994082840237
y[1] (numeric) = 0.0902886926775147928319101811484
absolute error = 6.74981028753e-20
relative error = 7.47580908236026675200000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.328
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.328
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.671
y[1] (closed_form) = 0.0902344570922072530276141802007
y[1] (numeric) = 0.0902344570922072529599832396893
absolute error = 6.76309405114e-20
relative error = 7.49502381803998047399999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.329
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.329
Order of pole (three term test) = 1.619e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.67
y[1] (closed_form) = 0.0901802703604505406307208109009
y[1] (numeric) = 0.0901802703604505405629573516214
absolute error = 6.77634592795e-20
relative error = 7.51422223604447550000000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.33
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.33
Order of pole (three term test) = 3.268e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.669
y[1] (closed_form) = 0.0901261324235881358319782118274
y[1] (numeric) = 0.0901261324235881357640825517862
absolute error = 6.78956600412e-20
relative error = 7.53340437622397113199999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.331
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.331
Order of pole (three term test) = 1.649e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.668
y[1] (closed_form) = 0.0900720432230515255321816601792
y[1] (numeric) = 0.0900720432230515254641541165252
absolute error = 6.80275436540e-20
relative error = 7.55257027816486495999999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.332
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.332
Order of pole (three term test) = 8.318e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.667
y[1] (closed_form) = 0.090018002700360045005400630072
y[1] (numeric) = 0.0900180027003600449372415190982
absolute error = 6.81591109738e-20
relative error = 7.57171998146626108200000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.333
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.333
Order of pole (three term test) = 1.679e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.666
y[1] (closed_form) = 0.0899640107971207198272403107861
y[1] (numeric) = 0.0899640107971207197589499479321
absolute error = 6.82903628540e-20
relative error = 7.59085352563956824000000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.334
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.334
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.665
y[1] (closed_form) = 0.0899100674550281081348381281622
y[1] (numeric) = 0.0899100674550281080664168280174
absolute error = 6.84213001448e-20
relative error = 7.60997095002998180000000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.335
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.335
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.664
y[1] (closed_form) = 0.0898561726158641432177998608306
y[1] (numeric) = 0.0898561726158641431492479371361
absolute error = 6.85519236945e-20
relative error = 7.62907229396026272000000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.336
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.336
Order of pole (three term test) = 8.623e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.663
y[1] (closed_form) = 0.0898023262214979764392820878753
y[1] (numeric) = 0.0898023262214979763705998535267
absolute error = 6.86822343486e-20
relative error = 7.64815759663005353400000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.337
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.337
Order of pole (three term test) = 8.701e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.662
y[1] (closed_form) = 0.0897485282138858204864298430371
y[1] (numeric) = 0.0897485282138858204176176100871
absolute error = 6.88122329500e-20
relative error = 7.66722689713739799999999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.338
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.338
Order of pole (three term test) = 8.780e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.661
y[1] (closed_form) = 0.0896947785350707929493804826493
y[1] (numeric) = 0.0896947785350707928804385623106
absolute error = 6.89419203387e-20
relative error = 7.68628023444459542700000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.339
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.339
Order of pole (three term test) = 8.859e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.66
y[1] (closed_form) = 0.0896410771271827602280469002117
y[1] (numeric) = 0.0896410771271827601589756028583
absolute error = 6.90712973534e-20
relative error = 7.70531764755589039999999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.34
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.34
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.659
y[1] (closed_form) = 0.0895874239324381817658953398503
y[1] (numeric) = 0.0895874239324381816966949750217
absolute error = 6.92003648286e-20
relative error = 7.72433917519350036600000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.341
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.341
Order of pole (three term test) = 9.019e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.658
y[1] (closed_form) = 0.0895338188931399546099351739339
y[1] (numeric) = 0.0895338188931399545406060503359
absolute error = 6.93291235980e-20
relative error = 7.74334485617612471999999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.342
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.342
Order of pole (three term test) = 9.101e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.657
y[1] (closed_form) = 0.0894802619516772582961401167843
y[1] (numeric) = 0.0894802619516772582266825422929
absolute error = 6.94575744914e-20
relative error = 7.76233472907239918600000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.343
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.343
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.656
y[1] (closed_form) = 0.0894267530505254000595224468304
y[1] (numeric) = 0.0894267530505253999899367284933
absolute error = 6.95857183371e-20
relative error = 7.78130883246813465600000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.344
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.344
Order of pole (three term test) = 9.266e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.655
y[1] (closed_form) = 0.0893732921322456603680839036466
y[1] (numeric) = 0.0893732921322456602983703476861
absolute error = 6.97135559605e-20
relative error = 7.80026720480933512500000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.345
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.345
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.654
y[1] (closed_form) = 0.0893198791394851387798690141835
y[1] (numeric) = 0.089319879139485138710027925999
absolute error = 6.98410881845e-20
relative error = 7.81920988444617602000000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.346
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.346
Order of pole (three term test) = 9.433e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.653
y[1] (closed_form) = 0.0892665140149766001223486841091
y[1] (numeric) = 0.089266514014976600052380368279
absolute error = 6.99683158301e-20
relative error = 7.83813690969954710899999999998e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.347
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.347
Order of pole (three term test) = 9.518e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.652
y[1] (closed_form) = 0.0892131967015383209933639655765
y[1] (numeric) = 0.089213196701538320923268725862
absolute error = 7.00952397145e-20
relative error = 7.85704831864760808000000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.348
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.348
Order of pole (three term test) = 9.604e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.651
y[1] (closed_form) = 0.0891599271420739365828619819486
y[1] (numeric) = 0.0891599271420739365126401212944
absolute error = 7.02218606542e-20
relative error = 7.87594414947237014199999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.349
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.349
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.65
y[1] (closed_form) = 0.0891067052795722878146580530185
y[1] (numeric) = 0.0891067052795722877443098735566
absolute error = 7.03481794619e-20
relative error = 7.89482444011172750000000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.35
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.35
Order of pole (three term test) = 9.777e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.649
y[1] (closed_form) = 0.0890535310571072688074601211608
y[1] (numeric) = 0.0890535310571072687369859242123
absolute error = 7.04741969485e-20
relative error = 7.91368922848293148500000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.351
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.351
Order of pole (three term test) = 9.865e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.648
y[1] (closed_form) = 0.0890004044178376746543936295647
y[1] (numeric) = 0.089000404417837674583793715642
absolute error = 7.05999139227e-20
relative error = 7.93253855243720620800000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.352
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.352
Order of pole (three term test) = 9.954e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.647
y[1] (closed_form) = 0.0889473253050070495202670483337
y[1] (numeric) = 0.0889473253050070494495417171436
absolute error = 7.07253311901e-20
relative error = 7.95137244965798970900000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.353
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.353
Order of pole (three term test) = 2.009e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.646
y[1] (closed_form) = 0.0888942936619435350558202827621
y[1] (numeric) = 0.0888942936619435349849698332077
absolute error = 7.08504495544e-20
relative error = 7.97019095779504790400000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.354
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.354
Order of pole (three term test) = 1.013e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.645
y[1] (closed_form) = 0.0888413094320597191282002305431
y[1] (numeric) = 0.0888413094320597190572249607264
absolute error = 7.09752698167e-20
relative error = 7.98899411438520617500000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.355
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.355
Order of pole (three term test) = 1.022e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.644
y[1] (closed_form) = 0.0887883725588524848669097810691
y[1] (numeric) = 0.0887883725588524847958099882932
absolute error = 7.10997927759e-20
relative error = 8.00778195689668862400000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.356
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.356
Order of pole (three term test) = 1.032e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.643
y[1] (closed_form) = 0.0887354829859028600244785703366
y[1] (numeric) = 0.088735482985902859953254551108
absolute error = 7.12240192286e-20
relative error = 8.02655452271727041399999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.357
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.357
Order of pole (three term test) = 1.041e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.642
y[1] (closed_form) = 0.0886826406568758666511058193195
y[1] (numeric) = 0.0886826406568758665797578693511
absolute error = 7.13479499684e-20
relative error = 8.04531184907473217599999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.358
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.358
Order of pole (three term test) = 1.050e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.641
y[1] (closed_form) = 0.088629845515520371082527592022
y[1] (numeric) = 0.0886298455155203710110560062349
absolute error = 7.14715857871e-20
relative error = 8.06405397317140635099999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.359
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.359
Order of pole (three term test) = 1.060e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.64
y[1] (closed_form) = 0.0885770975056689342403628117914
y[1] (numeric) = 0.0885770975056689341687678843173
absolute error = 7.15949274741e-20
relative error = 8.08278093211599360000000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.36
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.36
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.639
y[1] (closed_form) = 0.0885243965712376622441943708929
y[1] (numeric) = 0.0885243965712376621724763950765
absolute error = 7.17179758164e-20
relative error = 8.10149276292291464400000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.361
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.361
Order of pole (three term test) = 1.079e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.638
y[1] (closed_form) = 0.0884717426562260573346436588233
y[1] (numeric) = 0.0884717426562260572628029272245
absolute error = 7.18407315988e-20
relative error = 8.12018950253426747199999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.362
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.362
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.637
y[1] (closed_form) = 0.0884191357047168691066988194011
y[1] (numeric) = 0.0884191357047168690347356237979
absolute error = 7.19631956032e-20
relative error = 8.13887118774007660800000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.363
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.363
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.636
y[1] (closed_form) = 0.088366575660875946052559025338
y[1] (numeric) = 0.0883665756608759459804736567279
absolute error = 7.20853686101e-20
relative error = 8.15753785534722209599999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.364
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.364
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.635
y[1] (closed_form) = 0.0883140624689520874132590317688
y[1] (numeric) = 0.0883140624689520873410517803722
absolute error = 7.22072513966e-20
relative error = 8.17618954195266035000000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.365
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.365
Order of pole (three term test) = 1.118e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.634
y[1] (closed_form) = 0.0882615960732768953383402371554
y[1] (numeric) = 0.088261596073276895266011392417
absolute error = 7.23288447384e-20
relative error = 8.19482628416903510400000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.366
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.366
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.633
y[1] (closed_form) = 0.0882091764182646273528364410454
y[1] (numeric) = 0.088209176418264627280386291637
absolute error = 7.24501494084e-20
relative error = 8.21344811846564787600000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.367
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.367
Order of pole (three term test) = 1.138e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.632
y[1] (closed_form) = 0.0881568034484120491308444434415
y[1] (numeric) = 0.0881568034484120490582732772637
absolute error = 7.25711661778e-20
relative error = 8.23205508129244787199999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.368
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.368
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.631
y[1] (closed_form) = 0.0881044771082982875749515799819
y[1] (numeric) = 0.0881044771082982875022596841675
absolute error = 7.26918958144e-20
relative error = 8.25064720888666118400000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.369
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.369
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.63
y[1] (closed_form) = 0.0880521973425846842007942308202
y[1] (numeric) = 0.088052197342584684127981891735
absolute error = 7.28123390852e-20
relative error = 8.26922453756707879999999999998e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.37
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.37
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.629
y[1] (closed_form) = 0.0879999640960146488260232789825
y[1] (numeric) = 0.0879999640960146487530907822293
absolute error = 7.29324967532e-20
relative error = 8.28778710337030401200000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.371
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.371
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.628
y[1] (closed_form) = 0.0879477773134135135629544261655
y[1] (numeric) = 0.0879477773134135134899020565846
absolute error = 7.30523695809e-20
relative error = 8.30633494244752065599999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.372
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.372
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=142.7MB, alloc=44.3MB, time=1.13
TOP MAIN SOLVE Loop
x[1] = 2.627
y[1] (closed_form) = 0.0878956369396883871141832003487
y[1] (numeric) = 0.0878956369396883870410112420216
absolute error = 7.31719583271e-20
relative error = 8.32486809070040895900000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.373
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.373
Order of pole (three term test) = 2.401e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.626
y[1] (closed_form) = 0.0878435429198280093704464103438
y[1] (numeric) = 0.0878435429198280092971551465946
absolute error = 7.32912637492e-20
relative error = 8.34338658404187899200000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.374
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.374
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.625
y[1] (closed_form) = 0.087791495198902606310013717421
y[1] (numeric) = 0.0877914951989026062366034308188
absolute error = 7.34102866022e-20
relative error = 8.36189045828184375000000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.375
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.375
Order of pole (three term test) = 2.444e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.624
y[1] (closed_form) = 0.0877394937220637451988949035287
y[1] (numeric) = 0.0877394937220637451253658758898
absolute error = 7.35290276389e-20
relative error = 8.38037974914935526400000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.376
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.376
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.623
y[1] (closed_form) = 0.0876875384345441900911503193272
y[1] (numeric) = 0.0876875384345441900175028317179
absolute error = 7.36474876093e-20
relative error = 8.39885449222358799700000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.377
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.377
Order of pole (three term test) = 1.244e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.622
y[1] (closed_form) = 0.087635629281657757628593893339
y[1] (numeric) = 0.0876356292816577575548282260769
absolute error = 7.37656672621e-20
relative error = 8.41731472310420696400000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.378
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.378
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.621
y[1] (closed_form) = 0.0875837662087991731391799759686
y[1] (numeric) = 0.0875837662087991730652964086257
absolute error = 7.38835673429e-20
relative error = 8.43576047720556098900000000002e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.379
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.379
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.62
y[1] (closed_form) = 0.0875319491614439270333671790204
y[1] (numeric) = 0.0875319491614439269593659904242
absolute error = 7.40011885962e-20
relative error = 8.45419178998427279999999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.38
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.38
Order of pole (three term test) = 1.278e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.619
y[1] (closed_form) = 0.0874801780851481314977542526084
y[1] (numeric) = 0.0874801780851481314236357208454
absolute error = 7.41185317630e-20
relative error = 8.47260869666466842999999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.381
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.381
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.618
y[1] (closed_form) = 0.0874284529255483774852849170881
y[1] (numeric) = 0.0874284529255483774110493195054
absolute error = 7.42355975827e-20
relative error = 8.49101123245506314800000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.382
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.382
Order of pole (three term test) = 1.300e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.617
y[1] (closed_form) = 0.0873767736283615920013204378031
y[1] (numeric) = 0.0873767736283615919269680510102
absolute error = 7.43523867929e-20
relative error = 8.50939943252447908100000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.383
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.383
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.616
y[1] (closed_form) = 0.0873251401393848956848805950963
y[1] (numeric) = 0.0873251401393848956104116949679
absolute error = 7.44689001284e-20
relative error = 8.52777333188766950400000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.384
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.384
Order of pole (three term test) = 1.324e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.615
y[1] (closed_form) = 0.0872735524044954606843555611799
y[1] (numeric) = 0.0872735524044954606097704228574
absolute error = 7.45851383225e-20
relative error = 8.54613296555327562500000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.385
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.385
Order of pole (three term test) = 1.335e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.614
y[1] (closed_form) = 0.0872220103696503688269930491037
y[1] (numeric) = 0.0872220103696503687522919469981
absolute error = 7.47011021056e-20
relative error = 8.56447836836295577599999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.386
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.386
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.613
y[1] (closed_form) = 0.0871705139808864700814669472513
y[1] (numeric) = 0.087170513980886470006650155045
absolute error = 7.48167922063e-20
relative error = 8.58280957511673944699999999998e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.387
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.387
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.612
y[1] (closed_form) = 0.0871190631843202413128354955124
y[1] (numeric) = 0.0871190631843202412379032861614
absolute error = 7.49322093510e-20
relative error = 8.60112662052664943999999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.388
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.388
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.611
y[1] (closed_form) = 0.0870676579261476453291988965742
y[1] (numeric) = 0.0870676579261476452541515423101
absolute error = 7.50473542641e-20
relative error = 8.61942953923907276100000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.389
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.389
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.61
y[1] (closed_form) = 0.0870162981526439902193680876428
y[1] (numeric) = 0.0870162981526439901442058599751
absolute error = 7.51622276677e-20
relative error = 8.63771836579975170000000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.39
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.39
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.609
y[1] (closed_form) = 0.0869649838101637889808582243786
y[1] (numeric) = 0.0869649838101637889055813940966
absolute error = 7.52768302820e-20
relative error = 8.65599313469914441999999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.391
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.391
Order of pole (three term test) = 1.408e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.608
y[1] (closed_form) = 0.086913714845140619437522249911
y[1] (numeric) = 0.0869137148451406193621310870864
absolute error = 7.53911628246e-20
relative error = 8.67425388029138534400000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.392
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.392
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.607
y[1] (closed_form) = 0.0868624912040869844461417375225
y[1] (numeric) = 0.086862491204086984370636511511
absolute error = 7.55052260115e-20
relative error = 8.69250063690867163500000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.393
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.393
Order of pole (three term test) = 1.434e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.606
y[1] (closed_form) = 0.0868113128335941723912940059567
y[1] (numeric) = 0.0868113128335941723156749854001
absolute error = 7.56190205566e-20
relative error = 8.71073343880326757599999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.394
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.394
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.605
y[1] (closed_form) = 0.0867601796803321179678163113476
y[1] (numeric) = 0.0867601796803321178920837641766
absolute error = 7.57325471710e-20
relative error = 8.72895232006625275000000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.395
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.395
Order of pole (three term test) = 1.459e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.604
y[1] (closed_form) = 0.0867090916910492632501897194926
y[1] (numeric) = 0.0867090916910492631743439129282
absolute error = 7.58458065644e-20
relative error = 8.74715731478817350400000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.396
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.396
Order of pole (three term test) = 1.472e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.603
y[1] (closed_form) = 0.0866580488125724190481670566135
y[1] (numeric) = 0.0866580488125724189722082571691
absolute error = 7.59587994444e-20
relative error = 8.76534845697793239599999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.397
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.397
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.602
y[1] (closed_form) = 0.086607050991806626547971125902
y[1] (numeric) = 0.086607050991806626471899599386
absolute error = 7.60715265160e-20
relative error = 8.78352578050448464000000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.398
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.398
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.601
y[1] (closed_form) = 0.0865560981757350192383911610297
y[1] (numeric) = 0.086556098175735019162207172547
absolute error = 7.61839884827e-20
relative error = 8.80168931922318122700000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.399
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.399
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.6
y[1] (closed_form) = 0.0865051903114186851211072664359
y[1] (numeric) = 0.0865051903114186850448110803904
absolute error = 7.62961860455e-20
relative error = 8.81983910685980000000000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.4
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.4
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.599
y[1] (closed_form) = 0.0864543273459965292045743676233
y[1] (numeric) = 0.0864543273459965291281662477196
absolute error = 7.64081199037e-20
relative error = 8.83797517710237063700000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.401
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.401
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.598
y[1] (closed_form) = 0.0864035092266851362807989628815
y[1] (numeric) = 0.0864035092266851362042791721271
absolute error = 7.65197907544e-20
relative error = 8.85609756354286857599999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.402
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.402
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.597
y[1] (closed_form) = 0.0863527359007786339843437308648
y[1] (numeric) = 0.0863527359007786339077125315725
absolute error = 7.66311992923e-20
relative error = 8.87420629965344550700000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.403
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.403
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.596
y[1] (closed_form) = 0.0863020073156485561328968062735
y[1] (numeric) = 0.0863020073156485560561544600627
absolute error = 7.67423462108e-20
relative error = 8.89230141891321132799999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.404
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.404
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.595
y[1] (closed_form) = 0.0862513234187437063487442885451
y[1] (numeric) = 0.0862513234187437062718910563448
absolute error = 7.68532322003e-20
relative error = 8.91038295461083207500000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.405
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.405
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.594
y[1] (closed_form) = 0.0862006841575900219604862959877
y[1] (numeric) = 0.0862006841575900218835224380373
absolute error = 7.69638579504e-20
relative error = 8.92845094009886534399999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.406
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.406
Order of pole (three term test) = 1.608e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.593
y[1] (closed_form) = 0.0861500894797904381843386201632
y[1] (numeric) = 0.0861500894797904381072643960158
absolute error = 7.70742241474e-20
relative error = 8.94650540850343462600000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.407
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.407
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.592
y[1] (closed_form) = 0.08609953933302475258436377262
y[1] (numeric) = 0.0860995393330247525071794411433
absolute error = 7.71843314767e-20
relative error = 8.96454639300198988800000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.408
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.408
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.591
y[1] (closed_form) = 0.0860490336650494898109769482382
y[1] (numeric) = 0.0860490336650494897336827676174
absolute error = 7.72941806208e-20
relative error = 8.98257392659071244800000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.409
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.409
Order of pole (three term test) = 1.651e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.59
y[1] (closed_form) = 0.0859985724236977666170741565689
y[1] (numeric) = 0.0859985724236977665396703843081
absolute error = 7.74037722608e-20
relative error = 9.00058804225808480000000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.41
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.41
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.589
y[1] (closed_form) = 0.0859481555568791571511314945758
y[1] (numeric) = 0.0859481555568791570736183875001
absolute error = 7.75131070757e-20
relative error = 9.01858877290310519699999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.411
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.411
Order of pole (three term test) = 1.680e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.588
y[1] (closed_form) = 0.085897783012579558526626251187
y[1] (numeric) = 0.0858977830125795584490040654452
absolute error = 7.76221857418e-20
relative error = 9.03657615126485699200000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.412
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.412
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.587
y[1] (closed_form) = 0.0858474547388610566671322460296
y[1] (numeric) = 0.0858474547388610565894012370948
absolute error = 7.77310089348e-20
relative error = 9.05455021016634301199999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.413
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.413
Order of pole (three term test) = 1.710e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.586
y[1] (closed_form) = 0.0857971706838617924264435116576
y[1] (numeric) = 0.0857971706838617923486039343305
absolute error = 7.78395773271e-20
relative error = 9.07251098219972031600000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.414
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.414
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.585
y[1] (closed_form) = 0.085746930795795827983082130554
y[1] (numeric) = 0.0857469307957958279051342389641
absolute error = 7.79478915899e-20
relative error = 9.09045849997021527500000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.415
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.415
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.584
y[1] (closed_form) = 0.0856967350229530135085477351382
y[1] (numeric) = 0.085696735022953013430491782746
absolute error = 7.80559523922e-20
relative error = 9.10839279597915763199999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.416
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.416
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.583
y[1] (closed_form) = 0.085646583313698854108667871029
y[1] (numeric) = 0.0856465833136988540305041106281
absolute error = 7.81637604009e-20
relative error = 9.12631390263503900099999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.417
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.417
Order of pole (three term test) = 1.771e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.582
y[1] (closed_form) = 0.085596475616474377037410110861
y[1] (numeric) = 0.08559647561647437695913879458
absolute error = 7.82713162810e-20
relative error = 9.14422185227629444000000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.418
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.418
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.581
y[1] (closed_form) = 0.0855464118797959991825184880766
y[1] (numeric) = 0.0855464118797959991041398673804
absolute error = 7.83786206962e-20
relative error = 9.16211667724092368200000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.419
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.419
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.58
y[1] (closed_form) = 0.0854963920522553948223384973155
y[1] (numeric) = 0.0854963920522553947438528230081
absolute error = 7.84856743074e-20
relative error = 9.17999840969073359999999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.42
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.42
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.579
y[1] (closed_form) = 0.0854464160825193636531965803318
y[1] (numeric) = 0.0854464160825193635746041025582
absolute error = 7.85924777736e-20
relative error = 9.19786708171584237600000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.421
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.421
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.578
y[1] (closed_form) = 0.0853964839193296990867016837797
y[1] (numeric) = 0.0853964839193296990080026520268
absolute error = 7.86990317529e-20
relative error = 9.21572272545126243599999999998e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.422
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.422
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.577
y[1] (closed_form) = 0.0853465955115030568163381377493
y[1] (numeric) = 0.0853465955115030567375328008494
absolute error = 7.88053368999e-20
relative error = 9.23356537277208407099999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.423
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.423
Order of pole (three term test) = 1.867e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.576
y[1] (closed_form) = 0.0852967508079308236527207616384
y[1] (numeric) = 0.08529675080793082357380936777
absolute error = 7.89113938684e-20
relative error = 9.25139505560895078400000000002e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.424
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.424
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.575
y[1] (closed_form) = 0.0852469497575789866268847567799
y[1] (numeric) = 0.0852469497575789865478675534692
absolute error = 7.90172033107e-20
relative error = 9.26921180586580187499999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.425
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.425
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.574
y[1] (closed_form) = 0.0851971923094880023609845932805
y[1] (numeric) = 0.085197192309488002281861827405
absolute error = 7.91227658755e-20
relative error = 9.28701565517300238000000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.426
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.426
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.573
y[1] (closed_form) = 0.0851474784127726667057777417508
y[1] (numeric) = 0.0851474784127726666265496595396
absolute error = 7.92280822112e-20
relative error = 9.30480663527380284800000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.427
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.427
Order of pole (three term test) = 1.933e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.572
y[1] (closed_form) = 0.0850978080166219846442707390166
y[1] (numeric) = 0.0850978080166219845649375860527
absolute error = 7.93331529639e-20
relative error = 9.32258477778934257600000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.428
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.428
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.571
y[1] (closed_form) = 0.0850481810702990404609067105652
y[1] (numeric) = 0.0850481810702990403814687317879
absolute error = 7.94379787773e-20
relative error = 9.34035011420623269299999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.429
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.429
Order of pole (three term test) = 1.967e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.57
y[1] (closed_form) = 0.0849985975231408681756751013609
y[1] (numeric) = 0.0849985975231408680961325410672
absolute error = 7.95425602937e-20
relative error = 9.35810267599351129999999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.43
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.43
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.569
y[1] (closed_form) = 0.0849490573245583222425259908012
y[1] (numeric) = 0.0849490573245583221628790926479
absolute error = 7.96468981533e-20
relative error = 9.37584249451988961300000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.431
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.431
Order of pole (three term test) = 2.002e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.568
y[1] (closed_form) = 0.0848995604240359485114729869974
y[1] (numeric) = 0.0848995604240359484317219940027
absolute error = 7.97509929947e-20
relative error = 9.39356960111205292800000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.432
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.432
Order of pole (three term test) = 2.020e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.567
y[1] (closed_form) = 0.084850106771131855453770310252
y[1] (numeric) = 0.0848501067711318553739154647973
absolute error = 7.98548454547e-20
relative error = 9.41128402703066848299999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.433
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.433
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.566
y[1] (closed_form) = 0.0848006963154775856495512855955
y[1] (numeric) = 0.084800696315477585569592829428
absolute error = 7.99584561675e-20
relative error = 9.42898580337555630000000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.434
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.434
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.565
y[1] (closed_form) = 0.0847513290067779875373170695534
y[1] (numeric) = 0.0847513290067779874572552437868
absolute error = 8.00618257666e-20
relative error = 9.44667496130910884999999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.435
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.435
Order of pole (three term test) = 2.073e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.564
y[1] (closed_form) = 0.0847020047948110874246660369354
y[1] (numeric) = 0.084702004794811087344501082053
absolute error = 8.01649548824e-20
relative error = 9.46435153177283110400000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.436
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.436
Order of pole (three term test) = 8.366e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.563
y[1] (closed_form) = 0.0846527236294279617596558494312
y[1] (numeric) = 0.0846527236294279616793880052865
absolute error = 8.02678441447e-20
relative error = 9.48201554578172614300000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.437
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.437
Order of pole (three term test) = 1.266e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.562
y[1] (closed_form) = 0.0846034854605526096621918191137
y[1] (numeric) = 0.084603485460552609581821324933
absolute error = 8.03704941807e-20
relative error = 9.49966703418781810800000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.438
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.438
Order of pole (three term test) = 6.385e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.561
y[1] (closed_form) = 0.0845542902381818257148367666743
y[1] (numeric) = 0.0845542902381818256343638610585
absolute error = 8.04729056158e-20
relative error = 9.51730602777399791800000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.439
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.439
Order of pole (three term test) = 8.588e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.56
y[1] (closed_form) = 0.0845051379123850730124391563006
y[1] (numeric) = 0.0845051379123850729318640772267
absolute error = 8.05750790739e-20
relative error = 9.53493255728903040000000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.44
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.44
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.559
y[1] (closed_form) = 0.0844560284333043564699778666085
y[1] (numeric) = 0.0844560284333043563893008514316
absolute error = 8.06770151769e-20
relative error = 9.55254665338796088900000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.441
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.441
Order of pole (three term test) = 6.555e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.558
y[1] (closed_form) = 0.0844069617511540963880235299599
y[1] (numeric) = 0.0844069617511540963072448154148
absolute error = 8.07787145451e-20
relative error = 9.57014834667894116400000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.442
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.442
Order of pole (three term test) = 2.204e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.557
y[1] (closed_form) = 0.0843579378162210022752179408414
y[1] (numeric) = 0.0843579378162210021943377630447
absolute error = 8.08801777967e-20
relative error = 9.58773766766353178299999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.443
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.443
Order of pole (three term test) = 4.447e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.556
y[1] (closed_form) = 0.0843089565788639469271745977787
y[1] (numeric) = 0.0843089565788639468461931922308
absolute error = 8.09814055479e-20
relative error = 9.60531464674796414400000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.444
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.444
Order of pole (three term test) = 8.971e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.555
y[1] (closed_form) = 0.0842600179895138407612050025173
y[1] (numeric) = 0.0842600179895138406801226041031
absolute error = 8.10823984142e-20
relative error = 9.62287931439685955000000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.445
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.445
Order of pole (three term test) = 9.049e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.554
y[1] (closed_form) = 0.0842111219986735064062768949272
y[1] (numeric) = 0.0842111219986735063250937379192
absolute error = 8.11831570080e-20
relative error = 9.64043170084811327999999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.446
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.446
Order of pole (three term test) = 1.141e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.553
y[1] (closed_form) = 0.0841622685569175535476121523246
y[1] (numeric) = 0.0841622685569175534663284703841
absolute error = 8.12836819405e-20
relative error = 9.65797183633770364500000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.447
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.447
Order of pole (three term test) = 6.906e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.552
y[1] (closed_form) = 0.0841134576148922540253336276183
y[1] (numeric) = 0.0841134576148922539439496537969
absolute error = 8.13839738214e-20
relative error = 9.67549975106373465600000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.448
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.448
Order of pole (three term test) = 9.289e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.551
y[1] (closed_form) = 0.0840646891233154171865717419406
y[1] (numeric) = 0.0840646891233154171050877086824
absolute error = 8.14840332582e-20
relative error = 9.69301547510277178200000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.449
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.449
Order of pole (three term test) = 2.342e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.55
y[1] (closed_form) = 0.0840159630329762654904431842049
y[1] (numeric) = 0.0840159630329762654088593233482
absolute error = 8.15838608567e-20
relative error = 9.71051903846871750000000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.45
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.45
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.549
y[1] (closed_form) = 0.0839672792947353103653156023547
y[1] (numeric) = 0.0839672792947353102836321451335
absolute error = 8.16834572212e-20
relative error = 9.72801047113616501200000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.451
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.451
Order of pole (three term test) = 2.384e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.548
y[1] (closed_form) = 0.0839186378595242283177736989589
y[1] (numeric) = 0.0839186378595242282359908760048
absolute error = 8.17828229541e-20
relative error = 9.74548980299233646400000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.452
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.452
Order of pole (three term test) = 4.809e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.547
y[1] (closed_form) = 0.0838700386783457372927036672763
y[1] (numeric) = 0.08387003867834573721082170862
absolute error = 8.18819586563e-20
relative error = 9.76295706388424066699999999998e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.453
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.453
Order of pole (three term test) = 4.851e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.546
y[1] (closed_form) = 0.0838214817022734732839144229612
y[1] (numeric) = 0.0838214817022734732019335580352
absolute error = 8.19808649260e-20
relative error = 9.78041228347511416000000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.454
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.454
Order of pole (three term test) = 2.447e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.545
y[1] (closed_form) = 0.0837729668824518671947156012489
y[1] (numeric) = 0.0837729668824518671126360588882
absolute error = 8.20795423607e-20
relative error = 9.79785549148234917500000000002e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.455
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.455
Order of pole (three term test) = 2.468e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.544
y[1] (closed_form) = 0.0837244941700960219478737997257
y[1] (numeric) = 0.0837244941700960218656958081693
absolute error = 8.21779915564e-20
relative error = 9.81528671758181990399999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.456
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.456
Order of pole (three term test) = 1.245e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.543
y[1] (closed_form) = 0.0836760635164915898443700527049
y[1] (numeric) = 0.083676063516491589762093839599
absolute error = 8.22762131059e-20
relative error = 9.83270599120431909100000000002e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.457
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.457
Order of pole (three term test) = 2.511e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.542
y[1] (closed_form) = 0.0836276748729946501703830247863
y[1] (numeric) = 0.0836276748729946500880088171842
absolute error = 8.23742076021e-20
relative error = 9.85011334192917704399999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.458
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.458
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.541
y[1] (closed_form) = 0.0835793281910315870519239083767
y[1] (numeric) = 0.083579328191031586969451932742
absolute error = 8.24719756347e-20
relative error = 9.86750879908958030700000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.459
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.459
Order of pole (three term test) = 2.555e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.54
y[1] (closed_form) = 0.0835310234220989675565505028566
y[1] (numeric) = 0.0835310234220989674739809850643
absolute error = 8.25695177923e-20
relative error = 9.88489239202298680000000000002e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.46
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.46
Order of pole (three term test) = 1.289e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.539
y[1] (closed_form) = 0.0834827605177634200415894416348
y[1] (numeric) = 0.0834827605177634199589226069724
absolute error = 8.26668346624e-20
relative error = 9.90226415007086310399999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.461
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.461
Order of pole (three term test) = 7.799e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.538
y[1] (closed_form) = 0.0834345394296615127482970176158
y[1] (numeric) = 0.0834345394296615126655330907861
absolute error = 8.27639268297e-20
relative error = 9.91962410237466886799999999999e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.462
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.462
Order of pole (three term test) = 7.867e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.537
y[1] (closed_form) = 0.0833863601094996326413905375995
y[1] (numeric) = 0.0833863601094996325585297427217
absolute error = 8.28607948778e-20
relative error = 9.93697227807887508199999999998e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.463
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.463
Order of pole (three term test) = 2.645e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.536
y[1] (closed_form) = 0.0833382225090538644933836118386
y[1] (numeric) = 0.0833382225090538644104261724502
absolute error = 8.29574393884e-20
relative error = 9.95430870623470566400000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.464
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.464
Order of pole (three term test) = 8.005e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.535
y[1] (closed_form) = 0.0832901265801698702131602564502
y[1] (numeric) = 0.0832901265801698701301063955084
absolute error = 8.30538609418e-20
relative error = 9.97163341585962705000000000001e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.465
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.465
Order of pole (three term test) = 1.346e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.534
y[1] (closed_form) = 0.0832420722747627684182241535863
y[1] (numeric) = 0.0832420722747627683350740934695
absolute error = 8.31500601168e-20
relative error = 9.98894643592496620800000000000e-17 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.466
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.466
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.533
y[1] (closed_form) = 0.083194059544817014250060877253
y[1] (numeric) = 0.0831940595448170141668148397633
absolute error = 8.32460374897e-20
relative error = 1.00062477952353058330000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.467
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.467
Order of pole (three term test) = 1.095e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.532
y[1] (closed_form) = 0.083146088342386279432052351438
y[1] (numeric) = 0.0831460883423862793487105578018
absolute error = 8.33417936362e-20
relative error = 1.00235375226562466880000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.468
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.468
Order of pole (three term test) = 2.762e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.531
y[1] (closed_form) = 0.0830981586195933325693842617573
y[1] (numeric) = 0.083098158619593332485946932628
absolute error = 8.34373291293e-20
relative error = 1.00408156468616015730000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.469
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.469
Order of pole (three term test) = 2.786e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.53
y[1] (closed_form) = 0.083050270328629919690388592215
y[1] (numeric) = 0.0830502703286299196068559476739
absolute error = 8.35326445411e-20
relative error = 1.00580821965493099000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.47
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.47
Order of pole (three term test) = 8.431e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.529
y[1] (closed_form) = 0.083002423421756645028764904849
y[1] (numeric) = 0.0830024234217566449451371644074
absolute error = 8.36277404416e-20
relative error = 1.00753372002966658560000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.471
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.471
Order of pole (three term test) = 8.504e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.528
y[1] (closed_form) = 0.0829546178513028520461254220732
y[1] (numeric) = 0.0829546178513028519624028046736
absolute error = 8.37226173996e-20
relative error = 1.00925806866681968640000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.472
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.472
Order of pole (three term test) = 5.719e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.527
y[1] (closed_form) = 0.0829068535696665046943104093948
y[1] (numeric) = 0.0829068535696665046104931334131
absolute error = 8.38172759817e-20
relative error = 1.01098126840947435930000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.473
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.473
Order of pole (three term test) = 8.653e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.526
y[1] (closed_form) = 0.0828591305293140689169217899295
y[1] (numeric) = 0.0828591305293140688330100731759
absolute error = 8.39117167536e-20
relative error = 1.01270332210297023360000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.474
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.474
Order of pole (three term test) = 2.909e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.525
y[1] (closed_form) = 0.0828114486827803943895243517416
y[1] (numeric) = 0.0828114486827803943055184114628
absolute error = 8.40059402788e-20
relative error = 1.01442423257918425000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.475
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.475
Order of pole (three term test) = 5.869e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.524
y[1] (closed_form) = 0.0827638079826685964979653345446
y[1] (numeric) = 0.0827638079826685964138653874252
absolute error = 8.40999471194e-20
relative error = 1.01614400266613157440000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.476
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.476
Order of pole (three term test) = 8.880e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.523
y[1] (closed_form) = 0.0827162083816499385542646036914
y[1] (numeric) = 0.0827162083816499384700708658557
absolute error = 8.41937378357e-20
relative error = 1.01786263518309238530000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.477
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.477
Order of pole (three term test) = 2.986e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.522
y[1] (closed_form) = 0.0826686498324637142495290367018
y[1] (numeric) = 0.0826686498324637141652417237153
absolute error = 8.42873129865e-20
relative error = 1.01958013294418946600000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.478
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.478
Order of pole (three term test) = 6.023e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.521
y[1] (closed_form) = 0.0826211322879171303433461608149
y[1] (numeric) = 0.0826211322879171302589654876856
absolute error = 8.43806731293e-20
relative error = 1.02129649876076792130000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.479
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.479
Order of pole (three term test) = 9.112e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.52
y[1] (closed_form) = 0.0825736557008851895891134892325
y[1] (numeric) = 0.0825736557008851895046396704129
absolute error = 8.44738188196e-20
relative error = 1.02301173543288384000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.48
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.48
Order of pole (three term test) = 6.128e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.519
y[1] (closed_form) = 0.0825262200243105738947614088578
y[1] (numeric) = 0.0825262200243105738101946582468
absolute error = 8.45667506110e-20
relative error = 1.02472584575045757100000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.481
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.481
Order of pole (three term test) = 3.090e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.518
y[1] (closed_form) = 0.0824788252112035277183288734282
y[1] (numeric) = 0.0824788252112035276336694043717
absolute error = 8.46594690565e-20
relative error = 1.02643883250898030600000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.482
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.482
Order of pole (three term test) = 1.247e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.517
y[1] (closed_form) = 0.0824314712146417416978525530141
y[1] (numeric) = 0.082431471214641741613100578307
absolute error = 8.47519747071e-20
relative error = 1.02815069849252045190000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.483
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.483
Order of pole (three term test) = 9.432e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.516
y[1] (closed_form) = 0.0823841579877702365150314839297
y[1] (numeric) = 0.0823841579877702364301872158186
absolute error = 8.48442681111e-20
relative error = 1.02986144646516824160000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.484
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.484
Order of pole (three term test) = 9.514e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.515
y[1] (closed_form) = 0.0823368854838012469921306521699
y[1] (numeric) = 0.0823368854838012469071943023527
absolute error = 8.49363498172e-20
relative error = 1.03157107920860287000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.485
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.485
Order of pole (three term test) = 1.279e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.514
y[1] (closed_form) = 0.0822896536560141064215883285622
y[1] (numeric) = 0.0822896536560141063365601081911
absolute error = 8.50282203711e-20
relative error = 1.03327959948079993560000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.486
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.486
Order of pole (three term test) = 6.453e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.513
y[1] (closed_form) = 0.082242462457755131127793354957
y[1] (numeric) = 0.0822424624577551310426734746397
absolute error = 8.51198803173e-20
relative error = 1.03498701003782432370000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.487
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.487
Order of pole (three term test) = 6.508e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.512
y[1] (closed_form) = 0.082195311842437505260499957916
y[1] (numeric) = 0.082195311842437505175288627717
absolute error = 8.52113301990e-20
relative error = 1.03669331363258265600000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.488
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.488
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.511
y[1] (closed_form) = 0.0821482017635411658193490395767
y[1] (numeric) = 0.0821482017635411657340464690191
absolute error = 8.53025705576e-20
relative error = 1.03839851300870226960000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.489
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.489
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.51
y[1] (closed_form) = 0.0821011321746126879089662646447
y[1] (numeric) = 0.0821011321746126878235726627121
absolute error = 8.53936019326e-20
relative error = 1.04010261089926126000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.49
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.49
Order of pole (three term test) = 6.678e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.509
y[1] (closed_form) = 0.0820541030292651702241086278167
y[1] (numeric) = 0.0820541030292651701386242029536
absolute error = 8.54844248631e-20
relative error = 1.04180561004501361110000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.491
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.491
Order of pole (three term test) = 6.736e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.508
y[1] (closed_form) = 0.0820071142811781207643325473771
y[1] (numeric) = 0.0820071142811781206787575074919
absolute error = 8.55750398852e-20
relative error = 1.04350751316268145280000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.492
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.492
Order of pole (three term test) = 6.794e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.507
y[1] (closed_form) = 0.0819601658840973427776578882685
y[1] (numeric) = 0.0819601658840973426919924407338
absolute error = 8.56654475347e-20
relative error = 1.04520832297780390030000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.493
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.493
Order of pole (three term test) = 1.028e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.506
y[1] (closed_form) = 0.0819132577918348209327036715816
y[1] (numeric) = 0.0819132577918348208469480232366
absolute error = 8.57556483450e-20
relative error = 1.04690804219910042000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.494
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.494
Order of pole (three term test) = 6.912e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.505
y[1] (closed_form) = 0.0818663899582686077187725772154
y[1] (numeric) = 0.081866389958268607632926934367
absolute error = 8.58456428484e-20
relative error = 1.04860667353427721000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.495
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.495
Order of pole (three term test) = 6.972e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.504
y[1] (closed_form) = 0.0818195623373427100733626923741
y[1] (numeric) = 0.0818195623373427099874272607986
absolute error = 8.59354315755e-20
relative error = 1.05030421968266620800000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.496
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.496
Order of pole (three term test) = 3.516e-28
NO COMPLEX POLE (six term test) for Equation 1
memory used=186.5MB, alloc=44.3MB, time=1.48
TOP MAIN SOLVE Loop
x[1] = 2.503
y[1] (closed_form) = 0.081772774883066976236586300656
y[1] (numeric) = 0.0817727748830669761505612856003
absolute error = 8.60250150557e-20
relative error = 1.05200068334129080130000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.497
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.497
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.502
y[1] (closed_form) = 0.0817260275495169828319768447281
y[1] (numeric) = 0.0817260275495169827458624509114
absolute error = 8.61143938167e-20
relative error = 1.05369606719871646680000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.498
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.498
Order of pole (three term test) = 7.153e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.501
y[1] (closed_form) = 0.0816793202908339221731665300034
y[1] (numeric) = 0.0816793202908339220869629616192
absolute error = 8.62035683842e-20
relative error = 1.05539037393132898420000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.499
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.499
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.5
y[1] (closed_form) = 0.0816326530612244897959183673469
y[1] (numeric) = 0.0816326530612244897096258280634
absolute error = 8.62925392835e-20
relative error = 1.05708360622287500000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.5
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.5
Order of pole (three term test) = 3.639e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.499
y[1] (closed_form) = 0.0815860258149607722149977796364
y[1] (numeric) = 0.0815860258149607721286164725989
absolute error = 8.63813070375e-20
relative error = 1.05877576673994453750000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.501
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.501
Order of pole (three term test) = 1.468e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.498
y[1] (closed_form) = 0.0815394385063801349053702200357
y[1] (numeric) = 0.0815394385063801348189003478682
absolute error = 8.64698721675e-20
relative error = 1.06046685814170867000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.502
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.502
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.497
y[1] (closed_form) = 0.0814928910898851105072125690722
y[1] (numeric) = 0.0814928910898851104206543338781
absolute error = 8.65582351941e-20
relative error = 1.06215688309091784690000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.503
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.503
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.496
y[1] (closed_form) = 0.0814463835199432872542273930902
y[1] (numeric) = 0.0814463835199432871675809964541
absolute error = 8.66463966361e-20
relative error = 1.06384584424038197760000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.504
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.504
Order of pole (three term test) = 3.765e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.495
y[1] (closed_form) = 0.0813999157510871976247504583832
y[1] (numeric) = 0.0813999157510871975380161013729
absolute error = 8.67343570103e-20
relative error = 1.06553374423046075750000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.505
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.505
Order of pole (three term test) = 7.595e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.494
y[1] (closed_form) = 0.0813534877379142072151432032904
y[1] (numeric) = 0.0813534877379142071283210864575
absolute error = 8.68221168329e-20
relative error = 1.06722058570621278440000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.506
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.506
Order of pole (three term test) = 7.661e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.493
y[1] (closed_form) = 0.081307099435086403834963174795
y[1] (numeric) = 0.0813070994350864037480534981774
absolute error = 8.69096766176e-20
relative error = 1.06890637129401666240000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.507
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.507
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.492
y[1] (closed_form) = 0.0812607507973304868234067367112
y[1] (numeric) = 0.0812607507973304867364096998335
absolute error = 8.69970368777e-20
relative error = 1.07059110362733637280000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.508
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.508
Order of pole (three term test) = 7.793e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.491
y[1] (closed_form) = 0.0812144417794376565865196533671
y[1] (numeric) = 0.0812144417794376564994354552426
absolute error = 8.70841981245e-20
relative error = 1.07227478532701658450000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.509
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.509
Order of pole (three term test) = 7.860e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.49
y[1] (closed_form) = 0.0811681723362635043546724458405
y[1] (numeric) = 0.0811681723362635042675012849729
absolute error = 8.71711608676e-20
relative error = 1.07395741900491876000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.51
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.51
Order of pole (three term test) = 3.964e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.489
y[1] (closed_form) = 0.0811219424227279021597987072569
y[1] (numeric) = 0.0811219424227279020725407816412
absolute error = 8.72579256157e-20
relative error = 1.07563900727373339970000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.511
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.511
Order of pole (three term test) = 1.999e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.488
y[1] (closed_form) = 0.0810757519938148930318958494405
y[1] (numeric) = 0.0810757519938148929445513565646
absolute error = 8.73444928759e-20
relative error = 1.07731955273832472960000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.512
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.512
Order of pole (three term test) = 4.032e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.487
y[1] (closed_form) = 0.0810296010045725814142890353419
y[1] (numeric) = 0.0810296010045725813268581721885
absolute error = 8.74308631534e-20
relative error = 1.07899905799198232460000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.513
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.513
Order of pole (three term test) = 1.627e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.486
y[1] (closed_form) = 0.0809834894101130237971603301406
y[1] (numeric) = 0.0809834894101130237096432931882
absolute error = 8.75170369524e-20
relative error = 1.08067752562747787040000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.514
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.514
Order of pole (three term test) = 4.101e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.485
y[1] (closed_form) = 0.0809374171656121195688463787587
y[1] (numeric) = 0.0809374171656121194812433639831
absolute error = 8.76030147756e-20
relative error = 1.08235495823086251000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.515
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.515
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.484
y[1] (closed_form) = 0.0808913842263095020844091887435
y[1] (numeric) = 0.080891384226309501996720391619
absolute error = 8.76887971245e-20
relative error = 1.08403135838513287200000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.516
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.516
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.483
y[1] (closed_form) = 0.0808453905475084299509858650728
y[1] (numeric) = 0.080845390547508429863211480574
absolute error = 8.77743844988e-20
relative error = 1.08570672866277735320000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.517
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.517
Order of pole (three term test) = 1.262e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.482
y[1] (closed_form) = 0.0807994360845756785294244074412
y[1] (numeric) = 0.0807994360845756784415646300444
absolute error = 8.78597773968e-20
relative error = 1.08738107163067336320000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.518
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.518
Order of pole (three term test) = 4.244e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.481
y[1] (closed_form) = 0.0807535207929414316517139409889
y[1] (numeric) = 0.0807535207929414315637689646735
absolute error = 8.79449763154e-20
relative error = 1.08905438985004805940000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.519
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.519
Order of pole (three term test) = 4.280e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.48
y[1] (closed_form) = 0.0807076446280991735537190082645
y[1] (numeric) = 0.0807076446280991734656890265138
absolute error = 8.80299817507e-20
relative error = 1.09072668588387328000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.52
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.52
Order of pole (three term test) = 1.295e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.479
y[1] (closed_form) = 0.0806618075456055810227288034683
y[1] (numeric) = 0.0806618075456055809346140092721
absolute error = 8.81147941962e-20
relative error = 1.09239796227453192420000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.521
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.521
Order of pole (three term test) = 1.306e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.478
y[1] (closed_form) = 0.080616009501080415759333479732
y[1] (numeric) = 0.0806160095010804156711340655867
absolute error = 8.81994141453e-20
relative error = 1.09406822157474752520000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.522
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.522
Order of pole (three term test) = 4.391e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.477
y[1] (closed_form) = 0.0805702504502064169531409063298
y[1] (numeric) = 0.080570250450206416864857064241
absolute error = 8.82838420888e-20
relative error = 1.09573746631656177520000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.523
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.523
Order of pole (three term test) = 8.857e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.476
y[1] (closed_form) = 0.0805245303487291940718484953507
y[1] (numeric) = 0.0805245303487291939834804168336
absolute error = 8.83680785171e-20
relative error = 1.09740569903857364960000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.524
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.524
Order of pole (three term test) = 4.466e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.475
y[1] (closed_form) = 0.0804788491524571198631859564409
y[1] (numeric) = 0.080478849152457119774733832522
absolute error = 8.84521239189e-20
relative error = 1.09907292226978181250000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.525
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.525
Order of pole (three term test) = 9.009e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.474
y[1] (closed_form) = 0.080433206817261223569246073814
y[1] (numeric) = 0.080433206817261223480710095033
absolute error = 8.85359787810e-20
relative error = 1.10073913852704795600000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.526
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.526
Order of pole (three term test) = 9.086e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.473
y[1] (closed_form) = 0.0803876032990750843527218318021
y[1] (numeric) = 0.0803876032990750842641021882127
absolute error = 8.86196435894e-20
relative error = 1.10240435032872327260000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.527
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.527
Order of pole (three term test) = 9.164e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.472
y[1] (closed_form) = 0.0803420385538947249345694438016
y[1] (numeric) = 0.0803420385538947248458663249733
absolute error = 8.87031188283e-20
relative error = 1.10406856018218318720000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.528
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.528
Order of pole (three term test) = 4.621e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.471
y[1] (closed_form) = 0.0802965125377785054426180645795
y[1] (numeric) = 0.080296512537778505353831659598
absolute error = 8.87864049815e-20
relative error = 1.10573177060120894150000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.529
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.529
Order of pole (three term test) = 9.321e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.47
y[1] (closed_form) = 0.0802510252068470174706481875306
y[1] (numeric) = 0.0802510252068470173817786850006
absolute error = 8.88695025300e-20
relative error = 1.10739398407607700000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.53
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.53
Order of pole (three term test) = 9.401e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.469
y[1] (closed_form) = 0.0802055765172829783474619466647
y[1] (numeric) = 0.0802055765172829782585095347103
absolute error = 8.89524119544e-20
relative error = 1.10905520310339297840000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.531
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.531
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.468
y[1] (closed_form) = 0.0801601664253311256154697578137
y[1] (numeric) = 0.0801601664253311255264346240799
absolute error = 8.90351337338e-20
relative error = 1.11071543017236461120000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.532
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.532
Order of pole (three term test) = 9.562e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.467
y[1] (closed_form) = 0.0801147948872981117183189448497
y[1] (numeric) = 0.080114794887298111629201276504
absolute error = 8.91176683457e-20
relative error = 1.11237466776351016730000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.533
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.533
Order of pole (three term test) = 4.822e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.466
y[1] (closed_form) = 0.0800694618595523988970912045617
y[1] (numeric) = 0.0800694618595523988078911882953
absolute error = 8.92000162664e-20
relative error = 1.11403291835360715840000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.534
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.534
Order of pole (three term test) = 4.863e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.465
y[1] (closed_form) = 0.0800241672985241542945969682843
y[1] (numeric) = 0.0800241672985241542053147903134
absolute error = 8.92821779709e-20
relative error = 1.11569018441440985250000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.535
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.535
Order of pole (three term test) = 9.808e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.464
y[1] (closed_form) = 0.079978911160705145267295919412
y[1] (numeric) = 0.079978911160705145177931765479
absolute error = 8.93641539330e-20
relative error = 1.11734646841386316800000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.536
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.536
Order of pole (three term test) = 4.946e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.463
y[1] (closed_form) = 0.079933693402648634904374123577
y[1] (numeric) = 0.0799336934026486348149281789525
absolute error = 8.94459446245e-20
relative error = 1.11900177280606144050000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.537
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.537
Order of pole (three term test) = 4.988e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.462
y[1] (closed_form) = 0.0798885139809692777535094225308
y[1] (numeric) = 0.079888513980969277663981872014
absolute error = 8.95275505168e-20
relative error = 1.12065610005121505920000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.538
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.538
Order of pole (three term test) = 1.006e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.461
y[1] (closed_form) = 0.0798433728523430157528579336488
y[1] (numeric) = 0.0798433728523430156632489615697
absolute error = 8.96089720791e-20
relative error = 1.12230945259310161110000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.539
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.539
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.46
y[1] (closed_form) = 0.0797982699735069743687956845096
y[1] (numeric) = 0.0797982699735069742791054747298
absolute error = 8.96902097798e-20
relative error = 1.12396183287654168000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.54
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.54
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.459
y[1] (closed_form) = 0.0797532053012593589389505961593
y[1] (numeric) = 0.0797532053012593588491793320733
absolute error = 8.97712640860e-20
relative error = 1.12561324334111056600000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.541
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.541
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.458
y[1] (closed_form) = 0.0797081787924593512200612095045
y[1] (numeric) = 0.0797081787924593511302090740416
absolute error = 8.98521354629e-20
relative error = 1.12726368641357415560000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.542
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.542
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.457
y[1] (closed_form) = 0.0796631904040270061401997267711
y[1] (numeric) = 0.0796631904040270060502669023956
absolute error = 8.99328243755e-20
relative error = 1.12891316452917079950000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.543
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.543
Order of pole (three term test) = 1.050e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.456
y[1] (closed_form) = 0.0796182400929431487548981141306
y[1] (numeric) = 0.079618240092943148664884782844
absolute error = 9.00133312866e-20
relative error = 1.13056168010649365760000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.544
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.544
Order of pole (three term test) = 1.059e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.455
y[1] (closed_form) = 0.0795733278162492714067171824677
y[1] (numeric) = 0.0795733278162492713166235258101
absolute error = 9.00936566576e-20
relative error = 1.13220923555747564000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.545
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.545
Order of pole (three term test) = 5.338e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.454
y[1] (closed_form) = 0.0795284535310474310877997308122
y[1] (numeric) = 0.0795284535310474309976259298631
absolute error = 9.01738009491e-20
relative error = 1.13385583329489349560000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.546
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.546
Order of pole (three term test) = 5.383e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.453
y[1] (closed_form) = 0.0794836171945001470049500012281
y[1] (numeric) = 0.079483617194500146914696236608
absolute error = 9.02537646201e-20
relative error = 1.13550147572228370090000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.547
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.547
Order of pole (three term test) = 1.629e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.452
y[1] (closed_form) = 0.0794388187638302983467828549422
y[1] (numeric) = 0.0794388187638302982564493068137
absolute error = 9.03335481285e-20
relative error = 1.13714616524018906400000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.548
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.548
Order of pole (three term test) = 5.475e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.451
y[1] (closed_form) = 0.0793940581963210222524872372065
y[1] (numeric) = 0.0793940581963210221620740852758
absolute error = 9.04131519307e-20
relative error = 1.13878990424109071070000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.549
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.549
Order of pole (three term test) = 1.656e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.45
y[1] (closed_form) = 0.0793493354493156119817496528468
y[1] (numeric) = 0.0793493354493156118912570763642
absolute error = 9.04925764826e-20
relative error = 1.14043269512196650000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.55
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.55
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.449
y[1] (closed_form) = 0.0793046504802174152853845256483
y[1] (numeric) = 0.0793046504802174151948127034112
absolute error = 9.05718222371e-20
relative error = 1.14207454025275839710000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.551
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.551
Order of pole (three term test) = 1.685e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.448
y[1] (closed_form) = 0.0792600032464897329762194627061
y[1] (numeric) = 0.0792600032464897328855685730582
absolute error = 9.06508896479e-20
relative error = 1.14371544202421852160000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.552
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.552
Order of pole (three term test) = 5.663e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.447
y[1] (closed_form) = 0.0792153937056557176997845895798
y[1] (numeric) = 0.0792153937056557176090548104144
absolute error = 9.07297791654e-20
relative error = 1.14535540279618900860000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.553
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.553
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.446
y[1] (closed_form) = 0.0791708218152982729043562636311
y[1] (numeric) = 0.0791708218152982728135477723906
absolute error = 9.08084912405e-20
relative error = 1.14699442494549129800000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.554
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.554
Order of pole (three term test) = 5.760e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.445
y[1] (closed_form) = 0.0791262875330599520099066111992
y[1] (numeric) = 0.0791262875330599519190195848771
absolute error = 9.08870263221e-20
relative error = 1.14863251083435785250000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.555
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.555
Order of pole (three term test) = 5.809e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.444
y[1] (closed_form) = 0.0790817908166428577755114693903
y[1] (numeric) = 0.079081790816642857684546084533
absolute error = 9.09653848573e-20
relative error = 1.15026966281289909280000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.556
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.556
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.443
y[1] (closed_form) = 0.0790373316238085418647704451597
y[1] (numeric) = 0.0790373316238085417737268778668
absolute error = 9.10435672929e-20
relative error = 1.15190588323802673210000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.557
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.557
Order of pole (three term test) = 5.907e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.442
y[1] (closed_form) = 0.0789929099123779046087939330916
y[1] (numeric) = 0.0789929099123779045176723590181
absolute error = 9.11215740735e-20
relative error = 1.15354117444939925400000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.558
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.558
Order of pole (three term test) = 1.191e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.441
y[1] (closed_form) = 0.0789485256402310949663130588519
y[1] (numeric) = 0.0789485256402310948751136532083
absolute error = 9.11994056436e-20
relative error = 1.15517553879595217160000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.559
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.559
Order of pole (three term test) = 2.403e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.44
y[1] (closed_form) = 0.0789041787653074106804696376719
y[1] (numeric) = 0.0789041787653074105891925752266
absolute error = 9.12770624453e-20
relative error = 1.15680897860675408000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.56
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.56
Order of pole (three term test) = 1.818e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.439
y[1] (closed_form) = 0.0788598692456051986318443564841
y[1] (numeric) = 0.0788598692456051985404898115638
absolute error = 9.13545449203e-20
relative error = 1.15844149621629153630000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.561
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.561
Order of pole (three term test) = 1.222e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.438
y[1] (closed_form) = 0.0788155970391817553872825044191
y[1] (numeric) = 0.0788155970391817552958506509106
absolute error = 9.14318535085e-20
relative error = 1.16007309394670067400000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.562
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.562
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.437
y[1] (closed_form) = 0.0787713621041532279440776893587
y[1] (numeric) = 0.0787713621041532278525687007096
absolute error = 9.15089886491e-20
relative error = 1.16170377412167637790000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.563
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.563
Order of pole (three term test) = 1.864e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.436
y[1] (closed_form) = 0.07872716439869451466907508808
y[1] (numeric) = 0.0787271643986945145774891373006
absolute error = 9.15859507794e-20
relative error = 1.16333353905121362240000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.564
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.564
Order of pole (three term test) = 1.253e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.435
y[1] (closed_form) = 0.078683003881039166432256884271
y[1] (numeric) = 0.0786830038810391663405941439352
absolute error = 9.16627403358e-20
relative error = 1.16496239104425775500000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.565
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.565
Order of pole (three term test) = 6.319e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.434
y[1] (closed_form) = 0.0786388805094792879343736523261
y[1] (numeric) = 0.0786388805094792878426342945723
absolute error = 9.17393577538e-20
relative error = 1.16659033240868115280000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.566
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.566
Order of pole (three term test) = 2.549e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.433
y[1] (closed_form) = 0.0785947942423654392281865453729
y[1] (numeric) = 0.0785947942423654391363707419055
absolute error = 9.18158034674e-20
relative error = 1.16821736544362575860000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.567
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.567
Order of pole (three term test) = 1.928e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.432
y[1] (closed_form) = 0.0785507450381065374328862434395
y[1] (numeric) = 0.0785507450381065373409941655302
absolute error = 9.18920779093e-20
relative error = 1.16984349244200440320000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.568
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.568
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.431
y[1] (closed_form) = 0.0785067328551697586412557120518
y[1] (numeric) = 0.0785067328551697585492875305408
absolute error = 9.19681815110e-20
relative error = 1.17146871569173687100000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.569
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.569
Order of pole (three term test) = 6.535e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.43
y[1] (closed_form) = 0.0784627576520804400191449128672
y[1] (numeric) = 0.0784627576520804399271007981643
absolute error = 9.20441147029e-20
relative error = 1.17309303747699021000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.57
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.57
Order of pole (three term test) = 6.591e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.429
y[1] (closed_form) = 0.0784188193874219820968266962128
y[1] (numeric) = 0.0784188193874219820047068182988
absolute error = 9.21198779140e-20
relative error = 1.17471646007432247400000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.571
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.571
Order of pole (three term test) = 1.329e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.428
y[1] (closed_form) = 0.0783749180198357512518041906128
y[1] (numeric) = 0.0783749180198357511596087190403
absolute error = 9.21954715725e-20
relative error = 1.17633898576029684000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.572
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.572
Order of pole (three term test) = 2.011e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.427
y[1] (closed_form) = 0.0783310535080209823826410865645
y[1] (numeric) = 0.0783310535080209822903701904594
absolute error = 9.22708961051e-20
relative error = 1.17796061680252517790000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.573
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.573
Order of pole (three term test) = 1.352e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.426
y[1] (closed_form) = 0.0782872258107346817733872909771
y[1] (numeric) = 0.0782872258107346816810411390397
absolute error = 9.23461519374e-20
relative error = 1.17958135546473240240000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.574
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.574
Order of pole (three term test) = 6.816e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.425
y[1] (closed_form) = 0.0782434348867915301481735048168
y[1] (numeric) = 0.0782434348867915300557522653233
absolute error = 9.24212394935e-20
relative error = 1.18120120400161343750000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.575
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.575
Order of pole (three term test) = 2.062e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.424
y[1] (closed_form) = 0.0781996806950637859155493496289
y[1] (numeric) = 0.0781996806950637858230531904319
absolute error = 9.24961591970e-20
relative error = 1.18282016467157587200000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.576
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.576
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.423
y[1] (closed_form) = 0.0781559631944811886021407387255
y[1] (numeric) = 0.0781559631944811885095698272558
absolute error = 9.25709114697e-20
relative error = 1.18443823972009715130000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.577
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.577
Order of pole (three term test) = 6.990e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.422
y[1] (closed_form) = 0.0781122823440308624752032559698
y[1] (numeric) = 0.0781122823440308623825577592375
absolute error = 9.26454967323e-20
relative error = 1.18605543138863011320000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.578
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.578
Order of pole (three term test) = 7.048e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.421
y[1] (closed_form) = 0.0780686381027572203536493692327
y[1] (numeric) = 0.078068638102757220260929453828
absolute error = 9.27199154047e-20
relative error = 1.18767174191841483270000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.579
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.579
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.42
y[1] (closed_form) = 0.0780250304297618676071283667802
y[1] (numeric) = 0.0780250304297618675143341988748
absolute error = 9.27941679054e-20
relative error = 1.18928717354276856000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.58
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.58
Order of pole (three term test) = 7.168e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.419
y[1] (closed_form) = 0.0779814592842035063427389630695
y[1] (numeric) = 0.0779814592842035062498707084183
absolute error = 9.28682546512e-20
relative error = 1.19090172848319692320000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.581
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.581
Order of pole (three term test) = 7.228e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.418
y[1] (closed_form) = 0.0779379246252978397789555756946
y[1] (numeric) = 0.0779379246252978396860133996357
absolute error = 9.29421760589e-20
relative error = 1.19251540897115364360000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.582
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.582
Order of pole (three term test) = 7.289e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.417
y[1] (closed_form) = 0.0778944264123174768063503275345
y[1] (numeric) = 0.0778944264123174767133343949911
absolute error = 9.30159325434e-20
relative error = 1.19412821722365688260000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.583
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.583
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.416
y[1] (closed_form) = 0.0778509646045918367346938775511
y[1] (numeric) = 0.077850964604591836641604353033
absolute error = 9.30895245181e-20
relative error = 1.19574015544836751360000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.584
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.584
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.415
y[1] (closed_form) = 0.0778075391615070542260192301333
y[1] (numeric) = 0.0778075391615070541328562777374
absolute error = 9.31629523959e-20
relative error = 1.19735122585639587750000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.585
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.585
Order of pole (three term test) = 7.474e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.414
y[1] (closed_form) = 0.0777641500425058844132337164202
y[1] (numeric) = 0.0777641500425058843199974998318
absolute error = 9.32362165884e-20
relative error = 1.19896143065200460640000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.586
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.586
Order of pole (three term test) = 7.537e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.413
y[1] (closed_form) = 0.0777207972070876082038653816724
y[1] (numeric) = 0.0777207972070876081105560641663
absolute error = 9.33093175061e-20
relative error = 1.20057077203514357090000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.587
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.587
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.412
y[1] (closed_form) = 0.0776774806148079377685310504855
y[1] (numeric) = 0.0776774806148079376751487949273
absolute error = 9.33822555582e-20
relative error = 1.20217925219884390080000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.588
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.588
Order of pole (three term test) = 7.664e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.411
y[1] (closed_form) = 0.0776342002252789222137143764798
y[1] (numeric) = 0.0776342002252789221202593453273
absolute error = 9.34550311525e-20
relative error = 1.20378687332789145250000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.589
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.589
Order of pole (three term test) = 2.318e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.41
y[1] (closed_form) = 0.0775909559981688534384432150588
y[1] (numeric) = 0.0775909559981688533449155703627
absolute error = 9.35276446961e-20
relative error = 1.20539363760780641000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.59
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.59
Order of pole (three term test) = 7.793e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.409
y[1] (closed_form) = 0.0775477478932021721744566869073
y[1] (numeric) = 0.0775477478932021720808565903123
absolute error = 9.36000965950e-20
relative error = 1.20699954721966819500000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.591
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.591
Order of pole (three term test) = 7.859e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.408
y[1] (closed_form) = 0.0775045758701593742094533261244
y[1] (numeric) = 0.0775045758701593741157809388705
absolute error = 9.36723872539e-20
relative error = 1.20860460433750360960000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.592
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.592
Order of pole (three term test) = 2.377e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.407
y[1] (closed_form) = 0.0774614398888769167930127302455
y[1] (numeric) = 0.0774614398888769166992682131692
absolute error = 9.37445170763e-20
relative error = 1.21020881112953921870000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.593
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.593
Order of pole (three term test) = 7.991e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.406
y[1] (closed_form) = 0.0774183399092471252247841499265
y[1] (numeric) = 0.0774183399092471251309676634621
absolute error = 9.38164864644e-20
relative error = 1.21181216975687463840000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.594
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.594
Order of pole (three term test) = 1.612e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.405
y[1] (closed_form) = 0.077375275891218099624536473738
y[1] (numeric) = 0.077375275891218099530648177918
absolute error = 9.38882958200e-20
relative error = 1.21341468238507550000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.595
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.595
Order of pole (three term test) = 8.125e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.404
y[1] (closed_form) = 0.0773322477947936218836650783654
y[1] (numeric) = 0.0773322477947936217897051328225
absolute error = 9.39599455429e-20
relative error = 1.21501635116347716640000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.596
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.596
Order of pole (three term test) = 8.194e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.403
y[1] (closed_form) = 0.0772892555800330627977520265435
y[1] (numeric) = 0.0772892555800330627037205905111
absolute error = 9.40314360324e-20
relative error = 1.21661717824452845160000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.597
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.597
Order of pole (three term test) = 1.652e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.402
y[1] (closed_form) = 0.0772462992070512893797771042588
y[1] (numeric) = 0.077246299207051289285674336572
absolute error = 9.41027676868e-20
relative error = 1.21821716577730882720000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.598
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.598
Order of pole (three term test) = 1.666e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.401
y[1] (closed_form) = 0.0772033786360185723535781951717
y[1] (numeric) = 0.0772033786360185722594042542694
absolute error = 9.41739409023e-20
relative error = 1.21981631589325234230000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.599
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.599
Order of pole (three term test) = 1.680e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.4
y[1] (closed_form) = 0.0771604938271604938271604938272
y[1] (numeric) = 0.0771604938271604937329155377517
absolute error = 9.42449560755e-20
relative error = 1.22141463073848000000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.6
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.6
Order of pole (three term test) = 8.471e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.399
y[1] (closed_form) = 0.0771176447407578551454550600394
y[1] (numeric) = 0.0771176447407578550511392464391
absolute error = 9.43158136003e-20
relative error = 1.22301211243362376030000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.601
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.601
Order of pole (three term test) = 8.542e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.398
y[1] (closed_form) = 0.0770748313371465849221282149067
y[1] (numeric) = 0.0770748313371465848277417010357
absolute error = 9.43865138710e-20
relative error = 1.22460876311395788400000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.602
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.602
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.397
y[1] (closed_form) = 0.0770320535767176472500442741729
y[1] (numeric) = 0.0770320535767176471555872168929
absolute error = 9.44570572800e-20
relative error = 1.22620458489956352000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.603
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.603
Order of pole (three term test) = 8.686e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.396
y[1] (closed_form) = 0.0769893114199169500899851071876
y[1] (numeric) = 0.0769893114199169499954576629694
absolute error = 9.45274442182e-20
relative error = 1.22779957990046365120000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.604
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.604
Order of pole (three term test) = 2.628e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.395
y[1] (closed_form) = 0.0769466048272452538372309994788
y[1] (numeric) = 0.0769466048272452537426333244023
absolute error = 9.45976750765e-20
relative error = 1.22939375023607091250000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.605
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.605
Order of pole (three term test) = 2.649e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.394
y[1] (closed_form) = 0.0769039337592580800656082839687
y[1] (numeric) = 0.076903933759258079970940533725
absolute error = 9.46677502437e-20
relative error = 1.23098709800788861320000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.606
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.606
Order of pole (three term test) = 8.905e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.393
y[1] (closed_form) = 0.0768612981765656204486101901633
y[1] (numeric) = 0.076861298176565620353872520055
absolute error = 9.47376701083e-20
relative error = 1.23257962532286162670000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.607
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.607
Order of pole (three term test) = 8.980e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.392
y[1] (closed_form) = 0.076818698039832645857198342191
y[1] (numeric) = 0.0768186980398326457623909071337
absolute error = 9.48074350573e-20
relative error = 1.23417133427775214720000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.608
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.608
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.391
y[1] (closed_form) = 0.0767761333097784156338933154167
y[1] (numeric) = 0.0767761333097784155390162699401
absolute error = 9.48770454766e-20
relative error = 1.23576222696430328460000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.609
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.609
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.39
y[1] (closed_form) = 0.0767336039471765870427636374798
y[1] (numeric) = 0.0767336039471765869478171357282
absolute error = 9.49465017516e-20
relative error = 1.23735230547702636000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.61
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.61
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.389
y[1] (closed_form) = 0.0766911099128551248949235930307
y[1] (numeric) = 0.0766911099128551247999077887649
absolute error = 9.50158042658e-20
relative error = 1.23894157189493552180000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.611
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.611
Order of pole (three term test) = 9.283e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.388
y[1] (closed_form) = 0.0766486511676962113491511621775
y[1] (numeric) = 0.0766486511676962112540662087755
absolute error = 9.50849534020e-20
relative error = 1.24053002829714268800000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.612
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.612
Order of pole (three term test) = 1.872e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.387
y[1] (closed_form) = 0.07660622767263615588723839069
y[1] (numeric) = 0.0766062276726361557920844411479
absolute error = 9.51539495421e-20
relative error = 1.24211767676022917490000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.613
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.613
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.386
y[1] (closed_form) = 0.0765638393886653054636874553824
y[1] (numeric) = 0.0765638393886653053684646623154
absolute error = 9.52227930670e-20
relative error = 1.24370451935691473200000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.614
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.614
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.385
y[1] (closed_form) = 0.0765214862768279548293666507884
y[1] (numeric) = 0.0765214862768279547340751664323
absolute error = 9.52914843561e-20
relative error = 1.24529055814949492250000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.615
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.615
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.384
y[1] (closed_form) = 0.0764791682982222570287414832799
y[1] (numeric) = 0.0764791682982222569333814594916
absolute error = 9.53600237883e-20
relative error = 1.24687579520286996480000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.616
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.616
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.383
y[1] (closed_form) = 0.0764368854140001340702970161562
y[1] (numeric) = 0.0764368854140001339748686044155
absolute error = 9.54284117407e-20
relative error = 1.24846023256752674230000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.617
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.617
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.382
y[1] (closed_form) = 0.0763946375853671877697685639735
y[1] (numeric) = 0.076394637585367187674271915383
absolute error = 9.54966485905e-20
relative error = 1.25004387230435212200000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.618
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.618
Order of pole (three term test) = 9.839e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.381
y[1] (closed_form) = 0.0763524247735826107657987864697
y[1] (numeric) = 0.0763524247735826106702340517574
absolute error = 9.55647347123e-20
relative error = 1.25162671644928178030000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.619
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.619
Order of pole (three term test) = 9.921e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.38
y[1] (closed_form) = 0.0763102469399590977076401819238
y[1] (numeric) = 0.0763102469399590976120075114421
absolute error = 9.56326704817e-20
relative error = 1.25320876706038948000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.62
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.62
Order of pole (three term test) = 1.000e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=230.5MB, alloc=44.3MB, time=1.83
x[1] = 2.379
y[1] (closed_form) = 0.0762681040458627566145229266114
y[1] (numeric) = 0.0762681040458627565188224703406
absolute error = 9.57004562708e-20
relative error = 1.25479002615892838280000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.621
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.621
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.378
y[1] (closed_form) = 0.0762259960527130204063089512797
y[1] (numeric) = 0.0762259960527130203105408588265
absolute error = 9.57680924532e-20
relative error = 1.25637049579480622880000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.622
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.622
Order of pole (three term test) = 1.017e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.377
y[1] (closed_form) = 0.0761839229219825586050540871571
y[1] (numeric) = 0.0761839229219825585092185077574
absolute error = 9.58355793997e-20
relative error = 1.25795017799020476130000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.623
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.623
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.376
y[1] (closed_form) = 0.0761418846151971892071010530728
y[1] (numeric) = 0.0761418846151971891111981355923
absolute error = 9.59029174805e-20
relative error = 1.25952907476837916800000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.624
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.624
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.375
y[1] (closed_form) = 0.0760998810939357907253269916767
y[1] (numeric) = 0.0760998810939357906293568846115
absolute error = 9.59701070652e-20
relative error = 1.26110718815364375000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.625
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.625
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.374
y[1] (closed_form) = 0.0760579123198302144011701966158
y[1] (numeric) = 0.076057912319830214305133048094
absolute error = 9.60371485218e-20
relative error = 1.26268452015820969680000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.626
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.626
Order of pole (three term test) = 1.051e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.373
y[1] (closed_form) = 0.0760159782545651965860616038048
y[1] (numeric) = 0.076015978254565196489957561587
absolute error = 9.61040422178e-20
relative error = 1.26426107279660509620000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.627
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.627
Order of pole (three term test) = 1.060e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.372
y[1] (closed_form) = 0.0759740788598782712918875486386
y[1] (numeric) = 0.0759740788598782711957167601189
absolute error = 9.61707885197e-20
relative error = 1.26583684807908296480000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.628
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.628
Order of pole (three term test) = 1.069e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.371
y[1] (closed_form) = 0.0759322140975596829101112171546
y[1] (numeric) = 0.0759322140975596828138738293622
absolute error = 9.62373877924e-20
relative error = 1.26741184800369052840000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.629
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.629
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.37
y[1] (closed_form) = 0.0758903839294522990991811427573
y[1] (numeric) = 0.075890383929452299002877302357
absolute error = 9.63038404003e-20
relative error = 1.26898607457071307000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.63
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.63
Order of pole (three term test) = 1.087e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.369
y[1] (closed_form) = 0.0758485883174515238398560211757
y[1] (numeric) = 0.075848588317451523743485874469
absolute error = 9.63701467067e-20
relative error = 1.27055952977475257870000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.631
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.631
Order of pole (three term test) = 1.096e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.368
y[1] (closed_form) = 0.0758068272235052106580760348541
y[1] (numeric) = 0.0758068272235052105616397277804
absolute error = 9.64363070737e-20
relative error = 1.27213221560337594880000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.632
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.632
Order of pole (three term test) = 1.105e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.367
y[1] (closed_form) = 0.0757651006096135760150117939744
y[1] (numeric) = 0.0757651006096135759185094721116
absolute error = 9.65023218628e-20
relative error = 1.27370413404499786920000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.633
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.633
Order of pole (three term test) = 1.114e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.366
y[1] (closed_form) = 0.0757234084378291128639229147818
y[1] (numeric) = 0.0757234084378291127673547233477
absolute error = 9.65681914341e-20
relative error = 1.27527528707830149960000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.634
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.634
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.365
y[1] (closed_form) = 0.0756817506702565043734591668575
y[1] (numeric) = 0.0756817506702565042768252507106
absolute error = 9.66339161469e-20
relative error = 1.27684567668012275250000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.635
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.635
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.364
y[1] (closed_form) = 0.0756401272690525378170380294356
y[1] (numeric) = 0.0756401272690525377203385330761
absolute error = 9.66994963595e-20
relative error = 1.27841530482278431200000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.636
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.636
Order of pole (three term test) = 1.142e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.363
y[1] (closed_form) = 0.0755985381964260186279334028284
y[1] (numeric) = 0.0755985381964260185311684703995
absolute error = 9.67649324289e-20
relative error = 1.27998417347009812410000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.637
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.637
Order of pole (three term test) = 1.151e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.362
y[1] (closed_form) = 0.0755569834146376846197111244964
y[1] (numeric) = 0.0755569834146376845228808997843
absolute error = 9.68302247121e-20
relative error = 1.28155228459453083240000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.638
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.638
Order of pole (three term test) = 1.161e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.361
y[1] (closed_form) = 0.0755154628860001203716478402841
y[1] (numeric) = 0.0755154628860001202747524667201
absolute error = 9.68953735640e-20
relative error = 1.28311964014940204400000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.639
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.639
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.36
y[1] (closed_form) = 0.0754739765728776717787706798695
y[1] (numeric) = 0.0754739765728776716818103005304
absolute error = 9.69603793391e-20
relative error = 1.28468624209133936000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.64
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.64
Order of pole (three term test) = 1.180e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.359
y[1] (closed_form) = 0.0754325244376863607661560815098
y[1] (numeric) = 0.0754325244376863606691308391189
absolute error = 9.70252423909e-20
relative error = 1.28625209237231678290000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.641
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.641
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.358
y[1] (closed_form) = 0.0753911064428938001671270047625
y[1] (numeric) = 0.0753911064428938000700370416912
absolute error = 9.70899630713e-20
relative error = 1.28781719293166689320000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.642
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.642
Order of pole (three term test) = 1.200e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.357
y[1] (closed_form) = 0.075349722551019108764988660997
y[1] (numeric) = 0.0753497225510191086678341192645
absolute error = 9.71545417325e-20
relative error = 1.28938154572124539250000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.643
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.643
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.356
y[1] (closed_form) = 0.075308372724632826497943780191
y[1] (numeric) = 0.0753083727246328264007248014666
absolute error = 9.72189787244e-20
relative error = 1.29094515267092435840000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.644
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.644
Order of pole (three term test) = 1.220e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.355
y[1] (closed_form) = 0.0752670569263568298268293187767
y[1] (numeric) = 0.0752670569263568297295460443797
absolute error = 9.72832743970e-20
relative error = 1.29250801572040192500000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.645
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.645
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.354
y[1] (closed_form) = 0.0752257751188642472653173971039
y[1] (numeric) = 0.0752257751188642471679699680054
absolute error = 9.73474290985e-20
relative error = 1.29407013679395562600000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.646
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.646
Order of pole (three term test) = 1.240e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.353
y[1] (closed_form) = 0.0751845272648793750722241365037
y[1] (numeric) = 0.0751845272648793749748126933271
absolute error = 9.74114431766e-20
relative error = 1.29563151781767454940000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.647
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.647
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.352
y[1] (closed_form) = 0.0751433133271775931055709449062
y[1] (numeric) = 0.0751433133271775930080956279278
absolute error = 9.74753169784e-20
relative error = 1.29719216071811727360000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.648
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.648
Order of pole (three term test) = 1.260e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.351
y[1] (closed_form) = 0.0751021332685852808380436765467
y[1] (numeric) = 0.0751021332685852807405046256978
absolute error = 9.75390508489e-20
relative error = 1.29875206740232412890000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.649
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.649
Order of pole (three term test) = 1.271e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.35
y[1] (closed_form) = 0.0750609870519797335334959654721
y[1] (numeric) = 0.0750609870519797334358933203384
absolute error = 9.76026451337e-20
relative error = 1.30031123979371825000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.65
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.65
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.349
y[1] (closed_form) = 0.0750198746402890785841439043237
y[1] (numeric) = 0.0750198746402890784864778041481
absolute error = 9.76661001756e-20
relative error = 1.30186967978681305560000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.651
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.651
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.348
y[1] (closed_form) = 0.0749787959964921920081001092892
y[1] (numeric) = 0.0749787959964921919103706929705
absolute error = 9.77294163187e-20
relative error = 1.30342738930179904480000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.652
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.652
Order of pole (three term test) = 1.303e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.347
y[1] (closed_form) = 0.0749377510836186151068960790994
y[1] (numeric) = 0.0749377510836186150091034851955
absolute error = 9.77925939039e-20
relative error = 1.30498437022454829510000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.653
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.653
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.346
y[1] (closed_form) = 0.074896739864748471282642620619
y[1] (numeric) = 0.074896739864748471184786987346
absolute error = 9.78556332730e-20
relative error = 1.30654062446124646800000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.654
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.654
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.345
y[1] (closed_form) = 0.0748557623030123830144789758235
y[1] (numeric) = 0.0748557623030123829165604410579
absolute error = 9.79185347656e-20
relative error = 1.30809615389701954000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.655
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.655
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.344
y[1] (closed_form) = 0.0748148183615913889939621448991
y[1] (numeric) = 0.074814818361591388895980846178
absolute error = 9.79812987211e-20
relative error = 1.30965096042259288960000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.656
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.656
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.343
y[1] (closed_form) = 0.0747739080037168614190487577473
y[1] (numeric) = 0.07477390800371686132100483227
absolute error = 9.80439254773e-20
relative error = 1.31120504591556766770000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.657
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.657
Order of pole (three term test) = 1.357e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.342
y[1] (closed_form) = 0.0747330311926704234463227014136
y[1] (numeric) = 0.0747330311926704233482162860415
absolute error = 9.81064153721e-20
relative error = 1.31275841226311670440000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.658
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.658
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.341
y[1] (closed_form) = 0.0746921878917838668011225638303
y[1] (numeric) = 0.0746921878917838667029537950885
absolute error = 9.81687687418e-20
relative error = 1.31431106133923484580000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.659
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.659
Order of pole (three term test) = 1.380e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.34
y[1] (closed_form) = 0.0746513780644390695452238048314
y[1] (numeric) = 0.07465137806443906944699281891
absolute error = 9.82309859214e-20
relative error = 1.31586299500870584000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.66
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.66
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.339
y[1] (closed_form) = 0.0746106016740679140017314136225
y[1] (numeric) = 0.0746106016740679139034383463766
absolute error = 9.82930672459e-20
relative error = 1.31741421514448527390000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.661
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.661
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.338
y[1] (closed_form) = 0.074569858684152204836839657802
y[1] (numeric) = 0.0745698586841522047384846447532
absolute error = 9.83550130488e-20
relative error = 1.31896472360759190720000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.662
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.662
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.337
y[1] (closed_form) = 0.0745291490582235872981163726454
y[1] (numeric) = 0.0745291490582235871996995489828
absolute error = 9.84168236626e-20
relative error = 1.32051452225376821940000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.663
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.663
Order of pole (three term test) = 1.426e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.336
y[1] (closed_form) = 0.0744884727598634656089700806621
y[1] (numeric) = 0.0744884727598634655104915812425
absolute error = 9.84784994196e-20
relative error = 1.32206361294419036160000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.664
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.664
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.335
y[1] (closed_form) = 0.0744478297527029215189590704445
y[1] (numeric) = 0.0744478297527029214204190297941
absolute error = 9.85400406504e-20
relative error = 1.32361199752531914000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.665
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.665
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.334
y[1] (closed_form) = 0.0744072200004226330096024005554
y[1] (numeric) = 0.0744072200004226329110009528706
absolute error = 9.86014476848e-20
relative error = 1.32515967784093994880000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.666
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.666
Order of pole (three term test) = 1.461e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.333
y[1] (closed_form) = 0.0743666434667527931553536286349
y[1] (numeric) = 0.0743666434667527930566909077823
absolute error = 9.86627208526e-20
relative error = 1.32670665574289756140000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.667
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.667
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.332
y[1] (closed_form) = 0.0743261001154730291393988980709
y[1] (numeric) = 0.0743261001154730290406750375896
absolute error = 9.87238604813e-20
relative error = 1.32825293306015801120000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.668
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.668
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.331
y[1] (closed_form) = 0.074285589910412321423941844486
y[1] (numeric) = 0.0742855899104123213251569775872
absolute error = 9.87848668988e-20
relative error = 1.32979851163507702680000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.669
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.669
Order of pole (three term test) = 1.497e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.33
y[1] (closed_form) = 0.0742451128154489230746386119134
y[1] (numeric) = 0.0742451128154489229757928714823
absolute error = 9.88457404311e-20
relative error = 1.33134339329244279000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.67
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.67
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.329
y[1] (closed_form) = 0.0742046687945102792388470939338
y[1] (numeric) = 0.0742046687945102791399406125298
absolute error = 9.89064814040e-20
relative error = 1.33288757986232236400000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.671
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.671
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.328
y[1] (closed_form) = 0.0741642578115729467773553381653
y[1] (numeric) = 0.0741642578115729466783882480234
absolute error = 9.89670901419e-20
relative error = 1.33443107316388056960000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.672
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.672
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.327
y[1] (closed_form) = 0.0741238798306625140492548734043
y[1] (numeric) = 0.0741238798306625139502273064354
absolute error = 9.90275669689e-20
relative error = 1.33597387502017510810000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.673
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.673
Order of pole (three term test) = 1.547e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.326
y[1] (closed_form) = 0.074083534815853520849625537365
y[1] (numeric) = 0.0740835348158535207505376251574
absolute error = 9.90879122076e-20
relative error = 1.33751598724195409760000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.674
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.674
Order of pole (three term test) = 1.560e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.325
y[1] (closed_form) = 0.0740432227312693784996991994076
y[1] (numeric) = 0.0740432227312693784005510732275
absolute error = 9.91481261801e-20
relative error = 1.33905741164111306250000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.675
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.675
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.324
y[1] (closed_form) = 0.0740029435410822900891705868493
y[1] (numeric) = 0.0740029435410822899899623776415
absolute error = 9.92082092078e-20
relative error = 1.34059815002798041280000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.676
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.676
Order of pole (three term test) = 1.585e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.323
y[1] (closed_form) = 0.0739626972095131708703242354531
y[1] (numeric) = 0.0739626972095131707710560738425
absolute error = 9.92681616106e-20
relative error = 1.34213820420048188740000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.677
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.677
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.322
y[1] (closed_form) = 0.0739224837008315688036473944837
y[1] (numeric) = 0.0739224837008315687043194107756
absolute error = 9.93279837081e-20
relative error = 1.34367757596032504040000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.678
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.678
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.321
y[1] (closed_form) = 0.0738823029793555852545995243014
y[1] (numeric) = 0.0738823029793555851552118484825
absolute error = 9.93876758189e-20
relative error = 1.34521626710352007490000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.679
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.679
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.32
y[1] (closed_form) = 0.0738421550094517958412098298677
y[1] (numeric) = 0.0738421550094517957417625916072
absolute error = 9.94472382605e-20
relative error = 1.34675427941899520000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.68
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.68
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.319
y[1] (closed_form) = 0.0738020397555351714321750767411
y[1] (numeric) = 0.0738020397555351713326684053915
absolute error = 9.95066713496e-20
relative error = 1.34829161469262744560000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.681
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.681
Order of pole (three term test) = 1.651e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.318
y[1] (closed_form) = 0.0737619571820689992951307371681
y[1] (numeric) = 0.0737619571820689991955647617656
absolute error = 9.95659754025e-20
relative error = 1.34982827471264241000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.682
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.682
Order of pole (three term test) = 1.665e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.317
y[1] (closed_form) = 0.0737219072535648043947693127252
y[1] (numeric) = 0.0737219072535648042951441619912
absolute error = 9.96251507340e-20
relative error = 1.35136426125468492600000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.683
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.683
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.316
y[1] (closed_form) = 0.0736818899345822708404804766569
y[1] (numeric) = 0.0736818899345822707407962789984
absolute error = 9.96841976585e-20
relative error = 1.35289957609669917600000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.684
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.684
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.315
y[1] (closed_form) = 0.0736419051897291634831884735691
y[1] (numeric) = 0.0736419051897291633834453570796
absolute error = 9.97431164895e-20
relative error = 1.35443422101213063750000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.685
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.685
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.314
y[1] (closed_form) = 0.0736019529836612496610630065103
y[1] (numeric) = 0.0736019529836612495612610989712
absolute error = 9.98019075391e-20
relative error = 1.35596819776310590360000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.686
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.686
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.313
y[1] (closed_form) = 0.0735620332810822210937806316905
y[1] (numeric) = 0.0735620332810822209939200605712
absolute error = 9.98605711193e-20
relative error = 1.35750150811805950170000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.687
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.687
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.312
y[1] (closed_form) = 0.0735221460467436159250144691584
y[1] (numeric) = 0.0735221460467436158250953616176
absolute error = 9.99191075408e-20
relative error = 1.35903415383541483520000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.688
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.688
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.311
y[1] (closed_form) = 0.0734822912454447409128308237048
y[1] (numeric) = 0.0734822912454447408128533065913
absolute error = 9.99775171135e-20
relative error = 1.36056613667034683350000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.689
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.689
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.31
y[1] (closed_form) = 0.073442468842032593767672094065
y[1] (numeric) = 0.0734424688420325936676362939181
absolute error = 1.000358001469e-19
relative error = 1.36209745838020509000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.69
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.69
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.309
y[1] (closed_form) = 0.0734026788014017856376061301807
y[1] (numeric) = 0.0734026788014017855375121732314
absolute error = 1.000939569493e-19
relative error = 1.36362812071360651330000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.691
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.691
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.308
y[1] (closed_form) = 0.0733629210884944637405229778537
y[1] (numeric) = 0.073362921088494463640370990026
absolute error = 1.001519878277e-19
relative error = 1.36515812540903413280000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.692
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.692
Order of pole (three term test) = 1.806e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.307
y[1] (closed_form) = 0.0733231956683002341429607275833
y[1] (numeric) = 0.0733231956683002340427508344938
absolute error = 1.002098930895e-19
relative error = 1.36668747421798028550000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.693
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.693
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.306
y[1] (closed_form) = 0.0732835025058560846852429597271
y[1] (numeric) = 0.0732835025058560845849752866875
absolute error = 1.002676730396e-19
relative error = 1.36821616886539518560000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.694
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.694
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.305
y[1] (closed_form) = 0.073243841566246308052611051397
y[1] (numeric) = 0.0732438415662463079522857234132
absolute error = 1.003253279838e-19
relative error = 1.36974421109602099500000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.695
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.695
Order of pole (three term test) = 1.851e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.304
y[1] (closed_form) = 0.0732042128146024249920353816458
y[1] (numeric) = 0.0732042128146024248916525234198
absolute error = 1.003828582260e-19
relative error = 1.37127160263618201600000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.696
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.696
Order of pole (three term test) = 1.866e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.303
y[1] (closed_form) = 0.073164616216103107674390240601
y[1] (numeric) = 0.0731646162161031075739499765317
absolute error = 1.004402640693e-19
relative error = 1.37279834520875516370000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.697
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.697
Order of pole (three term test) = 1.881e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.302
y[1] (closed_form) = 0.0731250517359741032016780151871
y[1] (numeric) = 0.0731250517359741031011804693705
absolute error = 1.004975458166e-19
relative error = 1.37432444054135158640000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.698
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.698
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.301
y[1] (closed_form) = 0.0730855193394881572589889890086
y[1] (numeric) = 0.0730855193394881571584342852392
absolute error = 1.005547037694e-19
relative error = 1.37584989034989620940000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.699
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.699
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.3
y[1] (closed_form) = 0.0730460189919649379108838568297
y[1] (numeric) = 0.0730460189919649378102721186009
absolute error = 1.006117382288e-19
relative error = 1.37737469635227200000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.7
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.7
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.299
y[1] (closed_form) = 0.0730065506587709595418868148781
y[1] (numeric) = 0.0730065506587709594412181653834
absolute error = 1.006686494947e-19
relative error = 1.37889886025735327470000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.701
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.701
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.298
y[1] (closed_form) = 0.0729671143053195069407778469506
y[1] (numeric) = 0.072967114305319506840052409084
absolute error = 1.007254378666e-19
relative error = 1.38042238377593114640000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.702
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.702
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.297
y[1] (closed_form) = 0.0729277098970705595283735829873
y[1] (numeric) = 0.0729277098970705594275914793446
absolute error = 1.007821036427e-19
relative error = 1.38194526860836372430000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.703
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.703
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.296
y[1] (closed_form) = 0.0728883373995307157284868614398
y[1] (numeric) = 0.0728883373995307156276482143192
absolute error = 1.008386471206e-19
relative error = 1.38346751645413768960000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.704
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.704
Order of pole (three term test) = 1.991e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.295
y[1] (closed_form) = 0.0728489967782531174817558793692
y[1] (numeric) = 0.0728489967782531173808608107718
absolute error = 1.008950685974e-19
relative error = 1.38498912901322473500000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.705
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.705
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.294
y[1] (closed_form) = 0.0728096879988373749020345647976
y[1] (numeric) = 0.0728096879988373748010831964283
absolute error = 1.009513683693e-19
relative error = 1.38651010798057521480000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.706
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.706
Order of pole (three term test) = 2.023e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.293
y[1] (closed_form) = 0.0727704110269294910750365543968
y[1] (numeric) = 0.0727704110269294909740290076655
absolute error = 1.010075467313e-19
relative error = 1.38803045504196817370000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.707
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.707
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.292
y[1] (closed_form) = 0.0727311658282217869989259061429
y[1] (numeric) = 0.0727311658282217868978623021653
absolute error = 1.010636039776e-19
relative error = 1.38955017187947248640000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.708
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.708
Order of pole (three term test) = 2.056e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.291
y[1] (closed_form) = 0.0726919523684528266665484210909
y[1] (numeric) = 0.0726919523684528265654288806882
absolute error = 1.011195404027e-19
relative error = 1.39106926018655543870000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.709
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.709
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.29
y[1] (closed_form) = 0.0726527706134073422889981909461
y[1] (numeric) = 0.0726527706134073421878228346474
absolute error = 1.011753562987e-19
relative error = 1.39258772163093667000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.71
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.71
Order of pole (three term test) = 6.269e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.289
y[1] (closed_form) = 0.0726136205289161596602147286419
y[1] (numeric) = 0.0726136205289161595589836766839
absolute error = 1.012310519580e-19
relative error = 1.39410555789168811800000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.711
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.711
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.288
y[1] (closed_form) = 0.0725745020808561236623067776457
y[1] (numeric) = 0.0725745020808561235610201499739
absolute error = 1.012866276718e-19
relative error = 1.39562277063858257920000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.712
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.712
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.287
y[1] (closed_form) = 0.0725354152351500239112996322672
y[1] (numeric) = 0.0725354152351500238099575485365
absolute error = 1.013420837307e-19
relative error = 1.39713936154032682830000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.713
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.713
Order of pole (three term test) = 4.282e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.286
y[1] (closed_form) = 0.0724963599577665205430035357924
y[1] (numeric) = 0.072496359957766520441606115368
absolute error = 1.013974204244e-19
relative error = 1.39865533226040702240000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.714
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.714
Order of pole (three term test) = 4.317e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.285
y[1] (closed_form) = 0.072457336214720070138701455849
y[1] (numeric) = 0.072457336214720070037248817807
absolute error = 1.014526380420e-19
relative error = 1.40017068446120145000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.715
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.715
Order of pole (three term test) = 6.528e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.284
y[1] (closed_form) = 0.0724183439720708517903552670151
y[1] (numeric) = 0.0724183439720708516888475301435
absolute error = 1.015077368716e-19
relative error = 1.40168541979844056960000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.716
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.716
Order of pole (three term test) = 2.194e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.283
y[1] (closed_form) = 0.0723793831959246933050300993285
y[1] (numeric) = 0.0723793831959246932034673821278
absolute error = 1.015627172007e-19
relative error = 1.40319953992670206230000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.717
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.717
Order of pole (three term test) = 2.211e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.282
y[1] (closed_form) = 0.0723404538524329975482373380334
y[1] (numeric) = 0.0723404538524329974466197587177
absolute error = 1.016175793157e-19
relative error = 1.40471304649248252680000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.718
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.718
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.281
y[1] (closed_form) = 0.0723015559077926689258974846362
y[1] (numeric) = 0.0723015559077926688242251611335
absolute error = 1.016723235027e-19
relative error = 1.40622594114522709470000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.719
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.719
Order of pole (three term test) = 4.495e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.28
y[1] (closed_form) = 0.0722626893282460400046248121169
y[1] (numeric) = 0.0722626893282460399028978620704
absolute error = 1.017269500465e-19
relative error = 1.40773822552348560000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.72
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.72
Order of pole (three term test) = 2.266e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.279
y[1] (closed_form) = 0.0722238540800807982700364679906
y[1] (numeric) = 0.0722238540800807981682550087587
absolute error = 1.017814592319e-19
relative error = 1.40924990127286952790000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.721
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.721
Order of pole (three term test) = 6.852e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.278
y[1] (closed_form) = 0.0721850501296299130227893978063
y[1] (numeric) = 0.0721850501296299129209535464642
absolute error = 1.018358513421e-19
relative error = 1.41076097002389245640000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.722
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.722
Order of pole (three term test) = 4.605e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.277
y[1] (closed_form) = 0.0721462774432715624120491786543
y[1] (numeric) = 0.0721462774432715623101590519942
absolute error = 1.018901266601e-19
relative error = 1.41227143341132121290000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.723
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.723
Order of pole (three term test) = 4.642e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.276
y[1] (closed_form) = 0.0721075359874290606060955672903
y[1] (numeric) = 0.0721075359874290605041512818223
absolute error = 1.019442854680e-19
relative error = 1.41378129306446636800000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.724
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.724
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.275
y[1] (closed_form) = 0.072068825728570785099770280618
y[1] (numeric) = 0.0720688257285707849977719525713
absolute error = 1.019983280467e-19
relative error = 1.41529055060299168750000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.725
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.725
Order of pole (three term test) = 9.435e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.274
y[1] (closed_form) = 0.0720301466332101041584732374871
y[1] (numeric) = 0.07203014663321010405642098281
absolute error = 1.020522546771e-19
relative error = 1.41679920765353475960000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.726
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.726
Order of pole (three term test) = 9.511e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.273
y[1] (closed_form) = 0.0719914986679053043984142000639
y[1] (numeric) = 0.071991498667905304296308134425
absolute error = 1.021060656389e-19
relative error = 1.41830726583304397810000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.727
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.727
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.272
y[1] (closed_form) = 0.0719528817992595185028274604431
y[1] (numeric) = 0.071952881799259518400667699232
absolute error = 1.021597612111e-19
relative error = 1.41981472675568842240000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.728
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.728
Order of pole (three term test) = 4.833e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.271
y[1] (closed_form) = 0.0719142959939206530738579236718
y[1] (numeric) = 0.0719142959939206529716445819996
absolute error = 1.022133416722e-19
relative error = 1.42132159203561844020000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.729
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.729
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.27
y[1] (closed_form) = 0.0718757412185813166198276419727
y[1] (numeric) = 0.0718757412185813165175608346731
absolute error = 1.022668072996e-19
relative error = 1.42282786327860484000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.73
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.73
Order of pole (three term test) = 4.911e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.269
y[1] (closed_form) = 0.0718372174399787476775925566872
y[1] (numeric) = 0.0718372174399787475752723983175
absolute error = 1.023201583697e-19
relative error = 1.42433354208339546170000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.731
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.731
Order of pole (three term test) = 2.475e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.268
y[1] (closed_form) = 0.0717987246248947430696999043065
y[1] (numeric) = 0.0717987246248947429673265091474
absolute error = 1.023733951591e-19
relative error = 1.42583863005839679840000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.732
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.732
Order of pole (three term test) = 2.495e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.267
y[1] (closed_form) = 0.0717602627401555862960574409328
y[1] (numeric) = 0.0717602627401555861936309229897
absolute error = 1.024265179431e-19
relative error = 1.42734312880078405590000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.733
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.733
Order of pole (three term test) = 2.515e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.266
y[1] (closed_form) = 0.0717218317526319760598263356253
y[1] (numeric) = 0.0717218317526319759573468086293
absolute error = 1.024795269960e-19
relative error = 1.42884703990064097600000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.734
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.734
Order of pole (three term test) = 5.072e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.265
y[1] (closed_form) = 0.0716834316292389549272502773253
y[1] (numeric) = 0.0716834316292389548247178547332
absolute error = 1.025324225921e-19
relative error = 1.43035036495487822250000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.735
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.735
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.264
y[1] (closed_form) = 0.0716450623369358381211340324363
y[1] (numeric) = 0.0716450623369358380185488274323
absolute error = 1.025852050040e-19
relative error = 1.43185310554351078400000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.736
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.736
Order of pole (three term test) = 5.154e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.263
y[1] (closed_form) = 0.0716067238427261424476853806781
y[1] (numeric) = 0.0716067238427261423450475061739
absolute error = 1.026378745042e-19
relative error = 1.43335526325194420980000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.737
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.737
Order of pole (three term test) = 5.195e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.262
y[1] (closed_form) = 0.0715684161136575153564350455075
y[1] (numeric) = 0.0715684161136575152537446141429
absolute error = 1.026904313646e-19
relative error = 1.43485683966399000240000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.738
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.738
Order of pole (three term test) = 7.856e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.261
y[1] (closed_form) = 0.0715301391168216641329499222503
y[1] (numeric) = 0.0715301391168216640302070463944
absolute error = 1.027428758559e-19
relative error = 1.43635783635346056390000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.739
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.739
Order of pole (three term test) = 2.640e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.26
y[1] (closed_form) = 0.0714918928193542852240555920957
y[1] (numeric) = 0.0714918928193542851212603838474
absolute error = 1.027952082483e-19
relative error = 1.43785825489392108000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.74
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.74
Order of pole (three term test) = 2.661e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.259
y[1] (closed_form) = 0.0714536771884349936952847932785
y[1] (numeric) = 0.0714536771884349935924373644667
absolute error = 1.028474288118e-19
relative error = 1.43935809686287475580000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.741
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.741
Order of pole (three term test) = 2.682e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.258
y[1] (closed_form) = 0.0714154921912872528202692021261
y[1] (numeric) = 0.0714154921912872527173696643117
absolute error = 1.028995378144e-19
relative error = 1.44085736381655612160000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.742
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.742
Order of pole (three term test) = 8.112e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.257
y[1] (closed_form) = 0.0713773377951783038017925561859
y[1] (numeric) = 0.0713773377951783036988410206613
absolute error = 1.029515355246e-19
relative error = 1.44235605732488670540000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.743
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.743
Order of pole (three term test) = 2.726e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.256
y[1] (closed_form) = 0.071339213967419095624223829352
y[1] (numeric) = 0.0713392139674190955212204071424
absolute error = 1.030034222096e-19
relative error = 1.44385417894626754560000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
memory used=274.3MB, alloc=44.3MB, time=2.19
Radius of convergence (given) for eq 1 = 3.744
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.744
Order of pole (three term test) = 1.649e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.255
y[1] (closed_form) = 0.071301120675364215037049844831
y[1] (numeric) = 0.0713011206753642149339946466948
absolute error = 1.030551981362e-19
relative error = 1.44535173024015840500000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.745
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.745
Order of pole (three term test) = 5.539e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.254
y[1] (closed_form) = 0.0712630578864118166692273858801
y[1] (numeric) = 0.07126305788641181656612052231
absolute error = 1.031068635701e-19
relative error = 1.44684871275724537160000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.746
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.746
Order of pole (three term test) = 1.396e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.253
y[1] (closed_form) = 0.0712250255680035532740755365612
y[1] (numeric) = 0.0712250255680035531709171177848
absolute error = 1.031584187764e-19
relative error = 1.44834512804642498760000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.747
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.747
Order of pole (three term test) = 5.629e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.252
y[1] (closed_form) = 0.0711870236876245061044296552612
y[1] (numeric) = 0.0711870236876245060012197912412
absolute error = 1.032098640200e-19
relative error = 1.44984097766040608000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.748
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.748
Order of pole (three term test) = 5.674e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.251
y[1] (closed_form) = 0.0711490522128031154177790524527
y[1] (numeric) = 0.0711490522128031153145178528882
absolute error = 1.032611995645e-19
relative error = 1.45133626314024706450000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.749
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.749
Order of pole (three term test) = 2.860e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.25
y[1] (closed_form) = 0.0711111111111111111111111111112
y[1] (numeric) = 0.0711111111111111110077986854384
absolute error = 1.033124256728e-19
relative error = 1.45283098602375000000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.75
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.75
Order of pole (three term test) = 1.153e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.249
y[1] (closed_form) = 0.0710732003501634434851852533628
y[1] (numeric) = 0.0710732003501634433818217107554
absolute error = 1.033635426074e-19
relative error = 1.45432514784966060740000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.751
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.751
Order of pole (three term test) = 1.162e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.248
y[1] (closed_form) = 0.0710353198976182141379608203273
y[1] (numeric) = 0.0710353198976182140345462696972
absolute error = 1.034145506301e-19
relative error = 1.45581875015343527040000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.752
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.752
Order of pole (three term test) = 2.929e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.247
y[1] (closed_form) = 0.0709974697211766069869035937429
y[1] (numeric) = 0.0709974697211766068834381437411
absolute error = 1.034654500018e-19
relative error = 1.45731179446440301620000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.753
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.753
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.246
y[1] (closed_form) = 0.0709596497885828194198963478205
y[1] (numeric) = 0.0709596497885828193163801068377
absolute error = 1.035162409828e-19
relative error = 1.45880428230996472480000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.754
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.754
Order of pole (three term test) = 2.977e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.245
y[1] (closed_form) = 0.0709218600676239935744794778732
y[1] (numeric) = 0.0709218600676239934709125540407
absolute error = 1.035669238325e-19
relative error = 1.46029621521134581250000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.755
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.755
Order of pole (three term test) = 9.001e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.244
y[1] (closed_form) = 0.0708841005261301477451484086235
y[1] (numeric) = 0.0708841005261301476415309098133
absolute error = 1.036174988102e-19
relative error = 1.46178759469485366720000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.756
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.756
Order of pole (three term test) = 6.049e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.243
y[1] (closed_form) = 0.0708463711319741079184351396867
y[1] (numeric) = 0.0708463711319741078147671735127
absolute error = 1.036679661740e-19
relative error = 1.46327842227635252600000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.757
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.757
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.242
y[1] (closed_form) = 0.0708086718530714394355019385998
y[1] (numeric) = 0.0708086718530714393317836124185
absolute error = 1.037183261813e-19
relative error = 1.46476869946828485320000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.758
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.758
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.241
y[1] (closed_form) = 0.0707710026573803787819758428843
y[1] (numeric) = 0.0707710026573803786782072637954
absolute error = 1.037685790889e-19
relative error = 1.46625842778106320090000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.759
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.759
Order of pole (three term test) = 1.239e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.24
y[1] (closed_form) = 0.0707333635129017655047532820282
y[1] (numeric) = 0.0707333635129017654009345568747
absolute error = 1.038187251535e-19
relative error = 1.46774760873012160000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.76
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.76
Order of pole (three term test) = 3.123e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.239
y[1] (closed_form) = 0.0706957543876789742555047779372
y[1] (numeric) = 0.0706957543876789741516360133074
absolute error = 1.038687646298e-19
relative error = 1.46923624380904120580000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.761
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.761
Order of pole (three term test) = 3.148e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.238
y[1] (closed_form) = 0.0706581752497978469606103283599
y[1] (numeric) = 0.0706581752497978468566916305867
absolute error = 1.039186977732e-19
relative error = 1.47072433452769234080000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.762
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.762
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.237
y[1] (closed_form) = 0.0706206260673866251172567220066
y[1] (numeric) = 0.0706206260673866250132881971692
absolute error = 1.039685248374e-19
relative error = 1.47221188237828152060000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.763
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.763
Order of pole (three term test) = 3.198e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.236
y[1] (closed_form) = 0.0705831068086158822154286766177
y[1] (numeric) = 0.0705831068086158821114104305413
absolute error = 1.040182460764e-19
relative error = 1.47369888886362797440000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.764
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.764
Order of pole (three term test) = 6.448e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.235
y[1] (closed_form) = 0.0705456174416984562855263320335
y[1] (numeric) = 0.0705456174416984561814584702912
absolute error = 1.040678617423e-19
relative error = 1.47518535546599451750000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.765
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.765
Order of pole (three term test) = 6.499e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.234
y[1] (closed_form) = 0.0705081579348893825713422694432
y[1] (numeric) = 0.0705081579348893824672248973555
absolute error = 1.041173720877e-19
relative error = 1.47667128368105970120000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.766
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.766
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.233
y[1] (closed_form) = 0.0704707282564858263281318653905
y[1] (numeric) = 0.0704707282564858262239650880264
absolute error = 1.041667773641e-19
relative error = 1.47815667499523722490000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.767
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.767
Order of pole (three term test) = 6.604e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.232
y[1] (closed_form) = 0.0704333283748270157455114248493
y[1] (numeric) = 0.0704333283748270156412953470273
absolute error = 1.042160778220e-19
relative error = 1.47964153088705932800000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.768
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.768
Order of pole (three term test) = 6.656e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.231
y[1] (closed_form) = 0.0703959582582941749949191717127
y[1] (numeric) = 0.070395958258294174890653898001
absolute error = 1.042652737117e-19
relative error = 1.48112585283850842370000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.769
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.769
Order of pole (three term test) = 3.355e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.23
y[1] (closed_form) = 0.0703586178753104574013748073934
y[1] (numeric) = 0.0703586178753104572970604421108
absolute error = 1.043143652826e-19
relative error = 1.48260964232506554000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.77
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.77
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.229
y[1] (closed_form) = 0.0703213071943408787392739789154
y[1] (numeric) = 0.070321307194340878634910626132
absolute error = 1.043633527834e-19
relative error = 1.48409290081852547940000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.771
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.771
Order of pole (three term test) = 3.409e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.228
y[1] (closed_form) = 0.0702840261838922506519546268818
y[1] (numeric) = 0.0702840261838922505475423904196
absolute error = 1.044122364622e-19
relative error = 1.48557562978839820480000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.772
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.772
Order of pole (three term test) = 1.031e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.227
y[1] (closed_form) = 0.0702467748125131141947728110419
y[1] (numeric) = 0.0702467748125131140903117944754
absolute error = 1.044610165665e-19
relative error = 1.48705783070189117850000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.773
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.773
Order of pole (three term test) = 6.927e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.226
y[1] (closed_form) = 0.0702095530487936735014262368606
y[1] (numeric) = 0.0702095530487936733969165435172
absolute error = 1.045096933434e-19
relative error = 1.48853950502674029840000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.774
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.774
Order of pole (three term test) = 1.396e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.225
y[1] (closed_form) = 0.0701723608613657295732643305118
y[1] (numeric) = 0.070172360861365729468706063473
absolute error = 1.045582670388e-19
relative error = 1.49002065421979925000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.775
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.775
Order of pole (three term test) = 1.408e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.224
y[1] (closed_form) = 0.0701351982189026141913243320885
y[1] (numeric) = 0.0701351982189026140867175941902
absolute error = 1.046067378983e-19
relative error = 1.49150127973983150080000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.776
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.776
Order of pole (three term test) = 3.547e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.223
y[1] (closed_form) = 0.070098065090119123950833497538
y[1] (numeric) = 0.0700980650901191238461783913714
absolute error = 1.046551061666e-19
relative error = 1.49298138303894445140000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.777
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.777
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.222
y[1] (closed_form) = 0.0700609614437714544179181189137
y[1] (numeric) = 0.0700609614437714543132147468254
absolute error = 1.047033720883e-19
relative error = 1.49446096557397897720000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.778
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.778
Order of pole (three term test) = 3.604e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.221
y[1] (closed_form) = 0.070023887248657134408260689969
y[1] (numeric) = 0.0700238872486571343035091540627
absolute error = 1.047515359063e-19
relative error = 1.49594002878366119830000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.779
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.779
Order of pole (three term test) = 3.632e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.22
y[1] (closed_form) = 0.0699868424736149603874471599339
y[1] (numeric) = 0.0699868424736149602826475620695
absolute error = 1.047995978644e-19
relative error = 1.49741857412569296000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.78
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.78
Order of pole (three term test) = 3.661e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.219
y[1] (closed_form) = 0.0699498270875249309927468324795
y[1] (numeric) = 0.0699498270875249308878992742752
absolute error = 1.048475582043e-19
relative error = 1.49889660303390283230000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.781
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.781
Order of pole (three term test) = 7.381e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.218
y[1] (closed_form) = 0.0699128410593081816760680794466
y[1] (numeric) = 0.069912841059308181571172662279
absolute error = 1.048954171676e-19
relative error = 1.50037411694677862240000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.782
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.782
Order of pole (three term test) = 1.116e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.217
y[1] (closed_form) = 0.0698758843579269194678336498361
y[1] (numeric) = 0.0698758843579269193628904748404
absolute error = 1.049431749957e-19
relative error = 1.50185111730603731730000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.783
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.783
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.216
y[1] (closed_form) = 0.0698389569523843578615199638848
y[1] (numeric) = 0.0698389569523843577565291319561
absolute error = 1.049908319287e-19
relative error = 1.50332760554087182720000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.784
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.784
Order of pole (three term test) = 3.779e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.215
y[1] (closed_form) = 0.0698020588117246518186053897659
y[1] (numeric) = 0.0698020588117246517135670015595
absolute error = 1.050383882064e-19
relative error = 1.50480358308223284000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.785
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.785
Order of pole (three term test) = 3.809e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.214
y[1] (closed_form) = 0.0697651899050328328936731065518
y[1] (numeric) = 0.0697651899050328327885872624838
absolute error = 1.050858440680e-19
relative error = 1.50627905135852212800000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.786
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.786
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.213
y[1] (closed_form) = 0.0697283502014347444794147615894
y[1] (numeric) = 0.0697283502014347443742815618376
absolute error = 1.051331997518e-19
relative error = 1.50775401179127221420000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.787
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.787
Order of pole (three term test) = 1.548e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.212
y[1] (closed_form) = 0.0696915396700969771712817333456
y[1] (numeric) = 0.06969153967009697706610127785
absolute error = 1.051804554956e-19
relative error = 1.50922846580085664640000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.788
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.788
Order of pole (three term test) = 3.901e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.211
y[1] (closed_form) = 0.0696547582802268042515314121019
y[1] (numeric) = 0.069654758280226804146303800565
absolute error = 1.052276115369e-19
relative error = 1.51070241480934712490000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.789
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.789
Order of pole (three term test) = 3.932e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.21
y[1] (closed_form) = 0.0696180060010721172924165106063
y[1] (numeric) = 0.0696180060010721171871418424943
absolute error = 1.052746681120e-19
relative error = 1.51217586022757920000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.79
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.79
Order of pole (three term test) = 1.189e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.209
y[1] (closed_form) = 0.0695812828019213618782660149499
y[1] (numeric) = 0.0695812828019213617729443894928
absolute error = 1.053216254571e-19
relative error = 1.51364880347092038510000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.791
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.791
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.208
y[1] (closed_form) = 0.0695445886521034734462069824992
y[1] (numeric) = 0.069544588652103473340838498692
absolute error = 1.053684838072e-19
relative error = 1.51512124594345390080000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.792
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.792
Order of pole (three term test) = 4.027e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.207
y[1] (closed_form) = 0.0695079235209878132452769887277
y[1] (numeric) = 0.0695079235209878131398617453302
absolute error = 1.054152433975e-19
relative error = 1.51659318905807947750000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.793
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.793
Order of pole (three term test) = 8.117e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.206
y[1] (closed_form) = 0.069471287377984104413677618213
y[1] (numeric) = 0.0694712873779841043082157137513
absolute error = 1.054619044617e-19
relative error = 1.51806463421205510120000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.794
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.794
Order of pole (three term test) = 1.227e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.205
y[1] (closed_form) = 0.0694346801925423681739199869462
y[1] (numeric) = 0.0694346801925423680684115197127
absolute error = 1.055084672335e-19
relative error = 1.51953558280854783750000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.795
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.795
Order of pole (three term test) = 4.123e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.204
y[1] (closed_form) = 0.0693981019341528601456138734023
y[1] (numeric) = 0.0693981019341528600400589414565
absolute error = 1.055549319458e-19
relative error = 1.52100603624511081280000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.796
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.796
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.203
y[1] (closed_form) = 0.0693615525723460067756526245823
y[1] (numeric) = 0.0693615525723460066700513257514
absolute error = 1.056012988309e-19
relative error = 1.52247599591654095810000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.797
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.797
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.202
y[1] (closed_form) = 0.0693250320766923418855465904423
y[1] (numeric) = 0.0693250320766923417798990223223
absolute error = 1.056475681200e-19
relative error = 1.52394546320764848000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.798
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.798
Order of pole (three term test) = 4.222e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.201
y[1] (closed_form) = 0.0692885404168024433356584257878
y[1] (numeric) = 0.0692885404168024432299646857431
absolute error = 1.056937400447e-19
relative error = 1.52541443951486832470000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.799
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.799
Order of pole (three term test) = 4.256e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.2
y[1] (closed_form) = 0.0692520775623268698060941828255
y[1] (numeric) = 0.0692520775623268697003543679902
absolute error = 1.057398148353e-19
relative error = 1.52688292622173200000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.8
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.8
Order of pole (three term test) = 1.287e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.199
y[1] (closed_form) = 0.0692156434829560976940047001576
y[1] (numeric) = 0.069215643482956097588218907436
absolute error = 1.057857927216e-19
relative error = 1.52835092471038088160000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.801
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.801
Order of pole (three term test) = 1.297e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.198
y[1] (closed_form) = 0.0691792381484204581270523750479
y[1] (numeric) = 0.0691792381484204580212207011152
absolute error = 1.058316739327e-19
relative error = 1.52981843635866077080000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.802
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.802
Order of pole (three term test) = 8.715e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.197
y[1] (closed_form) = 0.0691428615284900740927989853148
y[1] (numeric) = 0.0691428615284900739869215266176
absolute error = 1.058774586972e-19
relative error = 1.53128546254299243480000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.803
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.803
Order of pole (three term test) = 4.392e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.196
y[1] (closed_form) = 0.0691065135929747976837708052069
y[1] (numeric) = 0.0691065135929747975778476579639
absolute error = 1.059231472430e-19
relative error = 1.53275200463546308800000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.804
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.804
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.195
y[1] (closed_form) = 0.0690701943117241474579578360999
y[1] (numeric) = 0.0690701943117241473519890963018
absolute error = 1.059687397981e-19
relative error = 1.53421806401538675250000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.805
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.805
Order of pole (three term test) = 8.924e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.194
y[1] (closed_form) = 0.0690339036546272459145045478156
y[1] (numeric) = 0.0690339036546272458084903112267
absolute error = 1.060142365889e-19
relative error = 1.53568364204468704040000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.806
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.806
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.193
y[1] (closed_form) = 0.0689976415916127570843500998293
y[1] (numeric) = 0.0689976415916127569782904619877
absolute error = 1.060596378416e-19
relative error = 1.53714874008813135840000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.807
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.807
Order of pole (three term test) = 9.066e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.192
y[1] (closed_form) = 0.0689614080926488242355765835746
y[1] (numeric) = 0.0689614080926488241294716397927
absolute error = 1.061049437819e-19
relative error = 1.53861335950897756160000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.808
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.808
Order of pole (three term test) = 4.569e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.191
y[1] (closed_form) = 0.0689252031277430076932243975093
y[1] (numeric) = 0.0689252031277430075870742428743
absolute error = 1.061501546350e-19
relative error = 1.54007750166895943500000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.809
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.809
Order of pole (three term test) = 1.842e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.19
y[1] (closed_form) = 0.0688890266669422227733344355577
y[1] (numeric) = 0.0688890266669422226671391649326
absolute error = 1.061952706251e-19
relative error = 1.54154116792101411000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.81
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.81
Order of pole (three term test) = 4.641e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.189
y[1] (closed_form) = 0.068852878680332677830977337006
y[1] (numeric) = 0.0688528786803326777247370450298
absolute error = 1.062402919762e-19
relative error = 1.54300435962086744020000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.811
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.811
Order of pole (three term test) = 9.356e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.188
y[1] (closed_form) = 0.0688167591380398124220306118966
y[1] (numeric) = 0.0688167591380398123157453929848
absolute error = 1.062852189118e-19
relative error = 1.54446707812267145920000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.812
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.812
Order of pole (three term test) = 9.430e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.187
y[1] (closed_form) = 0.0687806680102282355784650204563
y[1] (numeric) = 0.0687806680102282354721349688021
absolute error = 1.063300516542e-19
relative error = 1.54592932476881251980000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.813
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.813
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.186
y[1] (closed_form) = 0.0687446052671016641969021481038
y[1] (numeric) = 0.0687446052671016640905273576781
absolute error = 1.063747904257e-19
relative error = 1.54739110090732591720000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.814
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.814
Order of pole (three term test) = 1.437e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.185
y[1] (closed_form) = 0.0687085708789028615402056791069
y[1] (numeric) = 0.0687085708789028614337862436589
absolute error = 1.064194354480e-19
relative error = 1.54885240788316780000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.815
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.815
Order of pole (three term test) = 4.827e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.184
y[1] (closed_form) = 0.0686725648159135758518694320286
y[1] (numeric) = 0.0686725648159135757454054450867
absolute error = 1.064639869419e-19
relative error = 1.55031324703382816640000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.816
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.816
Order of pole (three term test) = 1.946e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.183
y[1] (closed_form) = 0.0686365870484544790829657786901
y[1] (numeric) = 0.0686365870484544789764573335626
absolute error = 1.065084451275e-19
relative error = 1.55177361969221484750000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.817
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.817
Order of pole (three term test) = 9.808e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.182
y[1] (closed_form) = 0.068600637546885105731418625512
y[1] (numeric) = 0.0686006375468851056248658152874
absolute error = 1.065528102246e-19
relative error = 1.55323352719246205040000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.818
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.818
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.181
y[1] (closed_form) = 0.0685647162816037917933656917656
y[1] (numeric) = 0.0685647162816037916867686093125
absolute error = 1.065970824531e-19
relative error = 1.55469297087575720910000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.819
Order of pole (three term test) = 4.982e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.18
y[1] (closed_form) = 0.0685288232230476138263753734822
y[1] (numeric) = 0.0685288232230476137197341114511
absolute error = 1.066412620311e-19
relative error = 1.55615195206262364000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.82
Order of pole (three term test) = 5.021e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.179
y[1] (closed_form) = 0.0684929583416923281242840345449
y[1] (numeric) = 0.0684929583416923280175986853683
absolute error = 1.066853491766e-19
relative error = 1.55761047207767624060000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.821
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.821
Order of pole (three term test) = 5.060e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.178
y[1] (closed_form) = 0.0684571216080523100034201177957
y[1] (numeric) = 0.0684571216080523098966907736883
absolute error = 1.067293441074e-19
relative error = 1.55906853224816126160000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.822
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.822
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.177
y[1] (closed_form) = 0.0684213129926804931999820188789
y[1] (numeric) = 0.0684213129926804930932087718389
absolute error = 1.067732470400e-19
relative error = 1.56052613388787616000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.823
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.823
Order of pole (three term test) = 1.028e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.176
y[1] (closed_form) = 0.0683855324661683093783372139843
y[1] (numeric) = 0.068385532466168309271520155793
absolute error = 1.068170581913e-19
relative error = 1.56198327832198330880000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.824
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.824
Order of pole (three term test) = 5.181e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.175
y[1] (closed_form) = 0.0683497799991456277500106796531
y[1] (numeric) = 0.0683497799991456276431499018762
absolute error = 1.068607777769e-19
relative error = 1.56343996686215756250000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.825
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.825
Order of pole (three term test) = 5.222e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.174
y[1] (closed_form) = 0.0683140555622806948031311883996
y[1] (numeric) = 0.0683140555622806946962267823875
absolute error = 1.069044060121e-19
relative error = 1.56489620082117913960000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.826
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.826
Order of pole (three term test) = 5.263e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.173
y[1] (closed_form) = 0.0682783591262800741421046080449
y[1] (numeric) = 0.0682783591262800740351566649337
absolute error = 1.069479431112e-19
relative error = 1.56635198150267430480000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.827
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.827
Order of pole (three term test) = 5.304e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.172
y[1] (closed_form) = 0.0682426906618885864372838753986
y[1] (numeric) = 0.0682426906618885863302924861098
absolute error = 1.069913892888e-19
relative error = 1.56780731022013105920000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.828
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.828
Order of pole (three term test) = 5.346e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.171
y[1] (closed_form) = 0.0682070501398892494844058562301
y[1] (numeric) = 0.0682070501398892493773711114717
absolute error = 1.070347447584e-19
relative error = 1.56926218827638917440000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.829
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.829
Order of pole (three term test) = 5.388e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.17
y[1] (closed_form) = 0.068171437531103218373565843383
y[1] (numeric) = 0.0681714375311032182664878336503
absolute error = 1.070780097327e-19
relative error = 1.57071661696800303000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.83
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.83
Order of pole (three term test) = 5.431e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.169
y[1] (closed_form) = 0.0681358528063897257675009833707
y[1] (numeric) = 0.0681358528063897256603797989465
absolute error = 1.071211844242e-19
relative error = 1.57217059759402117620000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.831
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.831
Order of pole (three term test) = 5.473e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.168
y[1] (closed_form) = 0.0681002959366460222889544588805
y[1] (numeric) = 0.0681002959366460221817901898355
absolute error = 1.071642690450e-19
relative error = 1.57362413145304608000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.832
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.832
Order of pole (three term test) = 5.516e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.167
y[1] (closed_form) = 0.0680647668928073170168927903008
y[1] (numeric) = 0.0680647668928073169096855264945
absolute error = 1.072072638063e-19
relative error = 1.57507721983587710070000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.833
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.833
Order of pole (three term test) = 1.668e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.166
y[1] (closed_form) = 0.068029265645846718091349153675
y[1] (numeric) = 0.0680292656458467179840989847562
absolute error = 1.072501689188e-19
relative error = 1.57652986403136005280000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.834
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.834
Order of pole (three term test) = 1.121e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.165
y[1] (closed_form) = 0.067993792166775173426666145381
y[1] (numeric) = 0.0679937921667751733193731607878
absolute error = 1.072929845932e-19
relative error = 1.57798206533372587000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.835
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.835
Order of pole (three term test) = 5.647e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.164
y[1] (closed_form) = 0.067958346426641411532911955341
y[1] (numeric) = 0.0679583464266414114255762443025
absolute error = 1.073357110385e-19
relative error = 1.57943382501757949600000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.836
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.836
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.163
y[1] (closed_form) = 0.0679229283965318824452444406951
y[1] (numeric) = 0.0679229283965318823378660922307
absolute error = 1.073783484644e-19
relative error = 1.58088514437317304360000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.837
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.837
Order of pole (three term test) = 1.147e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.162
y[1] (closed_form) = 0.0678875380475706987609981206014
y[1] (numeric) = 0.0678875380475706986535772235222
absolute error = 1.074208970792e-19
relative error = 1.58233602467550332480000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.838
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.838
Order of pole (three term test) = 5.781e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.161
y[1] (closed_form) = 0.0678521753509195767842696402024
y[1] (numeric) = 0.0678521753509195766768062831112
absolute error = 1.074633570912e-19
relative error = 1.58378646720489539520000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.839
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.839
Order of pole (three term test) = 5.827e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.16
y[1] (closed_form) = 0.0678168402777777777777777777779
y[1] (numeric) = 0.0678168402777777776702720490702
absolute error = 1.075057287077e-19
relative error = 1.58523647323226112000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.84
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.84
Order of pole (three term test) = 5.872e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.159
y[1] (closed_form) = 0.0677815327993820493217745937326
y[1] (numeric) = 0.0677815327993820492142265815972
absolute error = 1.075480121354e-19
relative error = 1.58668604402496624740000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.841
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.841
Order of pole (three term test) = 5.918e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.158
y[1] (closed_form) = 0.0677462528870065667797848433204
y[1] (numeric) = 0.067746252887006566672194635739
absolute error = 1.075902075814e-19
relative error = 1.58813518086157246960000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.842
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.842
Order of pole (three term test) = 5.965e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.157
y[1] (closed_form) = 0.0677110005119628748709512968993
y[1] (numeric) = 0.0677110005119628747633189816479
absolute error = 1.076323152514e-19
relative error = 1.58958388500527335860000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.843
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.843
Order of pole (three term test) = 6.012e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.156
y[1] (closed_form) = 0.0676757756455998293487641320554
y[1] (numeric) = 0.067675775645599829241089796705
absolute error = 1.076743353504e-19
relative error = 1.59103215771418813440000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.844
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.844
Order of pole (three term test) = 6.059e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.155
y[1] (closed_form) = 0.0676405782593035387859530811129
y[1] (numeric) = 0.0676405782593035386782368130293
absolute error = 1.077162680836e-19
relative error = 1.59248000025464449000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.845
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.845
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.154
y[1] (closed_form) = 0.0676054083244973064653215353783
y[1] (numeric) = 0.0676054083244973063575634217232
absolute error = 1.077581136551e-19
relative error = 1.59392741388196115160000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.846
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.846
Order of pole (three term test) = 1.231e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.153
y[1] (closed_form) = 0.0675702658126415723763023239644
y[1] (numeric) = 0.0675702658126415722685024516956
absolute error = 1.077998722688e-19
relative error = 1.59537439985372913920000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.847
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.847
Order of pole (three term test) = 1.240e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.152
y[1] (closed_form) = 0.0675351506952338553170154001754
y[1] (numeric) = 0.0675351506952338552091738560476
absolute error = 1.078415441278e-19
relative error = 1.59682095942092389120000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.848
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.848
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.151
y[1] (closed_form) = 0.0675000629438086951016081822497
y[1] (numeric) = 0.0675000629438086949937250528146
absolute error = 1.078831294351e-19
relative error = 1.59826709383824891510000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.849
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.849
Order of pole (three term test) = 6.300e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.15
y[1] (closed_form) = 0.0674650025299375948726598077247
y[1] (numeric) = 0.0674650025299375947647351793323
absolute error = 1.079246283924e-19
relative error = 1.59971280434634900000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.85
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.85
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.149
y[1] (closed_form) = 0.0674299694252289635184310718377
y[1] (numeric) = 0.067429969425228963410465030636
absolute error = 1.079660412017e-19
relative error = 1.60115809219549254170000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.851
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.851
Order of pole (three term test) = 1.280e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.148
y[1] (closed_form) = 0.0673949636013280581947423301835
y[1] (numeric) = 0.0673949636013280580867349621193
absolute error = 1.080073680642e-19
relative error = 1.60260295862926543680000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.852
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.852
Order of pole (three term test) = 1.290e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.147
y[1] (closed_form) = 0.0673599850299169269512621543514
y[1] (numeric) = 0.0673599850299169268432135451711
absolute error = 1.080486091803e-19
relative error = 1.60404740488454430270000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.853
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.853
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.146
y[1] (closed_form) = 0.0673250336827143514619900364336
y[1] (numeric) = 0.0673250336827143513539002716833
absolute error = 1.080897647503e-19
relative error = 1.60549143220186699480000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.854
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.854
Order of pole (three term test) = 1.965e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.145
y[1] (closed_form) = 0.0672901095314757898597169441543
y[1] (numeric) = 0.0672901095314757897515861091806
absolute error = 1.081308349737e-19
relative error = 1.60693504181503004250000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.855
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.855
Order of pole (three term test) = 1.320e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.144
y[1] (closed_form) = 0.0672552125479933196742480329196
y[1] (numeric) = 0.0672552125479933195660762128702
absolute error = 1.081718200494e-19
relative error = 1.60837823495403555840000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.856
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.856
Order of pole (three term test) = 1.331e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.143
y[1] (closed_form) = 0.0672203427040955808741723243228
y[1] (numeric) = 0.0672203427040955807659596041468
absolute error = 1.082127201760e-19
relative error = 1.60982101284953502400000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.857
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.857
Order of pole (three term test) = 6.705e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.142
y[1] (closed_form) = 0.067185499971647719011964662577
y[1] (numeric) = 0.0671854999716477189037111270252
absolute error = 1.082535355518e-19
relative error = 1.61126337673282169520000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.858
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.858
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.141
y[1] (closed_form) = 0.067150684322551328472205760978
y[1] (numeric) = 0.0671506843225513283639114946041
absolute error = 1.082942663739e-19
relative error = 1.61270532782242030590000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.859
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.859
Order of pole (three term test) = 6.810e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.14
y[1] (closed_form) = 0.067115895728744395822706649843
y[1] (numeric) = 0.0671158957287443957143717370032
absolute error = 1.083349128398e-19
relative error = 1.61414686734788408000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.86
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.86
Order of pole (three term test) = 6.863e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.139
y[1] (closed_form) = 0.0670811341622012432683243354053
y[1] (numeric) = 0.0670811341622012431599488602599
absolute error = 1.083754751454e-19
relative error = 1.61558799651999947340000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.861
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.861
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.138
y[1] (closed_form) = 0.0670463995949324722072559759127
y[1] (numeric) = 0.0670463995949324720988400224254
absolute error = 1.084159534873e-19
relative error = 1.61702871656503294120000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.862
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.862
Order of pole (three term test) = 6.970e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.137
y[1] (closed_form) = 0.0670116919989849068895993766303
y[1] (numeric) = 0.0670116919989849067811430285699
absolute error = 1.084563480604e-19
relative error = 1.61846902868894724760000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.863
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.863
Order of pole (three term test) = 2.107e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.136
y[1] (closed_form) = 0.0669770113464415381779680996532
y[1] (numeric) = 0.066977011346441538069471440593
absolute error = 1.084966590602e-19
relative error = 1.61990893411167985920000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.864
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.864
Order of pole (three term test) = 7.079e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.135
y[1] (closed_form) = 0.0669423576094214674099499773232
y[1] (numeric) = 0.0669423576094214673014130906424
absolute error = 1.085368866808e-19
relative error = 1.62134843403729358000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.865
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.865
Order of pole (three term test) = 1.427e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.134
y[1] (closed_form) = 0.0669077307600798503621983096966
y[1] (numeric) = 0.0669077307600798502536212785802
absolute error = 1.085770311164e-19
relative error = 1.62278752967634527840000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.866
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.866
Order of pole (three term test) = 7.190e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=318.0MB, alloc=44.3MB, time=2.53
x[1] = 2.133
y[1] (closed_form) = 0.0668731307706078413159455168554
y[1] (numeric) = 0.066873130770607841207328424295
absolute error = 1.086170925604e-19
relative error = 1.62422622223243531560000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.867
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.867
Order of pole (three term test) = 7.246e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.132
y[1] (closed_form) = 0.0668385576132325372237295059615
y[1] (numeric) = 0.0668385576132325371150724347558
absolute error = 1.086570712057e-19
relative error = 1.62566451290666891680000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.868
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.868
Order of pole (three term test) = 7.303e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.131
y[1] (closed_form) = 0.0668040112602169219771235007759
y[1] (numeric) = 0.0668040112602169218684265335313
absolute error = 1.086969672446e-19
relative error = 1.62710240289614378060000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.869
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.869
Order of pole (three term test) = 7.359e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.13
y[1] (closed_form) = 0.0667694916838598107752605679413
y[1] (numeric) = 0.0667694916838598106665237870717
absolute error = 1.087367808696e-19
relative error = 1.62853989340591224000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.87
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.87
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.129
y[1] (closed_form) = 0.0667349988564957945939445596327
y[1] (numeric) = 0.066734998856495794485168047361
absolute error = 1.087765122717e-19
relative error = 1.62997698562351895970000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.871
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.871
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.128
y[1] (closed_form) = 0.0667005327504951847551396762515
y[1] (numeric) = 0.0667005327504951846463235146095
absolute error = 1.088161616420e-19
relative error = 1.63141368074293452800000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.872
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.872
Order of pole (three term test) = 7.533e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.127
y[1] (closed_form) = 0.0666660933382639575966313356372
y[1] (numeric) = 0.066666093338263957487775606466
absolute error = 1.088557291712e-19
relative error = 1.63284997995706308480000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.873
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.873
Order of pole (three term test) = 7.591e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.126
y[1] (closed_form) = 0.0666316805922436992416515168436
y[1] (numeric) = 0.0666316805922436991327563017946
absolute error = 1.088952150490e-19
relative error = 1.63428588444872592400000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.874
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.874
Order of pole (three term test) = 7.650e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.125
y[1] (closed_form) = 0.066597294484911550468262226847
y[1] (numeric) = 0.066597294484911550359327607382
absolute error = 1.089346194650e-19
relative error = 1.63572139540414062500000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.875
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.875
Order of pole (three term test) = 7.710e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.124
y[1] (closed_form) = 0.0665629349887801516782912176331
y[1] (numeric) = 0.0665629349887801515693172750248
absolute error = 1.089739426083e-19
relative error = 1.63715651400691162080000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.876
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.876
Order of pole (three term test) = 1.554e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.123
y[1] (closed_form) = 0.0665286020763975879656145589595
y[1] (numeric) = 0.0665286020763975878566013742922
absolute error = 1.090131846673e-19
relative error = 1.63859124143500838170000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.877
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.877
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.122
y[1] (closed_form) = 0.0664942957203473342835811487076
y[1] (numeric) = 0.0664942957203473341745288028773
absolute error = 1.090523458303e-19
relative error = 1.64002557886976538520000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.878
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.878
Order of pole (three term test) = 1.578e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.121
y[1] (closed_form) = 0.0664600158932482007113747181181
y[1] (numeric) = 0.0664600158932482006022832918336
absolute error = 1.090914262845e-19
relative error = 1.64145952748083536450000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.879
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.879
Order of pole (three term test) = 1.590e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.12
y[1] (closed_form) = 0.0664257625677542778191093633755
y[1] (numeric) = 0.0664257625677542777099789371582
absolute error = 1.091304262173e-19
relative error = 1.64289308844572112000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.88
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.88
Order of pole (three term test) = 8.014e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.119
y[1] (closed_form) = 0.0663915357165548821314551079356
y[1] (numeric) = 0.0663915357165548820222857621206
absolute error = 1.091693458150e-19
relative error = 1.64432626293020621500000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.881
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.881
Order of pole (three term test) = 8.076e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.118
y[1] (closed_form) = 0.0663573353123745016895904717236
y[1] (numeric) = 0.0663573353123745015803822864596
absolute error = 1.092081852640e-19
relative error = 1.64575905210639993600000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.882
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.882
Order of pole (three term test) = 1.628e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.117
y[1] (closed_form) = 0.0663231613279727417112794938269
y[1] (numeric) = 0.066323161327972741602032549077
absolute error = 1.092469447499e-19
relative error = 1.64719145713917498110000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.883
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.883
Order of pole (three term test) = 1.640e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.116
y[1] (closed_form) = 0.0662890137361442703488711246117
y[1] (numeric) = 0.0662890137361442702395855001539
absolute error = 1.092856244578e-19
relative error = 1.64862347919066575680000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.884
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.884
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.115
y[1] (closed_form) = 0.0662548925097187645450193712741
y[1] (numeric) = 0.0662548925097187644356951467019
absolute error = 1.093242245722e-19
relative error = 1.65005511941874334500000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.885
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.885
Order of pole (three term test) = 8.329e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.114
y[1] (closed_form) = 0.0662207976215608559859230477249
y[1] (numeric) = 0.0662207976215608558765603024471
absolute error = 1.093627452778e-19
relative error = 1.65148637898907668880000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.886
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.886
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.113
y[1] (closed_form) = 0.0661867290445700771518844453841
y[1] (numeric) = 0.0661867290445700770424832586263
absolute error = 1.094011867578e-19
relative error = 1.65291725904945914820000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.887
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.887
Order of pole (three term test) = 1.692e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.112
y[1] (closed_form) = 0.066152686751680807464986705956
y[1] (numeric) = 0.0661526867516808073555471567605
absolute error = 1.094395491955e-19
relative error = 1.65434776075394035200000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.888
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.888
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.111
y[1] (closed_form) = 0.0661186707158622195336901405359
y[1] (numeric) = 0.0661186707158622194242123077618
absolute error = 1.094778327741e-19
relative error = 1.65577788525980888610000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.889
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.889
Order of pole (three term test) = 1.718e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.11
y[1] (closed_form) = 0.0660846809101182254941482015054
y[1] (numeric) = 0.0660846809101182253846321638298
absolute error = 1.095160376756e-19
relative error = 1.65720763371094676000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.89
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.89
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.109
y[1] (closed_form) = 0.0660507173074874234480442745885
y[1] (numeric) = 0.0660507173074874233384901105065
absolute error = 1.095541640820e-19
relative error = 1.65863700725595424200000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.891
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.891
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.108
y[1] (closed_form) = 0.0660167798810430439967509181614
y[1] (numeric) = 0.0660167798810430438871587059869
absolute error = 1.095922121745e-19
relative error = 1.66006600703603536800000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.892
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.892
Order of pole (three term test) = 8.792e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.107
y[1] (closed_form) = 0.0659828686038928968716136354654
y[1] (numeric) = 0.0659828686038928967619834533311
absolute error = 1.096301821343e-19
relative error = 1.66149463419709480070000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.893
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.893
Order of pole (three term test) = 2.658e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.106
y[1] (closed_form) = 0.0659489834491793176601617227352
y[1] (numeric) = 0.0659489834491793175504936485935
absolute error = 1.096680741417e-19
relative error = 1.66292288987609454120000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.894
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.894
Order of pole (three term test) = 8.928e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.105
y[1] (closed_form) = 0.0659151243900791146280491924573
y[1] (numeric) = 0.0659151243900791145183433040807
absolute error = 1.097058883766e-19
relative error = 1.66435077520860801500000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.895
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.895
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.104
y[1] (closed_form) = 0.0658812913998035156365292259949
y[1] (numeric) = 0.0658812913998035155267856009762
absolute error = 1.097436250187e-19
relative error = 1.66577829133184385920000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.896
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.896
Order of pole (three term test) = 9.067e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.103
y[1] (closed_form) = 0.0658474844515981151552660636749
y[1] (numeric) = 0.0658474844515981150454847794278
absolute error = 1.097812842471e-19
relative error = 1.66720543937856708390000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.897
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.897
Order of pole (three term test) = 9.137e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.102
y[1] (closed_form) = 0.0658137035187428213702886931267
y[1] (numeric) = 0.0658137035187428212604698268865
absolute error = 1.098188662402e-19
relative error = 1.66863222047555984080000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.898
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.898
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.101
y[1] (closed_form) = 0.0657799485745518033868911481962
y[1] (numeric) = 0.0657799485745518032770347770199
absolute error = 1.098563711763e-19
relative error = 1.67005863575271903630000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.899
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.899
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.1
y[1] (closed_form) = 0.0657462195923734385272846811308
y[1] (numeric) = 0.0657462195923734384173908818977
absolute error = 1.098937992331e-19
relative error = 1.67148468633545100000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.9
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.9
Order of pole (three term test) = 9.350e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.099
y[1] (closed_form) = 0.0657125165455902597228075199564
y[1] (numeric) = 0.0657125165455902596128763693685
absolute error = 1.099311505879e-19
relative error = 1.67291037334769520790000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.901
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.901
Order of pole (three term test) = 9.422e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.098
y[1] (closed_form) = 0.0656788394076189030004983710333
y[1] (numeric) = 0.0656788394076189028905299456161
absolute error = 1.099684254172e-19
relative error = 1.67433569790582198880000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.902
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.902
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.097
y[1] (closed_form) = 0.0656451881519100550638402737036
y[1] (numeric) = 0.0656451881519100549538346498058
absolute error = 1.100056238978e-19
relative error = 1.67576066113536160020000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.903
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.903
Order of pole (three term test) = 9.568e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.096
y[1] (closed_form) = 0.0656115627519484009674818597152
y[1] (numeric) = 0.0656115627519484008574391135098
absolute error = 1.100427462054e-19
relative error = 1.67718526414968176640000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.904
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.904
Order of pole (three term test) = 9.642e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.095
y[1] (closed_form) = 0.0655779631812525718857435147493
y[1] (numeric) = 0.0655779631812525717756637222342
absolute error = 1.100797925151e-19
relative error = 1.67860950805757277750000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.905
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.905
Order of pole (three term test) = 9.717e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.094
y[1] (closed_form) = 0.0655443894133750929747163828725
y[1] (numeric) = 0.0655443894133750928645996198703
absolute error = 1.101167630022e-19
relative error = 1.68003339397543303920000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.906
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.906
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.093
y[1] (closed_form) = 0.065510841421902331327762597096
y[1] (numeric) = 0.0655108414219023312176089392547
absolute error = 1.101536578413e-19
relative error = 1.68145692301354220370000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.907
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.907
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.092
y[1] (closed_form) = 0.0654773191804544440242255604596
y[1] (numeric) = 0.0654773191804544439140350832532
absolute error = 1.101904772064e-19
relative error = 1.68288009627756456960000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.908
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.908
Order of pole (three term test) = 9.943e-28
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.091
y[1] (closed_form) = 0.0654438226626853262711595421576
y[1] (numeric) = 0.0654438226626853261609323208865
absolute error = 1.102272212711e-19
relative error = 1.68430291487158517910000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.909
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.909
Order of pole (three term test) = 2.004e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.09
y[1] (closed_form) = 0.065410351842282559637888292201
y[1] (numeric) = 0.0654103518422825595276244019924
absolute error = 1.102638902086e-19
relative error = 1.68572537989809766000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.91
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.91
Order of pole (three term test) = 1.010e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.089
y[1] (closed_form) = 0.0653769066929673603832028159665
y[1] (numeric) = 0.0653769066929673602729023317745
absolute error = 1.103004841920e-19
relative error = 1.68714749246258083200000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.911
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.911
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.088
y[1] (closed_form) = 0.0653434871884945278750088867142
y[1] (numeric) = 0.0653434871884945277646718833212
absolute error = 1.103370033930e-19
relative error = 1.68856925365360339200000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.912
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.912
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.087
y[1] (closed_form) = 0.0653100933026523931022353097843
y[1] (numeric) = 0.0653100933026523929918618618004
absolute error = 1.103734479839e-19
relative error = 1.68999066457339573910000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.913
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.913
Order of pole (three term test) = 1.033e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.086
y[1] (closed_form) = 0.0652767250092627672788143866768
y[1] (numeric) = 0.0652767250092627671684045685407
absolute error = 1.104098181361e-19
relative error = 1.69141172631489779560000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.914
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.914
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.085
y[1] (closed_form) = 0.0652433822821808905395464606281
y[1] (numeric) = 0.0652433822821808904291003466075
absolute error = 1.104461140206e-19
relative error = 1.69283243996939083500000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.915
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.915
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.084
y[1] (closed_form) = 0.0652100650952953807276608575802
y[1] (numeric) = 0.0652100650952953806171785217724
absolute error = 1.104823358078e-19
relative error = 1.69425280662341823680000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.916
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.916
Order of pole (three term test) = 2.114e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.083
y[1] (closed_form) = 0.0651767734225281822738859676298
y[1] (numeric) = 0.0651767734225281821633674839617
absolute error = 1.105184836681e-19
relative error = 1.69567282736797114090000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.917
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.917
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.082
y[1] (closed_form) = 0.0651435072378345151668416421271
y[1] (numeric) = 0.0651435072378345150562870843562
absolute error = 1.105545577709e-19
relative error = 1.69709250328314113160000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.918
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.918
Order of pole (three term test) = 1.074e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.081
y[1] (closed_form) = 0.0651102665152028240145675105889
y[1] (numeric) = 0.0651102665152028239039769523033
absolute error = 1.105905582856e-19
relative error = 1.69851183545344302160000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.919
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.919
Order of pole (three term test) = 1.082e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.08
y[1] (closed_form) = 0.0650770512286547271970012494793
y[1] (numeric) = 0.0650770512286547270863747640981
absolute error = 1.106264853812e-19
relative error = 1.69993082496167168000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.92
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.92
Order of pole (three term test) = 1.090e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.079
y[1] (closed_form) = 0.0650438613522449661092212617195
y[1] (numeric) = 0.0650438613522449659985589224935
absolute error = 1.106623392260e-19
relative error = 1.70134947288427746600000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.921
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.921
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.078
y[1] (closed_form) = 0.0650106968600613544952686515038
y[1] (numeric) = 0.065010696860061354384570531516
absolute error = 1.106981199878e-19
relative error = 1.70276778029441857520000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.922
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.922
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.077
y[1] (closed_form) = 0.0649775577262247278723638036276
y[1] (numeric) = 0.0649775577262247277616299757932
absolute error = 1.107338278344e-19
relative error = 1.70418574826963975760000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.923
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.923
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.076
y[1] (closed_form) = 0.0649444439248888930453333000818
y[1] (numeric) = 0.064944443924888892934563837149
absolute error = 1.107694629328e-19
relative error = 1.70560337787955745280000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.924
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.924
Order of pole (three term test) = 1.124e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.075
y[1] (closed_form) = 0.0649113554302405777110633291411
y[1] (numeric) = 0.0649113554302405776002583036915
absolute error = 1.108050254496e-19
relative error = 1.70702067019199400000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.925
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.925
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.074
y[1] (closed_form) = 0.064878292216499380152796163565
y[1] (numeric) = 0.0648782922164993800419556480137
absolute error = 1.108405155513e-19
relative error = 1.70843762627758931880000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.926
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.926
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.073
y[1] (closed_form) = 0.0648452542579177190240867048487
y[1] (numeric) = 0.0648452542579177189132107714454
absolute error = 1.108759334033e-19
relative error = 1.70985424719437898570000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.927
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.927
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.072
y[1] (closed_form) = 0.0648122415287807832222365097207
y[1] (numeric) = 0.0648122415287807831113252305491
absolute error = 1.109112791716e-19
relative error = 1.71127053401398397440000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.928
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.928
Order of pole (three term test) = 1.159e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.071
y[1] (closed_form) = 0.0647792540034064818510231332545
y[1] (numeric) = 0.0647792540034064817400765802336
absolute error = 1.109465530209e-19
relative error = 1.71268648779230715690000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.929
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.929
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.07
y[1] (closed_form) = 0.0647462916561453942725430400975
y[1] (numeric) = 0.0647462916561453941615612849814
absolute error = 1.109817551161e-19
relative error = 1.71410210959265289000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.93
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.93
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.069
y[1] (closed_form) = 0.0647133544613807202479867513643
y[1] (numeric) = 0.0647133544613807201369698657436
absolute error = 1.110168856207e-19
relative error = 1.71551740046101375270000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.931
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.931
Order of pole (three term test) = 1.186e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.068
y[1] (closed_form) = 0.0646804423935282301671653097571
y[1] (numeric) = 0.0646804423935282300561133650582
absolute error = 1.110519446989e-19
relative error = 1.71693236145848611360000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.932
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.932
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.067
y[1] (closed_form) = 0.0646475554270362153666075594068
y[1] (numeric) = 0.0646475554270362152555206268925
absolute error = 1.110869325143e-19
relative error = 1.71834699364119189270000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.933
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.933
Order of pole (three term test) = 1.204e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.066
y[1] (closed_form) = 0.0646146935363854385360481498358
y[1] (numeric) = 0.0646146935363854384249263006066
absolute error = 1.111218492292e-19
relative error = 1.71976129804942479520000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.934
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.934
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.065
y[1] (closed_form) = 0.0645818566960890842131265852828
y[1] (numeric) = 0.0645818566960890841019698902763
absolute error = 1.111566950065e-19
relative error = 1.72117527573702246250000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.935
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.935
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.064
y[1] (closed_form) = 0.0645490448806927093661180514243
y[1] (numeric) = 0.0645490448806927092549265814163
absolute error = 1.111914700080e-19
relative error = 1.72258892774505676800000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.936
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.936
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.063
y[1] (closed_form) = 0.0645162580647741940645171612924
y[1] (numeric) = 0.0645162580647741939532909868965
absolute error = 1.112261743959e-19
relative error = 1.72400225512504372710000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.937
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.937
Order of pole (three term test) = 1.241e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.062
y[1] (closed_form) = 0.0644834962229436922372961708926
y[1] (numeric) = 0.0644834962229436921260353625616
absolute error = 1.112608083310e-19
relative error = 1.72541525891104836400000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.938
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.938
Order of pole (three term test) = 1.251e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.061
y[1] (closed_form) = 0.0644507593298435825186596227144
y[1] (numeric) = 0.0644507593298435824073642507399
absolute error = 1.112953719745e-19
relative error = 1.72682794014756111450000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.939
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.939
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.06
y[1] (closed_form) = 0.0644180473601484191811177819579
y[1] (numeric) = 0.0644180473601484190697879164714
absolute error = 1.113298654865e-19
relative error = 1.72824029986623140000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.94
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.94
Order of pole (three term test) = 1.270e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.059
y[1] (closed_form) = 0.0643853602885648831557016359226
y[1] (numeric) = 0.0643853602885648830443373468954
absolute error = 1.113642890272e-19
relative error = 1.72965233910446528320000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.941
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.941
Order of pole (three term test) = 1.280e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.058
y[1] (closed_form) = 0.0643526980898317331391426315774
y[1] (numeric) = 0.0643526980898317330277439888212
absolute error = 1.113986427562e-19
relative error = 1.73106405889455505680000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.942
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.942
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.057
y[1] (closed_form) = 0.0643200607387197567878407298937
y[1] (numeric) = 0.0643200607387197566764078030608
absolute error = 1.114329268329e-19
relative error = 1.73247546026987769210000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.943
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.943
Order of pole (three term test) = 1.299e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.056
y[1] (closed_form) = 0.064287448210031721998444758053
y[1] (numeric) = 0.0642874482100317218869776166368
absolute error = 1.114671414162e-19
relative error = 1.73388654426022360320000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.944
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.944
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.055
y[1] (closed_form) = 0.0642548604786023282748694421554
y[1] (numeric) = 0.0642548604786023281633681554913
absolute error = 1.115012866641e-19
relative error = 1.73529731188555490250000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.945
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.945
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.054
y[1] (closed_form) = 0.064222297519298158181573903552
y[1] (numeric) = 0.0642222975192981580700385408171
absolute error = 1.115353627349e-19
relative error = 1.73670776417465816840000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.946
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.946
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.053
y[1] (closed_form) = 0.0641897593070176288829268014006
y[1] (numeric) = 0.0641897593070176287713574316143
absolute error = 1.115693697863e-19
relative error = 1.73811790215113851670000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.947
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.947
Order of pole (three term test) = 1.339e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.052
y[1] (closed_form) = 0.0641572458166909437684837025198
y[1] (numeric) = 0.0641572458166909436568803945444
absolute error = 1.116033079754e-19
relative error = 1.73952772683339908160000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.948
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.948
Order of pole (three term test) = 1.350e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.051
y[1] (closed_form) = 0.0641247570232800441640026570734
y[1] (numeric) = 0.0641247570232800440523654796144
absolute error = 1.116371774590e-19
relative error = 1.74093723923929885900000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.949
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.949
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.05
y[1] (closed_form) = 0.0640922929017785611280243550714
y[1] (numeric) = 0.0640922929017785610163533766776
absolute error = 1.116709783938e-19
relative error = 1.74234644038926450000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.95
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.95
Order of pole (three term test) = 1.370e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.049
y[1] (closed_form) = 0.0640598534272117673338436341258
y[1] (numeric) = 0.0640598534272117672221389231903
absolute error = 1.117047109355e-19
relative error = 1.74375533129224013550000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.951
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.951
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.048
y[1] (closed_form) = 0.064027438574636529036699503352
y[1] (numeric) = 0.0640274385746365289249611281121
absolute error = 1.117383752399e-19
relative error = 1.74516391296283112960000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.952
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.952
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.047
y[1] (closed_form) = 0.0639950483191412581260112417541
y[1] (numeric) = 0.0639950483191412580142392702919
absolute error = 1.117719714622e-19
relative error = 1.74657218641037279980000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.953
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.953
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.046
y[1] (closed_form) = 0.0639626826358458642624885218966
y[1] (numeric) = 0.0639626826358458641506830221391
absolute error = 1.118054997575e-19
relative error = 1.74798015264672687000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.954
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.954
Order of pole (three term test) = 1.412e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.045
y[1] (closed_form) = 0.0639303414999017070999439011254
y[1] (numeric) = 0.0639303414999017069881049408453
absolute error = 1.118389602801e-19
relative error = 1.74938781267533120250000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.955
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.955
Order of pole (three term test) = 1.423e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.044
y[1] (closed_form) = 0.0638980248864915485916364130819
y[1] (numeric) = 0.0638980248864915484797640598979
absolute error = 1.118723531840e-19
relative error = 1.75079516749899622400000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.956
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.956
Order of pole (three term test) = 1.434e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.043
y[1] (closed_form) = 0.06386573277082950538097538174
y[1] (numeric) = 0.063865732770829505269069703117
absolute error = 1.119056786230e-19
relative error = 1.75220221812146192700000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.957
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.957
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.042
y[1] (closed_form) = 0.0638334651281610012764139687026
y[1] (numeric) = 0.0638334651281610011644750319526
absolute error = 1.119389367500e-19
relative error = 1.75360896553642700000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.958
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.958
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.041
y[1] (closed_form) = 0.0638012219337627198103623520217
y[1] (numeric) = 0.0638012219337627196983902243032
absolute error = 1.119721277185e-19
relative error = 1.75501541075102679850000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.959
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.959
Order of pole (three term test) = 1.467e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.04
y[1] (closed_form) = 0.0637690031629425568819508213447
y[1] (numeric) = 0.0637690031629425567699455696638
absolute error = 1.120052516809e-19
relative error = 1.75642155475920144000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.96
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.96
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.039
y[1] (closed_form) = 0.0637368087910395734834734597698
y[1] (numeric) = 0.0637368087910395733714351509805
absolute error = 1.120383087893e-19
relative error = 1.75782739855420692530000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.961
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.961
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.038
y[1] (closed_form) = 0.0637046387934239485103434673824
y[1] (numeric) = 0.0637046387934239483982721681872
absolute error = 1.120712991952e-19
relative error = 1.75923294312389706880000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.962
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.962
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.037
y[1] (closed_form) = 0.0636724931454969316543915650757
y[1] (numeric) = 0.0636724931454969315422873420255
absolute error = 1.121042230502e-19
relative error = 1.76063818946169652380000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.963
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.963
Order of pole (three term test) = 1.512e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.036
y[1] (closed_form) = 0.0636403718226907963803392999152
y[1] (numeric) = 0.06364037182269079626820221941
absolute error = 1.121370805052e-19
relative error = 1.76204313855403713920000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.964
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.964
Order of pole (three term test) = 1.524e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.035
y[1] (closed_form) = 0.0636082748004687929852794550043
y[1] (numeric) = 0.0636082748004687928731095832934
absolute error = 1.121698717109e-19
relative error = 1.76344779138819385250000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.965
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.965
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.034
y[1] (closed_form) = 0.0635762020543251017409961475366
y[1] (numeric) = 0.0635762020543251016287935507189
absolute error = 1.122025968177e-19
relative error = 1.76485214895070686120000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.966
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.966
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.033
y[1] (closed_form) = 0.0635441535597847861189575784951
y[1] (numeric) = 0.06354415355978478600672232252
absolute error = 1.122352559751e-19
relative error = 1.76625621221793048390000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.967
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.967
Order of pole (three term test) = 1.559e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.032
y[1] (closed_form) = 0.0635121292924037460978147762747
y[1] (numeric) = 0.0635121292924037459855469269421
absolute error = 1.122678493326e-19
relative error = 1.76765998217017098240000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.968
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.968
Order of pole (three term test) = 1.570e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.031
y[1] (closed_form) = 0.0634801292277686715532400543618
y[1] (numeric) = 0.0634801292277686714409396773222
absolute error = 1.123003770396e-19
relative error = 1.76906345979011425560000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.969
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.969
Order of pole (three term test) = 1.582e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.03
y[1] (closed_form) = 0.0634481533414969957299392801171
y[1] (numeric) = 0.0634481533414969956176064408725
absolute error = 1.123328392446e-19
relative error = 1.77046664605021614000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.97
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.97
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.029
y[1] (closed_form) = 0.0634162016092368487956724276691
y[1] (numeric) = 0.0634162016092368486833071915729
absolute error = 1.123652360962e-19
relative error = 1.77186954192843850420000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.971
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.971
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.028
y[1] (closed_form) = 0.0633842740066670114771172629353
y[1] (numeric) = 0.0633842740066670113647196951929
absolute error = 1.123975677424e-19
relative error = 1.77327214839721244160000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.972
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.972
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.027
y[1] (closed_form) = 0.0633523705094968687774113828626
y[1] (numeric) = 0.0633523705094968686649815485322
absolute error = 1.124298343304e-19
relative error = 1.77467446642026046160000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.973
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.973
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.026
y[1] (closed_form) = 0.0633204910934663637752082041067
y[1] (numeric) = 0.0633204910934663636627461680992
absolute error = 1.124620360075e-19
relative error = 1.77607649696678107000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.974
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.974
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.025
y[1] (closed_form) = 0.0632886357343459515050828685575
y[1] (numeric) = 0.0632886357343459513925886956365
absolute error = 1.124941729210e-19
relative error = 1.77747824100987562500000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.975
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.975
Order of pole (three term test) = 1.656e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.024
y[1] (closed_form) = 0.063256804407936552919124404374
y[1] (numeric) = 0.063256804407936552806598159157
absolute error = 1.125262452170e-19
relative error = 1.77887969950758099200000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.976
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.976
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.023
y[1] (closed_form) = 0.0632249970900695089295508515175
y[1] (numeric) = 0.0632249970900695088169925984757
absolute error = 1.125582530418e-19
relative error = 1.78028087342496791220000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.977
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.977
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.022
y[1] (closed_form) = 0.0631932137566065345321844301526
y[1] (numeric) = 0.0631932137566065344195942336117
absolute error = 1.125901965409e-19
relative error = 1.78168176371832739560000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.978
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.978
Order of pole (three term test) = 1.694e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.021
y[1] (closed_form) = 0.0631614543834396730106241987575
y[1] (numeric) = 0.0631614543834396728980021228973
absolute error = 1.126220758602e-19
relative error = 1.78308237135414074820000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.979
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.979
Order of pole (three term test) = 1.706e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.02
y[1] (closed_form) = 0.0631297189464912502209540163128
y[1] (numeric) = 0.0631297189464912501083001251684
absolute error = 1.126538911444e-19
relative error = 1.78448269728375376000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.98
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.98
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.019
y[1] (closed_form) = 0.0630980074217138289568239895597
y[1] (numeric) = 0.0630980074217138288441383470215
absolute error = 1.126856425382e-19
relative error = 1.78588274246234989020000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.981
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.981
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.018
y[1] (closed_form) = 0.063066319785090163394743952003
y[1] (numeric) = 0.0630663197850901632820266218173
absolute error = 1.127173301857e-19
relative error = 1.78728250783943936680000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.982
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.982
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.017
y[1] (closed_form) = 0.0630346560126331536194278861157
y[1] (numeric) = 0.0630346560126331535066789318846
absolute error = 1.127489542311e-19
relative error = 1.78868199436994318790000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.983
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.983
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.016
y[1] (closed_form) = 0.0630030160803858002290285640555
y[1] (numeric) = 0.0630030160803858001162480492373
absolute error = 1.127805148182e-19
relative error = 1.79008120300626385920000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.984
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.984
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.015
y[1] (closed_form) = 0.0629713999644211590201020451536
y[1] (numeric) = 0.0629713999644211589072900330639
absolute error = 1.128120120897e-19
relative error = 1.79148013468715618250000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.985
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.985
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.014
y[1] (closed_form) = 0.0629398076408422957521420304734
y[1] (numeric) = 0.0629398076408422956392985842845
absolute error = 1.128434461889e-19
relative error = 1.79287879036469622440000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.986
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.986
Order of pole (three term test) = 1.799e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.013
y[1] (closed_form) = 0.0629082390857822409915244358563
y[1] (numeric) = 0.0629082390857822408786496185981
absolute error = 1.128748172582e-19
relative error = 1.79427717098046383580000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.987
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.987
Order of pole (three term test) = 1.812e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.012
y[1] (closed_form) = 0.0628766942754039450347029051046
y[1] (numeric) = 0.062876694275403944921796779665
absolute error = 1.129061254396e-19
relative error = 1.79567527747346170240000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.988
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.988
Order of pole (three term test) = 1.826e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.011
y[1] (closed_form) = 0.0628451731859002329104963442647
y[1] (numeric) = 0.0628451731859002327975589733901
absolute error = 1.129373708746e-19
relative error = 1.79707311077851102660000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.989
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.989
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.01
y[1] (closed_form) = 0.062813675793493759461309916395
y[1] (numeric) = 0.0628136757934937593483413626895
absolute error = 1.129685537055e-19
relative error = 1.79847067184693055000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.99
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.99
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=361.8MB, alloc=44.3MB, time=2.89
x[1] = 2.009
y[1] (closed_form) = 0.0627822020744369645031312937196
y[1] (numeric) = 0.0627822020744369643901316196469
absolute error = 1.129996740727e-19
relative error = 1.79986796160356548870000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.991
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.991
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.008
y[1] (closed_form) = 0.0627507520050120280641443207057
y[1] (numeric) = 0.0627507520050120279511135885885
absolute error = 1.130307321172e-19
relative error = 1.80126498098655470080000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.992
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.992
Order of pole (three term test) = 1.882e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.007
y[1] (closed_form) = 0.0627193255615308257018025973201
y[1] (numeric) = 0.0627193255615308255887408693411
absolute error = 1.130617279790e-19
relative error = 1.80266173092184697100000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.993
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.993
Order of pole (three term test) = 1.896e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.006
y[1] (closed_form) = 0.0626879227203348838982058465766
y[1] (numeric) = 0.0626879227203348837851131847779
absolute error = 1.130926617987e-19
relative error = 1.80405821234868715320000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.994
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.994
Order of pole (three term test) = 1.910e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.005
y[1] (closed_form) = 0.0626565434577953355336222844263
y[1] (numeric) = 0.0626565434577953354204987507107
absolute error = 1.131235337156e-19
relative error = 1.80545442618931889000000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.995
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.995
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.004
y[1] (closed_form) = 0.0626251877503128754380005631256
y[1] (numeric) = 0.0626251877503128753248462192567
absolute error = 1.131543438689e-19
relative error = 1.80685037336809710240000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.996
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.996
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.003
y[1] (closed_form) = 0.0625938555743177160203152113898
y[1] (numeric) = 0.0625938555743177159071301189917
absolute error = 1.131850923981e-19
relative error = 1.80824605481787718290000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.997
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.997
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.002
y[1] (closed_form) = 0.0625625469062695429755898459485
y[1] (numeric) = 0.0625625469062695428623740665071
absolute error = 1.132157794414e-19
relative error = 1.80964147145445536560000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.998
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.998
Order of pole (three term test) = 1.969e-27
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.001
y[1] (closed_form) = 0.0625312617226574710694427795496
y[1] (numeric) = 0.0625312617226574709561963744124
absolute error = 1.132464051372e-19
relative error = 1.81103662420050753720000000000e-16 %
Desired digits = 12
Estimated correct digits = 12
Correct digits = 30
h = -0.001
Radius of convergence (given) for eq 1 = 3.999
Order of pole (given) = 3
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.999
Order of pole (three term test) = 0
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff ( y , x , 1 ) = neg ( 2.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ;
Iterations = 1000
Total Elapsed Time = 2 Seconds
Elapsed Time(since restart) = 2 Seconds
Expected Time Remaining = 0 Seconds
Optimized Time Remaining = 0 Seconds
Expected Total Time = 2 Seconds
Time to Timeout = 2 Minutes 57 Seconds
Percent Done = 0 %
> quit
memory used=365.0MB, alloc=44.3MB, time=2.91