|\^/| Maple 18 (X86 64 WINDOWS)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2014
\ 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
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;# end if 0;
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
print(prelabel, "[", elemnt, "]", value, postlabel)
end if
end proc
# End Function number 7
# Begin Function number 8
> 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 8
# Begin Function number 9
> 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 9
# Begin Function number 10
> 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 10
# Begin Function number 11
> 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 11
# Begin Function number 12
> 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 12
# Begin Function number 13
> 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 13
# Begin Function number 14
> 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 14
# Begin Function number 15
> 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 15
# Begin Function number 16
> 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 16
# Begin Function number 17
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
# End Function number 17
# Begin Function number 18
> 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 18
# Begin Function number 19
> 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 19
# Begin Function number 20
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
# End Function number 20
# Begin Function number 21
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file) fprintf(file, "\n") end proc
# End Function number 21
# Begin Function number 22
> 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 22
# Begin Function number 23
> 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 23
# Begin Function number 24
> 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 24
# Begin Function number 25
> 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 25
# Begin Function number 26
> 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 26
# Begin Function number 27
> 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 27
# Begin Function number 28
> 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 28
# Begin Function number 29
> 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 29
# Begin Function number 30
> 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 30
# Begin Function number 31
> 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 31
# Begin Function number 32
> 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 32
# Begin Function number 33
> 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 33
# Begin Function number 34
> 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 34
# Begin Function number 35
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
# End Function number 35
# Begin Function number 36
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
# End Function number 36
# Begin Function number 37
> float_abs := proc(x)
> abs(x);
> end;
float_abs := proc(x) abs(x) end proc
# End Function number 37
# Begin Function number 38
> expt := proc(x,y)
> x^y;
> end;
expt := proc(x, y) x^y end proc
# End Function number 38
# Begin Function number 39
> neg := proc(x)
> -x;
> end;
neg := proc(x) -x end proc
# End Function number 39
# Begin Function number 40
> int_trunc := proc(x)
> trunc(x);
> end;
int_trunc := proc(x) trunc(x) end proc
# End Function number 40
# Begin Function number 41
> 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 41
#END ATS LIBRARY BLOCK
#BEGIN USER FUNCTION BLOCK
#BEGIN BLOCK 3
#BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return(c(10.0) * (c(0.1) * c(x) + c(0.2)) * ln(c(0.1) * c(x) + c(0.2)) - c(x) - c(2.0));
> end;
exact_soln_y := proc(x)
return
c(10.0)*(c(0.1)*c(x) + c(0.2))*ln(c(0.1)*c(x) + c(0.2)) - c(x) - c(2.0)
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_0D1,
> array_const_0D2,
#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_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_0D1,
array_const_0D2, 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_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_0D1,
> array_const_0D2,
#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_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_0D1,
array_const_0D2, 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_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_0D1,
> array_const_0D2,
#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_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_0D1,
array_const_0D2, 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_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_0D1,
> array_const_0D2,
#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_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_0D1,
array_const_0D2, 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_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_0D1,
> array_const_0D2,
#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_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*glob__100/float_abs(closed_form_val_y);
> if (c(relerr) > c(glob_prec)) then # if number 6
> glob_good_digits := -int_trunc(log10(c(relerr))) + 3;
> 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)*21*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,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_0D1,
array_const_0D2, 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_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*glob__100/float_abs(closed_form_val_y);
if c(glob_prec) < c(relerr) then
glob_good_digits := -int_trunc(log10(c(relerr))) + 3
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)*21*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, 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_0D1,
> array_const_0D2,
#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_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_0D1,
array_const_0D2, 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_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_0D1,
> array_const_0D2,
#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_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_0D1,
array_const_0D2, 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_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_0D1,
> array_const_0D2,
#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_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 mult CONST - LINEAR $eq_no = 1 i = 1
> array_tmp1[1] := array_const_0D1[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp2[1] := array_tmp1[1] + array_const_0D2[1];
> #emit pre ln 1 LINEAR $eq_no = 1
> array_tmp3[1] := ln(array_tmp2[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp4[1] := array_const_0D0[1] + array_tmp3[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_tmp4[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 mult CONST - LINEAR $eq_no = 1 i = 2
> array_tmp1[2] := array_const_0D1[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre ln 2 LINEAR $eq_no = 1
> array_tmp3[2] := array_tmp2[2] / array_tmp2[1];
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp4[2] := array_tmp3[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_tmp4[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
> #emit pre ln ID_LINEAR iii = 3 $eq_no = 1
> array_tmp3[3] := neg(array_tmp2[2]) * array_tmp3[2] * c(1) / array_tmp2[1] / c(2);
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp4[3] := array_tmp3[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_tmp4[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
> #emit pre ln ID_LINEAR iii = 4 $eq_no = 1
> array_tmp3[4] := neg(array_tmp2[2]) * array_tmp3[3] * c(2) / array_tmp2[1] / c(3);
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp4[4] := array_tmp3[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_tmp4[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
> #emit pre ln ID_LINEAR iii = 5 $eq_no = 1
> array_tmp3[5] := neg(array_tmp2[2]) * array_tmp3[4] * c(3) / array_tmp2[1] / c(4);
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp4[5] := array_tmp3[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_tmp4[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 ln LINEAR $eq_no = 1
> array_tmp3[kkk] := neg(array_tmp2[2]) * array_tmp3[kkk - 1] * c(kkk - 2)/ array_tmp2[1] / c(kkk - 1);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp4[kkk] := array_tmp3[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_tmp4[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_0D1,
array_const_0D2, 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_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] := array_const_0D1[1]*array_x[1];
array_tmp2[1] := array_tmp1[1] + array_const_0D2[1];
array_tmp3[1] := ln(array_tmp2[1]);
array_tmp4[1] := array_const_0D0[1] + array_tmp3[1];
if not array_y_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[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_tmp1[2] := array_const_0D1[1]*array_x[2];
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := array_tmp2[2]/array_tmp2[1];
array_tmp4[2] := array_tmp3[2];
if not array_y_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[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_tmp2[2])*array_tmp3[2]*c(1)/(array_tmp2[1]*c(2));
array_tmp4[3] := array_tmp3[3];
if not array_y_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[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_tmp2[2])*array_tmp3[3]*c(2)/(array_tmp2[1]*c(3));
array_tmp4[4] := array_tmp3[4];
if not array_y_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[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_tmp2[2])*array_tmp3[4]*c(3)/(array_tmp2[1]*c(4));
array_tmp4[5] := array_tmp3[5];
if not array_y_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[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] := neg(array_tmp2[2])*array_tmp3[kkk - 1]*
c(kkk - 2)/(array_tmp2[1]*c(kkk - 1));
array_tmp4[kkk] := array_tmp3[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_tmp4[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_0D1,
> array_const_0D2,
> #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_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 := 30;
> # before first input block
> #BEGIN FIRST INPUT BLOCK
> #BEGIN BLOCK 1
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=30;
> #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..(30),[]);
> array_norms:= Array(0..(30),[]);
> array_fact_1:= Array(0..(30),[]);
> 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..(30),[]);
> array_x:= Array(0..(30),[]);
> array_tmp0:= Array(0..(30),[]);
> array_tmp1:= Array(0..(30),[]);
> array_tmp2:= Array(0..(30),[]);
> array_tmp3:= Array(0..(30),[]);
> array_tmp4:= Array(0..(30),[]);
> array_m1:= Array(0..(30),[]);
> array_y_higher := Array(0..(2) ,(0..30+ 1),[]);
> array_y_higher_work := Array(0..(2) ,(0..30+ 1),[]);
> array_y_higher_work2 := Array(0..(2) ,(0..30+ 1),[]);
> array_y_set_initial := Array(0..(2) ,(0..30+ 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..(30) ,(0..30+ 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 <= 30) do # do number 1
> array_y_init[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_norms[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) 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 <= 30) do # do number 1
> array_y[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_x[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp0[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp3[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp4[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) 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 <= 30) 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 <= 30) 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 <= 30) 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 <= 30) 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 <=30) do # do number 1
> term := 1;
> while (term <= 30) 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_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_0D1);
> array_const_0D1[1] := c(0.1);
> zero_ats_ar(array_const_0D2);
> array_const_0D2[1] := c(0.2);
> 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;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> # before generate init omniout const
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> ATS_MAX_TERMS := 30;
> 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,"##############temp/lin_lnpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = ln ( 0.1 * x + 0.2 ) ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := c(20.0);");
> omniout_str(ALWAYS,"x_end := c(30.0) ;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_min_h := c(0.001);");
> 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(-2.0);");
> 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(1.0);");
> 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:=8;");
> omniout_str(ALWAYS,"glob_max_minutes:=(3.0);");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"glob_max_iter:=100000;");
> omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.0000001);");
> omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.9999999);");
> omniout_str(ALWAYS,"glob_look_poles:=true;");
> omniout_str(ALWAYS,"glob_h:=c(0.005);");
> omniout_str(ALWAYS,"glob_display_interval:=c(0.01);");
> 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(10.0) * (c(0.1) * c(x) + c(0.2)) * ln(c(0.1) * c(x) + c(0.2)) - c(x) - c(2.0));");
> 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(20.0);
> x_end := c(30.0) ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_min_h := c(0.001);
> glob_type_given_pole := 1;
> array_given_rad_poles[1,1] := c(-2.0);
> array_given_rad_poles[1,2] := c(0.0);
> array_given_ord_poles[1,1] := c(1.0);
> array_given_ord_poles[1,2] := c(0.0);
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=8;
> glob_max_minutes:=(3.0);
> glob_subiter_method:=3;
> glob_max_iter:=100000;
> glob_upper_ratio_limit:=c(1.0000001);
> glob_lower_ratio_limit:=c(0.9999999);
> glob_look_poles:=true;
> glob_h:=c(0.005);
> glob_display_interval:=c(0.01);
> #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 ) = ln ( 0.1 * x + 0.2 ) ; ");
> 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,"2015-05-02T21:34:29-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"lin_ln")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = ln ( 0.1 * x + 0.2 ) ; ")
> ;
> 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," 308.maple.seems.ok | ")
> ;
> logitem_str(html_log_file,"lin_ln diffeq.mxt")
> ;
> logitem_str(html_log_file,"lin_ln 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_0D1,
array_const_0D2, 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_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 := 30;
Digits := 32;
max_terms := 30;
glob_html_log := true;
array_y_init := Array(0 .. 30, []);
array_norms := Array(0 .. 30, []);
array_fact_1 := Array(0 .. 30, []);
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 .. 30, []);
array_x := Array(0 .. 30, []);
array_tmp0 := Array(0 .. 30, []);
array_tmp1 := Array(0 .. 30, []);
array_tmp2 := Array(0 .. 30, []);
array_tmp3 := Array(0 .. 30, []);
array_tmp4 := Array(0 .. 30, []);
array_m1 := Array(0 .. 30, []);
array_y_higher := Array(0 .. 2, 0 .. 31, []);
array_y_higher_work := Array(0 .. 2, 0 .. 31, []);
array_y_higher_work2 := Array(0 .. 2, 0 .. 31, []);
array_y_set_initial := Array(0 .. 2, 0 .. 31, []);
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 .. 30, 0 .. 31, []);
term := 1;
while term <= 30 do array_y_init[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 30 do array_norms[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 30 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 <= 30 do array_y[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_x[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp0[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp1[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp3[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp4[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_m1[term] := c(0.); term := term + 1 end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 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 <= 30 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 <= 30 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 <= 30 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 <= 30 do
term := 1;
while term <= 30 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_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_0D1);
array_const_0D1[1] := c(0.1);
zero_ats_ar(array_const_0D2);
array_const_0D2[1] := c(0.2);
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;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
ATS_MAX_TERMS := 30;
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,
"##############temp/lin_lnpostode.ode#################");
omniout_str(ALWAYS,
"diff ( y , x , 1 ) = ln ( 0.1 * x + 0.2 ) ; ")
;
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := c(20.0);");
omniout_str(ALWAYS, "x_end := c(30.0) ;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_min_h := c(0.001);");
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(-2.0);");
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(1.0);");
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:=8;");
omniout_str(ALWAYS, "glob_max_minutes:=(3.0);");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "glob_max_iter:=100000;");
omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.0000001);");
omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.9999999);");
omniout_str(ALWAYS, "glob_look_poles:=true;");
omniout_str(ALWAYS, "glob_h:=c(0.005);");
omniout_str(ALWAYS, "glob_display_interval:=c(0.01);");
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(10.0) * (c(0.1) * c(x) + c(0.2)) * ln(\
c(0.1) * c(x) + c(0.2)) - c(x) - c(2.0));");
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(20.0);
x_end := c(30.0);
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_min_h := c(0.001);
glob_type_given_pole := 1;
array_given_rad_poles[1, 1] := c(-2.0);
array_given_rad_poles[1, 2] := c(0.);
array_given_ord_poles[1, 1] := c(1.0);
array_given_ord_poles[1, 2] := c(0.);
glob_desired_digits_correct := 8;
glob_max_minutes := 3.0;
glob_subiter_method := 3;
glob_max_iter := 100000;
glob_upper_ratio_limit := c(1.0000001);
glob_lower_ratio_limit := c(0.9999999);
glob_look_poles := true;
glob_h := c(0.005);
glob_display_interval := c(0.01);
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 ) = ln ( 0.1 * \
x + 0.2 ) ; ");
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, "2015-05-02T21:34:29-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"lin_ln");
logitem_str(html_log_file, "diff ( y , x , 1 ) = ln\
( 0.1 * x + 0.2 ) ; ");
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, " 308.maple.seems.ok | ");
logitem_str(html_log_file,
"lin_ln diffeq.mxt");
logitem_str(html_log_file, "lin_ln 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#################
##############temp/lin_lnpostode.ode#################
diff ( y , x , 1 ) = ln ( 0.1 * x + 0.2 ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := c(20.0);
x_end := c(30.0) ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_min_h := c(0.001);
glob_type_given_pole := 1;
array_given_rad_poles[1,1] := c(-2.0);
array_given_rad_poles[1,2] := c(0.0);
array_given_ord_poles[1,1] := c(1.0);
array_given_ord_poles[1,2] := c(0.0);
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=8;
glob_max_minutes:=(3.0);
glob_subiter_method:=3;
glob_max_iter:=100000;
glob_upper_ratio_limit:=c(1.0000001);
glob_lower_ratio_limit:=c(0.9999999);
glob_look_poles:=true;
glob_h:=c(0.005);
glob_display_interval:=c(0.01);
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return(c(10.0) * (c(0.1) * c(x) + c(0.2)) * ln(c(0.1) * c(x) + c(0.2)) - c(x) - c(2.0));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
TOP MAIN SOLVE Loop
x[1] = 20
y[1] (closed_form) = -4.653938071986056271853946615743
y[1] (numeric) = -4.653938071986056271853946615743
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 14
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.01
y[1] (closed_form) = -4.646051225999415219345774709019
y[1] (numeric) = -4.6460512259994152193457747090192
absolute error = 2e-31
relative error = 4.3047308406931708943058658258804e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.01
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.01
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4.2MB, alloc=40.3MB, time=0.13
TOP MAIN SOLVE Loop
x[1] = 20.02
y[1] (closed_form) = -4.638159836623249387277872764637
y[1] (numeric) = -4.6381598366232493872778727646372
absolute error = 2e-31
relative error = 4.3120549322338003199372180464529e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.02
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.02
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.03
y[1] (closed_form) = -4.630263905920860245762876704971
y[1] (numeric) = -4.630263905920860245762876704971
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.03
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.03
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.04
y[1] (closed_form) = -4.622363435953676090439722877789
y[1] (numeric) = -4.6223634359536760904397228777887
absolute error = 3e-31
relative error = 6.4901863333925547270051188783109e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.04
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.04
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.05
y[1] (closed_form) = -4.614458428781254592167020495606
y[1] (numeric) = -4.6144584287812545921670204956054
absolute error = 6e-31
relative error = 1.3002609282547349842081263459570e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.05
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.05
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.06
y[1] (closed_form) = -4.606548886461285342091129181895
y[1] (numeric) = -4.6065488864612853420911291818946
absolute error = 4e-31
relative error = 8.6832900259803137992551374277587e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.06
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.06
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.07
y[1] (closed_form) = -4.598634811049592392099425068955
y[1] (numeric) = -4.5986348110495923920994250689544
absolute error = 6e-31
relative error = 1.3047350456233683888476058984499e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.07
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.07
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.08
y[1] (closed_form) = -4.590716204600136790669210391691
y[1] (numeric) = -4.5907162046001367906692103916909
absolute error = 1e-31
relative error = 2.1783093430997714581764521679494e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.08
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.08
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.09
y[1] (closed_form) = -4.582793069165019114122693111398
y[1] (numeric) = -4.582793069165019114122693111398
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.09
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.09
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.1
y[1] (closed_form) = -4.574865406794481993298434783459
y[1] (numeric) = -4.5748654067944819932984347834591
absolute error = 1e-31
relative error = 2.1858566560555500300618757559975e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.1
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.1
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.11
y[1] (closed_form) = -4.566933219536912635649636652446
y[1] (numeric) = -4.5669332195369126356496366524458
absolute error = 2e-31
relative error = 4.3793064270004809641079576845946e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.11
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.11
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.12
y[1] (closed_form) = -4.558996509438845342779605817013
y[1] (numeric) = -4.5589965094388453427796058170127
absolute error = 3e-31
relative error = 6.5803954747253402848062569324301e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.12
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.12
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.13
y[1] (closed_form) = -4.551055278544964023424715254968
y[1] (numeric) = -4.5510552785449640234247152549677
absolute error = 3e-31
relative error = 6.5918777434826982083929404904315e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.13
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.13
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.14
y[1] (closed_form) = -4.543109528898104701895143535609
y[1] (numeric) = -4.5431095288981047018951435356091
absolute error = 1e-31
relative error = 2.2011355738600079358702315391234e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.14
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.14
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.15
y[1] (closed_form) = -4.535159262539258021983652171543
y[1] (numeric) = -4.5351592625392580219836521715431
absolute error = 1e-31
relative error = 2.2049942286703622215068864423500e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.15
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.15
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.16
y[1] (closed_form) = -4.527204481507571746352630775412
y[1] (numeric) = -4.5272044815075717463526307754116
absolute error = 4e-31
relative error = 8.8354745546372776596588026610644e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.16
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.16
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.17
y[1] (closed_form) = -4.519245187840353251409612487949
y[1] (numeric) = -4.5192451878403532514096124879492
absolute error = 2e-31
relative error = 4.4255177952753555107275163651779e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.17
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.17
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.18
y[1] (closed_form) = -4.511281383573072017681434532236
y[1] (numeric) = -4.5112813835730720176814345322355
absolute error = 5e-31
relative error = 1.1083325500835525313676956602056e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.18
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.18
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.19
y[1] (closed_form) = -4.503313070739362115697191224598
y[1] (numeric) = -4.5033130707393621156971912245979
absolute error = 1e-31
relative error = 2.2205873415676565087330550749640e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.19
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.19
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.2
y[1] (closed_form) = -4.495340251371024687390099335036
y[1] (numeric) = -4.4953402513710246873900993350361
absolute error = 1e-31
relative error = 2.2245257179253829168971393419381e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.2
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.2
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.21
y[1] (closed_form) = -4.487362927498030423028368338973
y[1] (numeric) = -4.4873629274980304230283683389728
absolute error = 2e-31
relative error = 4.4569606522000617314820568790319e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.21
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.21
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.22
y[1] (closed_form) = -4.479381101148522033685140837267
y[1] (numeric) = -4.4793811011485220336851408372673
absolute error = 3e-31
relative error = 6.6973537911985076696027944308571e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.22
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.22
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.23
y[1] (closed_form) = -4.471394774348816719257541242461
y[1] (numeric) = -4.4713947743488167192575412424608
absolute error = 2e-31
relative error = 4.4728772585088201896809946359575e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.23
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.23
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.24
y[1] (closed_form) = -4.463403949123408632044843735829
y[1] (numeric) = -4.4634039491234086320448437358294
absolute error = 4e-31
relative error = 8.9617700875709020915221840073503e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.24
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.24
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.25
y[1] (closed_form) = -4.455408627494971335895743491712
y[1] (numeric) = -4.4554086274949713358957434917119
absolute error = 1e-31
relative error = 2.2444630416811946281421148059692e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.25
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.25
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.26
y[1] (closed_form) = -4.447408811484360260934688242435
y[1] (numeric) = -4.4474088114843602609346882424355
absolute error = 5e-31
relative error = 1.1242501447334246212026622321556e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.26
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.26
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.27
y[1] (closed_form) = -4.439404503110615153877200418682
y[1] (numeric) = -4.4394045031106151538772004186826
absolute error = 6e-31
relative error = 1.3515326201511716607032333506112e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.27
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.27
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.28
y[1] (closed_form) = -4.431395704390962523944093346025
y[1] (numeric) = -4.4313957043909625239440933460249
absolute error = 1e-31
relative error = 2.2566253765357136897186709403831e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.28
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.28
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.29
y[1] (closed_form) = -4.423382417340818084384458308287
y[1] (numeric) = -4.4233824173408180843844583082871
absolute error = 1e-31
relative error = 2.2607134216561018586444621209011e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.29
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.29
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.3
y[1] (closed_form) = -4.415364643973789189617272702097
y[1] (numeric) = -4.4153646439737891896172727020966
absolute error = 4e-31
relative error = 9.0592744258604093954830603338859e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.3
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.3
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.31
y[1] (closed_form) = -4.407342386301677268001453004124
y[1] (numeric) = -4.4073423863016772680014530041237
absolute error = 3e-31
relative error = 6.8068231080122251707007980699811e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.31
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.31
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.32
y[1] (closed_form) = -4.399315646334480250244149852818
y[1] (numeric) = -4.3993156463344802502441498528186
absolute error = 6e-31
relative error = 1.3638484897075329374689561768635e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.32
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.32
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.33
y[1] (closed_form) = -4.391284426080394993457056209616
y[1] (numeric) = -4.3912844260803949934570562096166
absolute error = 6e-31
relative error = 1.3663428322622964793900546637982e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.33
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.33
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.34
y[1] (closed_form) = -4.383248727545819700870473310299
y[1] (numeric) = -4.3832487275458197008704733102985
absolute error = 5e-31
relative error = 1.1407064282203075533038911886270e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.34
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.34
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.35
y[1] (closed_form) = -4.375208552735356337214852945186
y[1] (numeric) = -4.3752085527353563372148529451859
absolute error = 1e-31
relative error = 2.2856053327442082660736405998463e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.35
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.35
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.36
y[1] (closed_form) = -4.367163903651813039779508516804
y[1] (numeric) = -4.3671639036518130397795085168039
absolute error = 1e-31
relative error = 2.2898155921370438059225363166783e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.36
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.36
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.37
y[1] (closed_form) = -4.359114782296206525158161315281
y[1] (numeric) = -4.359114782296206525158161315281
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.37
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.37
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.38
y[1] (closed_form) = -4.351061190667764491690962524773
y[1] (numeric) = -4.351061190667764491690962524773
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.38
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.38
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.39
y[1] (closed_form) = -4.343003130763928017612605628314
y[1] (numeric) = -4.3430031307639280176126056283143
absolute error = 3e-31
relative error = 6.9076625313698641189037656679919e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.39
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.39
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.4
y[1] (closed_form) = -4.334940604580353954916118113417
y[1] (numeric) = -4.3349406045803539549161181134166
absolute error = 4e-31
relative error = 9.2273467271351967141104547458963e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.4
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.4
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.41
y[1] (closed_form) = -4.326873614110917318941895696169
y[1] (numeric) = -4.3268736141109173189418956961689
absolute error = 1e-31
relative error = 2.3111375306613369505719635391605e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.41
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.41
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.42
y[1] (closed_form) = -4.318802161347713673701516677257
y[1] (numeric) = -4.3188021613477136737015166772569
absolute error = 1e-31
relative error = 2.3154568388192681550056424774375e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.42
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.42
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.43
y[1] (closed_form) = -4.310726248281061512945848518924
y[1] (numeric) = -4.3107262482810615129458485189238
absolute error = 2e-31
relative error = 4.6395894445802882659086161413830e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.43
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.43
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.44
y[1] (closed_form) = -4.302645876899504636986933287157
y[1] (numeric) = -4.3026458768995046369869332871567
absolute error = 3e-31
relative error = 6.9724538942577493660641556885796e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.44
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.44
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.45
y[1] (closed_form) = -4.294561049189814525283113238018
y[1] (numeric) = -4.294561049189814525283113238018
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.45
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.45
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.46
y[1] (closed_form) = -4.286471767136992704796832540766
y[1] (numeric) = -4.2864717671369927047968325407659
absolute error = 1e-31
relative error = 2.3329209996591602051205954432142e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.46
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.46
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.47
y[1] (closed_form) = -4.278378032724273114134525922943
y[1] (numeric) = -4.2783780327242731141345259229428
absolute error = 2e-31
relative error = 4.6746687289026036963744454110713e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.47
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.47
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.48
y[1] (closed_form) = -4.270279847933124463477979893672
y[1] (numeric) = -4.2702798479331244634779798936718
absolute error = 2e-31
relative error = 4.6835337992380713489115248319748e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.48
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.48
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.49
y[1] (closed_form) = -4.262177214743252590316527150712
y[1] (numeric) = -4.2621772147432525903165271507123
absolute error = 3e-31
relative error = 7.0386561816874516660145058887981e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.49
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.49
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.5
y[1] (closed_form) = -4.254070135132602810989409804104
y[1] (numeric) = -4.2540701351326028109894098041044
absolute error = 4e-31
relative error = 9.4027598815676713352178141189331e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.5
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.5
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.51
y[1] (closed_form) = -4.245958611077362268047622154207
y[1] (numeric) = -4.2459586110773622680476221542077
absolute error = 7e-31
relative error = 1.6486265272905785545080354061131e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.51
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.51
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.52
y[1] (closed_form) = -4.237842644551962273444518944328
y[1] (numeric) = -4.237842644551962273444518944328
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.52
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.52
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.53
y[1] (closed_form) = -4.22972223752908064756445026766
y[1] (numeric) = -4.2297222375290806475644502676598
absolute error = 2e-31
relative error = 4.7284428803730622793802868238822e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.53
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.53
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.54
y[1] (closed_form) = -4.221597391979644054098659644669
y[1] (numeric) = -4.2215973919796440540986596446692
absolute error = 2e-31
relative error = 4.7375431958520683994680722031347e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.54
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.54
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.55
y[1] (closed_form) = -4.21346810987283033077765720004
y[1] (numeric) = -4.2134681098728303307776572000396
absolute error = 4e-31
relative error = 9.4933672112703538102875272053191e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.55
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.55
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.56
y[1] (closed_form) = -4.20533439317607081596925535762
y[1] (numeric) = -4.2053343931760708159692553576196
absolute error = 4e-31
relative error = 9.5117287378876132478442630513596e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.56
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.56
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.57
y[1] (closed_form) = -4.197196243855052671151430037182
y[1] (numeric) = -4.1971962438550526711514300371825
absolute error = 5e-31
relative error = 1.1912714368122053462648450710779e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.57
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.57
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.58
y[1] (closed_form) = -4.189053663873721199269145977963
y[1] (numeric) = -4.1890536638737211992691459779631
absolute error = 1e-31
relative error = 2.3871740021474810760808284202687e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.58
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.58
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.59
y[1] (closed_form) = -4.180906655194282158984260530603
y[1] (numeric) = -4.1809066551942821589842605306033
absolute error = 3e-31
relative error = 7.1754771091883975140996630539649e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.59
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.59
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.6
y[1] (closed_form) = -4.172755219777204074827596051056
y[1] (numeric) = -4.1727552197772040748275960510564
absolute error = 4e-31
relative error = 9.5859924422156064200811419830620e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.6
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.6
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.61
y[1] (closed_form) = -4.164599359581220543262246896894
y[1] (numeric) = -4.1645993595812205432622468968944
absolute error = 4e-31
relative error = 9.6047654399155164959304431608105e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.61
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.61
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.62
y[1] (closed_form) = -4.156439076563332534667162968076
y[1] (numeric) = -4.1564390765633325346671629680756
absolute error = 4e-31
relative error = 9.6236223515329833329743628997594e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.62
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.62
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.63
y[1] (closed_form) = -4.148274372678810691250027750294
y[1] (numeric) = -4.1482743726788106912500277502938
absolute error = 2e-31
relative error = 4.8212818640259560741440075741882e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.63
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.63
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.64
y[1] (closed_form) = -4.140105249881197620898424909281
y[1] (numeric) = -4.1401052498811976208984249092808
absolute error = 2e-31
relative error = 4.8307950626554505942561750174464e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.64
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.64
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=48.3MB, alloc=44.3MB, time=0.61
TOP MAIN SOLVE Loop
x[1] = 20.65
y[1] (closed_form) = -4.131931710122310186978263648611
y[1] (numeric) = -4.1319317101223101869782636486109
absolute error = 1e-31
relative error = 2.4201755260141963669803695916737e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.65
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.65
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.66
y[1] (closed_form) = -4.1237537553522417940884092814
y[1] (numeric) = -4.1237537553522417940884092814001
absolute error = 1e-31
relative error = 2.4249750574997227095890584320366e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.66
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.66
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.67
y[1] (closed_form) = -4.115571387519364669780441777537
y[1] (numeric) = -4.1155713875193646697804417775372
absolute error = 2e-31
relative error = 4.8595925369320047045970023076802e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.67
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.67
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.68
y[1] (closed_form) = -4.107384608570332142252441432478
y[1] (numeric) = -4.1073846085703321422524414324785
absolute error = 5e-31
relative error = 1.2173196514315134414101280227780e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.68
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.68
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.69
y[1] (closed_form) = -4.099193420450080914025677260917
y[1] (numeric) = -4.0991934204500809140256772609172
absolute error = 2e-31
relative error = 4.8790086118463888792154205030171e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.69
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.69
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.7
y[1] (closed_form) = -4.09099782510183333161305024855
y[1] (numeric) = -4.0909978251018333316130502485498
absolute error = 2e-31
relative error = 4.8887828483512232018895433030787e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.7
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.7
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.71
y[1] (closed_form) = -4.082797824467099651188120197447
y[1] (numeric) = -4.0827978244670996511881201974466
absolute error = 4e-31
relative error = 9.7972032218423485160695313495401e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.71
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.71
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.72
y[1] (closed_form) = -4.074593420485680300263521574941
y[1] (numeric) = -4.0745934204856803002635215749414
absolute error = 4e-31
relative error = 9.8169303957772823129216160747872e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.72
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.72
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.73
y[1] (closed_form) = -4.066384615095668135387550522224
y[1] (numeric) = -4.0663846150956681353875505222243
absolute error = 3e-31
relative error = 7.3775608654013664932919503668272e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.73
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.73
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.74
y[1] (closed_form) = -4.058171410233450695867681996707
y[1] (numeric) = -4.0581714102334506958676819967067
absolute error = 3e-31
relative error = 7.3924920776755010405709619867948e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.74
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.74
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.75
y[1] (closed_form) = -4.049953807833712453529752911473
y[1] (numeric) = -4.049953807833712453529752911473
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.75
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.75
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.76
y[1] (closed_form) = -4.041731809829437058521524095489
y[1] (numeric) = -4.0417318098294370585215240954892
absolute error = 2e-31
relative error = 4.9483738508726063146530261253325e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.76
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.76
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.77
y[1] (closed_form) = -4.033505418151909581169310929453
y[1] (numeric) = -4.0335054181519095811693109294529
absolute error = 1e-31
relative error = 2.4792330648664027017045245704598e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.77
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.77
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.78
y[1] (closed_form) = -4.025274634730718749896349613997
y[1] (numeric) = -4.0252746347307187498963496139967
absolute error = 3e-31
relative error = 7.4529076205521883057724123981242e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.78
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.78
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.79
y[1] (closed_form) = -4.017039461493759185211543199146
y[1] (numeric) = -4.0170394614937591852115431991459
absolute error = 1e-31
relative error = 2.4893955102650255247722265710407e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.79
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.79
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.8
y[1] (closed_form) = -4.008799900367233629777208746238
y[1] (numeric) = -4.0087999003672336297772087462375
absolute error = 5e-31
relative error = 1.2472560677179136895783455000681e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.8
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.8
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.81
y[1] (closed_form) = -4.000555953275655174564424305684
y[1] (numeric) = -4.0005559532756551745644243056843
absolute error = 3e-31
relative error = 7.4989577324711582398418771506959e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.81
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.81
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.82
y[1] (closed_form) = -3.992307622141849481104551775767
y[1] (numeric) = -3.9923076221418494811045517757671
absolute error = 1e-31
relative error = 2.5048169997068159314126440186116e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.82
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.82
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.83
y[1] (closed_form) = -3.984054908886956999845489158821
y[1] (numeric) = -3.9840549088869569998454891588208
absolute error = 2e-31
relative error = 5.0200111337289495975081120028689e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.83
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.83
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.84
y[1] (closed_form) = -3.975797815430435184621183251502
y[1] (numeric) = -3.975797815430435184621183251502
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.84
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.84
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.85
y[1] (closed_form) = -3.967536343690060703242911395038
y[1] (numeric) = -3.9675363436900607032429113950377
absolute error = 3e-31
relative error = 7.5613674081931900500864994870964e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.85
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.85
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.86
y[1] (closed_form) = -3.959270495581931644220818569227
y[1] (numeric) = -3.9592704955819316442208185692275
absolute error = 5e-31
relative error = 1.2628589043308349260395394670319e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.86
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.86
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.87
y[1] (closed_form) = -3.951000273020469719624173840255
y[1] (numeric) = -3.9510002730204697196241738402554
absolute error = 4e-31
relative error = 1.0124018536050545137255956459607e-29 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.87
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.87
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.88
y[1] (closed_form) = -3.942725677918422464088787966826
y[1] (numeric) = -3.9427256779184224640887879668259
absolute error = 1e-31
relative error = 2.5363164513336214019987586787900e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.88
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.88
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.89
y[1] (closed_form) = -3.934446712186865429980011831536
y[1] (numeric) = -3.9344467121868654299800118315358
absolute error = 2e-31
relative error = 5.0833068695657824621969977620015e-30 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.89
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.89
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.9
y[1] (closed_form) = -3.926163377735204378719713294487
y[1] (numeric) = -3.9261633777352043787197132944873
absolute error = 3e-31
relative error = 7.6410472804382914963493662636517e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.9
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.9
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.91
y[1] (closed_form) = -3.917875676471177468285608063706
y[1] (numeric) = -3.917875676471177468285608063706
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.91
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.91
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.92
y[1] (closed_form) = -3.909583610300857436891298241712
y[1] (numeric) = -3.9095836103008574368912982417117
absolute error = 3e-31
relative error = 7.6734514440251055447924735509730e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.92
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.92
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.93
y[1] (closed_form) = -3.901287181128653782855350339367
y[1] (numeric) = -3.9012871811286537828553503393671
absolute error = 1e-31
relative error = 2.5632565703883841679664091333541e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.93
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.93
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.94
y[1] (closed_form) = -3.892986390857314940667722746664
y[1] (numeric) = -3.8929863908573149406677227466645
absolute error = 5e-31
relative error = 1.2843610272418389066431407276108e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.94
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.94
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.95
y[1] (closed_form) = -3.884681241387930453261830915173
y[1] (numeric) = -3.8846812413879304532618309151736
absolute error = 6e-31
relative error = 1.5445282707047289617938056745645e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.95
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.95
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.96
y[1] (closed_form) = -3.876371734619933140500516838226
y[1] (numeric) = -3.8763717346199331405005168382258
absolute error = 2e-31
relative error = 5.1594638928407471835135957897253e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.96
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.96
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.97
y[1] (closed_form) = -3.868057872451101263884167812333
y[1] (numeric) = -3.8680578724511012638841678123334
absolute error = 4e-31
relative error = 1.0341106911787982059987942659515e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.97
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.97
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.98
y[1] (closed_form) = -3.859739656777560687489207926588
y[1] (numeric) = -3.8597396567775606874892079265881
absolute error = 1e-31
relative error = 2.5908483186010663409906153636493e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.98
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.98
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 20.99
y[1] (closed_form) = -3.851417089493787035145164255642
y[1] (numeric) = -3.8514170894937870351451642556426
absolute error = 6e-31
relative error = 1.5578681458228179210135545861315e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 22.99
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.99
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21
y[1] (closed_form) = -3.843090172492607843858488326106
y[1] (numeric) = -3.8430901724926078438584883261063
absolute error = 3e-31
relative error = 7.8062180832312242038463221047737e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.01
y[1] (closed_form) = -3.834758907665204713491292085566
y[1] (numeric) = -3.8347589076652047134912920855666
absolute error = 6e-31
relative error = 1.5646355206338391788703050225026e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.01
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.01
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.02
y[1] (closed_form) = -3.826423296901115452703136327745
y[1] (numeric) = -3.8264232969011154527031363277454
absolute error = 4e-31
relative error = 1.0453626506088487816528432246954e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.02
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.02
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.03
y[1] (closed_form) = -3.818083342088236221163988316297
y[1] (numeric) = -3.8180833420882362211639883162972
absolute error = 2e-31
relative error = 5.2382303391683790933040417042880e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.03
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.03
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.04
y[1] (closed_form) = -3.809739045112823668046444203222
y[1] (numeric) = -3.8097390451128236680464442032227
absolute error = 7e-31
relative error = 1.8373961883241528482113435411696e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.04
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.04
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.05
y[1] (closed_form) = -3.801390407859497066805290755582
y[1] (numeric) = -3.8013904078594970668052907555829
absolute error = 9e-31
relative error = 2.3675547719045668697209282909429e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.05
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.05
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.06
y[1] (closed_form) = -3.793037432211240446252459885941
y[1] (numeric) = -3.793037432211240446252459885942
absolute error = 1.0e-30
relative error = 2.6364095210550729087210580317890e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.06
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.06
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.07
y[1] (closed_form) = -3.784680120049404717935408527503
y[1] (numeric) = -3.7846801200494047179354085275036
absolute error = 6e-31
relative error = 1.5853387366120856699735043910362e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.07
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.07
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.08
y[1] (closed_form) = -3.776318473253709799826935504028
y[1] (numeric) = -3.7763184732537097998269355040292
absolute error = 1.2e-30
relative error = 3.1776980900820826648681967618106e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.08
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.08
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.09
y[1] (closed_form) = -3.767952493702246736334426217108
y[1] (numeric) = -3.7679524937022467363344262171086
absolute error = 6e-31
relative error = 1.5923767643112263130775273009751e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.09
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.09
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.1
y[1] (closed_form) = -3.759582183271479814636495208975
y[1] (numeric) = -3.7595821832714798146364952089762
absolute error = 1.2e-30
relative error = 3.1918440441054400992615976240772e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.1
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.1
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.11
y[1] (closed_form) = -3.751207543836248677354975957611
y[1] (numeric) = -3.7512075438362486773549759576118
absolute error = 8e-31
relative error = 2.1326465961994300416831495830026e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.11
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.11
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.12
y[1] (closed_form) = -3.742828577269770431570186622115
y[1] (numeric) = -3.7428285772697704315701866221158
absolute error = 8e-31
relative error = 2.1374208930069807584581699948264e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.12
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.12
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.13
y[1] (closed_form) = -3.734445285443641754187379880084
y[1] (numeric) = -3.7344452854436417541873798800849
absolute error = 9e-31
relative error = 2.4099964819623337802248228756723e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.13
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.13
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.14
y[1] (closed_form) = -3.726057670227840993662264484725
y[1] (numeric) = -3.7260576702278409936622644847253
absolute error = 3e-31
relative error = 8.0514051727400021280576212032393e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.14
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.14
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.15
y[1] (closed_form) = -3.717665733490730268093465717504
y[1] (numeric) = -3.7176657334907302680934657175044
absolute error = 4e-31
relative error = 1.0759439623540790591299879509593e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.15
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.15
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.16
y[1] (closed_form) = -3.70926947709905755968977152205
y[1] (numeric) = -3.7092694770990575596897715220503
absolute error = 3e-31
relative error = 8.0878459182378885760832187138531e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.16
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.16
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.17
y[1] (closed_form) = -3.700868902917958805619990776541
y[1] (numeric) = -3.7008689029179588056199907765417
absolute error = 7e-31
relative error = 1.8914477069103511092357801441088e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.17
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.17
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.18
y[1] (closed_form) = -3.692464012810959985253229894784
y[1] (numeric) = -3.6924640128109599852532298947847
absolute error = 7e-31
relative error = 1.8957530732089962792321636103907e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.18
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.18
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.19
y[1] (closed_form) = -3.684054808639979203797373740321
y[1] (numeric) = -3.6840548086399792037973737403217
absolute error = 7e-31
relative error = 1.9000803092243214304947308698182e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.19
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.19
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.2
y[1] (closed_form) = -3.675641292265328772343536693069
y[1] (numeric) = -3.6756412922653287723435366930698
absolute error = 8e-31
relative error = 2.1764909478066975445224235293612e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.2
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.2
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.21
y[1] (closed_form) = -3.667223465545717284324229623908
y[1] (numeric) = -3.6672234655457172843242296239085
absolute error = 5e-31
relative error = 1.3634293211133652727961005973821e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.21
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.21
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.22
y[1] (closed_form) = -3.65880133033825168839296850914
y[1] (numeric) = -3.6588013303382516883929685091409
absolute error = 9e-31
relative error = 2.4598219983614035299118275543297e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.22
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.22
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.23
y[1] (closed_form) = -3.650374888498439357733030453614
y[1] (numeric) = -3.6503748884984393577330304536144
absolute error = 4e-31
relative error = 1.0957778645155475836685623180321e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.23
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.23
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.24
y[1] (closed_form) = -3.641944141880190155803042988307
y[1] (numeric) = -3.6419441418801901558030429883075
absolute error = 5e-31
relative error = 1.3728931046753231914258796628971e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.24
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.24
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.25
y[1] (closed_form) = -3.633509092335818498527072665158
y[1] (numeric) = -3.6335090923358184985270726651588
absolute error = 8e-31
relative error = 2.2017283558955296786026820119270e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.25
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.25
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.26
y[1] (closed_form) = -3.625069741716045412936859188623
y[1] (numeric) = -3.6250697417160454129368591886234
absolute error = 4e-31
relative error = 1.1034270469253011054108361963415e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.26
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.26
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=92.4MB, alloc=44.3MB, time=1.09
TOP MAIN SOLVE Loop
x[1] = 21.27
y[1] (closed_form) = -3.616626091870000592273821599692
y[1] (numeric) = -3.6166260918700005922738215996931
absolute error = 1.1e-30
relative error = 3.0415087765714748760232815366449e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.27
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.27
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.28
y[1] (closed_form) = -3.608178144645224447558443363692
y[1] (numeric) = -3.608178144645224447558443363693
absolute error = 1.0e-30
relative error = 2.7714817836366153093229245025950e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.28
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.28
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.29
y[1] (closed_form) = -3.59972590188767015563462360788
y[1] (numeric) = -3.599725901887670155634623607881
absolute error = 1.0e-30
relative error = 2.7779892893389667601753220107197e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.29
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.29
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.3
y[1] (closed_form) = -3.591269365441705703696562208506
y[1] (numeric) = -3.591269365441705703696562208507
absolute error = 1.0e-30
relative error = 2.7845307556789343990347313159994e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.3
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.3
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.31
y[1] (closed_form) = -3.582808537150115930305726939346
y[1] (numeric) = -3.5828085371501159303057269393466
absolute error = 6e-31
relative error = 1.6746638671271554681005329898044e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.31
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.31
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.32
y[1] (closed_form) = -3.574343418854104562905431464604
y[1] (numeric) = -3.574343418854104562905431464605
absolute error = 1.0e-30
relative error = 2.7977166232129677995024227538237e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.32
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.32
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.33
y[1] (closed_form) = -3.565874012393296251840533588282
y[1] (numeric) = -3.5658740123932962518405335882831
absolute error = 1.1e-30
relative error = 3.0847977134831988061839605080254e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.33
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.33
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.34
y[1] (closed_form) = -3.557400319605738600889743859419
y[1] (numeric) = -3.5574003196057386008897438594194
absolute error = 4e-31
relative error = 1.1244166078118849623813835856624e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.34
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.34
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.35
y[1] (closed_form) = -3.548922342327904194318015377863
y[1] (numeric) = -3.5489223423279041943180153778638
absolute error = 8e-31
relative error = 2.2542054258511685928598360432417e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.35
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.35
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.36
y[1] (closed_form) = -3.540440082394692620456466448201
y[1] (numeric) = -3.5404400823946926204564664482016
absolute error = 6e-31
relative error = 1.6947045735460387918429275881160e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.36
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.36
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.37
y[1] (closed_form) = -3.531953541639432491817268589938
y[1] (numeric) = -3.5319535416394324918172685899387
absolute error = 7e-31
relative error = 1.9819060238121928605079900912441e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.37
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.37
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.38
y[1] (closed_form) = -3.523462721893883461750913329875
y[1] (numeric) = -3.5234627218938834617509133298753
absolute error = 3e-31
relative error = 8.5143514683972051693704109740788e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.38
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.38
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.39
y[1] (closed_form) = -3.514967624988238237653252177547
y[1] (numeric) = -3.5149676249882382376532521775478
absolute error = 8e-31
relative error = 2.2759811336887546863821053875989e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.39
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.39
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.4
y[1] (closed_form) = -3.506468252751124590729685216504
y[1] (numeric) = -3.506468252751124590729685216505
absolute error = 1.0e-30
relative error = 2.8518723910174129583089568739515e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.4
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.4
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.41
y[1] (closed_form) = -3.497964607009607362323854832815
y[1] (numeric) = -3.4979646070096073623238548328155
absolute error = 5e-31
relative error = 1.4294026846299269060906394381719e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.41
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.41
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.42
y[1] (closed_form) = -3.489456689589190466818182247381
y[1] (numeric) = -3.4894566895891904668181822473815
absolute error = 5e-31
relative error = 1.4328878231724503729947097752802e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.42
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.42
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.43
y[1] (closed_form) = -3.480944502313818891113565720166
y[1] (numeric) = -3.4809445023138188911135657201665
absolute error = 5e-31
relative error = 1.4363917599595309867094332997241e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.43
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.43
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.44
y[1] (closed_form) = -3.47242804700588069069554055214
y[1] (numeric) = -3.4724280470058806906955405521412
absolute error = 1.2e-30
relative error = 3.4557951489727952706003879096594e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.44
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.44
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.45
y[1] (closed_form) = -3.463907325486208982294182324419
y[1] (numeric) = -3.4639073254862089822941823244197
absolute error = 7e-31
relative error = 2.0208392841507241502983837705392e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.45
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.45
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.46
y[1] (closed_form) = -3.455382339574083933145016183504
y[1] (numeric) = -3.4553823395740839331450161835041
absolute error = 1e-31
relative error = 2.8940357440249626099069687339176e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.46
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.46
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.47
y[1] (closed_form) = -3.446853091087234746858176406594
y[1] (numeric) = -3.4468530910872347468581764065943
absolute error = 3e-31
relative error = 8.7035911329012149159693599807145e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.47
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.47
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.48
y[1] (closed_form) = -3.438319581841841645903041961355
y[1] (numeric) = -3.4383195818418416459030419613552
absolute error = 2e-31
relative error = 5.8167949557749907601011534951305e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.48
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.48
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.49
y[1] (closed_form) = -3.429781813652537850715555310185
y[1] (numeric) = -3.4297818136525378507155553101858
absolute error = 8e-31
relative error = 2.3325098897414758114163807540511e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.49
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.49
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.5
y[1] (closed_form) = -3.421239788332411555435413299704
y[1] (numeric) = -3.4212397883324115554354132997041
absolute error = 1e-31
relative error = 2.9229170180071542555191404517907e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.5
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.5
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.51
y[1] (closed_form) = -3.412693507693007900280300621674
y[1] (numeric) = -3.4126935076930079002803006216743
absolute error = 3e-31
relative error = 8.7907103091364624871051884220013e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.51
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.51
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.52
y[1] (closed_form) = -3.404142973544330940564318031758
y[1] (numeric) = -3.4041429735443309405643180317589
absolute error = 9e-31
relative error = 2.6438372506514806664243766717013e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.52
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.52
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.53
y[1] (closed_form) = -3.395588187694845612367739267103
y[1] (numeric) = -3.395588187694845612367739267103
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.53
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.53
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.54
y[1] (closed_form) = -3.387029151951479694865212412657
y[1] (numeric) = -3.3870291519514796948652124126576
absolute error = 6e-31
relative error = 1.7714639381072418861815086761051e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.54
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.54
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.55
y[1] (closed_form) = -3.378465868119625769319503329146
y[1] (numeric) = -3.3784658681196257693195033291467
absolute error = 7e-31
relative error = 2.0719463428813725179076115450657e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.55
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.55
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.56
y[1] (closed_form) = -3.369898338003143174747860672486
y[1] (numeric) = -3.3698983380031431747478606724862
absolute error = 2e-31
relative error = 5.9348971375353536202688106990626e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.56
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.56
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.57
y[1] (closed_form) = -3.361326563404359960268064005098
y[1] (numeric) = -3.3613265634043599602680640050988
absolute error = 8e-31
relative error = 2.3800127268495983228076521026886e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.57
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.57
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.58
y[1] (closed_form) = -3.352750546124074834131198523744
y[1] (numeric) = -3.3527505461240748341311985237447
absolute error = 7e-31
relative error = 2.0878380015752450931855693337140e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.58
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.58
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.59
y[1] (closed_form) = -3.344170287961559109448182006031
y[1] (numeric) = -3.3441702879615591094481820060317
absolute error = 7e-31
relative error = 2.0931948427383624532260467439901e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.59
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.59
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.6
y[1] (closed_form) = -3.335585790714558646617051708491
y[1] (numeric) = -3.3355857907145586466170517084915
absolute error = 5e-31
relative error = 1.4989870786471019897783767547693e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.6
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.6
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.61
y[1] (closed_form) = -3.326997056179295792458001132836
y[1] (numeric) = -3.326997056179295792458001132836
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.61
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.61
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.62
y[1] (closed_form) = -3.318404086150471316063138813554
y[1] (numeric) = -3.3184040861504713160631388135539
absolute error = 1e-31
relative error = 3.0134967714557458433791941987100e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.62
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.62
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.63
y[1] (closed_form) = -3.309806882421266341367923569203
y[1] (numeric) = -3.309806882421266341367923569204
absolute error = 1.0e-30
relative error = 3.0213243114306926385917253079974e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.63
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.63
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.64
y[1] (closed_form) = -3.301205446783344276451213001415
y[1] (numeric) = -3.3012054467833442764512130014151
absolute error = 1e-31
relative error = 3.0291965044901650316620761074212e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.64
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.64
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.65
y[1] (closed_form) = -3.292599781026852739570844419552
y[1] (numeric) = -3.2925997810268527395708444195522
absolute error = 2e-31
relative error = 6.0742274585715555424684351755349e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.65
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.65
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.66
y[1] (closed_form) = -3.283989886940425481941649815059
y[1] (numeric) = -3.2839898869404254819416498150597
absolute error = 7e-31
relative error = 2.1315534581385835643970166195416e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.66
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.66
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.67
y[1] (closed_form) = -3.27537576631118430726278900749
y[1] (numeric) = -3.2753757663111843072627890074908
absolute error = 8e-31
relative error = 2.4424678482035097082797296164661e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.67
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.67
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.68
y[1] (closed_form) = -3.266757420924740988001267633975
y[1] (numeric) = -3.2667574209247409880012676339753
absolute error = 3e-31
relative error = 9.1834183364333543487712235119905e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.68
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.68
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.69
y[1] (closed_form) = -3.258134852565199178438489255218
y[1] (numeric) = -3.2581348525651991784384892552187
absolute error = 7e-31
relative error = 2.1484684694645927399930755672160e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.69
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.69
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.7
y[1] (closed_form) = -3.249508063015156324486673503866
y[1] (numeric) = -3.249508063015156324486673503866
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.7
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.7
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.71
y[1] (closed_form) = -3.240877054055705570281954905049
y[1] (numeric) = -3.2408770540557055702819549050498
absolute error = 8e-31
relative error = 2.4684675989138872790698508184554e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.71
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.71
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.72
y[1] (closed_form) = -3.232241827466437661560959753982
y[1] (numeric) = -3.2322418274664376615609597539824
absolute error = 4e-31
relative error = 1.2375311667615422069924658918059e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.72
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.72
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.73
y[1] (closed_form) = -3.223602385025442845827641241394
y[1] (numeric) = -3.223602385025442845827641241394
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.73
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.73
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.74
y[1] (closed_form) = -3.214958728509312769317135874271
y[1] (numeric) = -3.2149587285093127693171358742711
absolute error = 1e-31
relative error = 3.1104598361785884446931408138408e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.74
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.74
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.75
y[1] (closed_form) = -3.206310859693142370763387146559
y[1] (numeric) = -3.206310859693142370763387146559
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.75
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.75
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.76
y[1] (closed_form) = -3.197658780350531771977265372074
y[1] (numeric) = -3.197658780350531771977265372074
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.76
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.76
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.77
y[1] (closed_form) = -3.189002492253588165241895599666
y[1] (numeric) = -3.1890024922535881652418955996668
absolute error = 8e-31
relative error = 2.5086214323860877351972655510801e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.77
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.77
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.78
y[1] (closed_form) = -3.180341997172927697531888588511
y[1] (numeric) = -3.1803419971729276975318885885117
absolute error = 7e-31
relative error = 2.2010211499965871375788710800350e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.78
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.78
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.79
y[1] (closed_form) = -3.171677296877677351563152929102
y[1] (numeric) = -3.1716772968776773515631529291023
absolute error = 3e-31
relative error = 9.4587176411462692992506351165496e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.79
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.79
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.8
y[1] (closed_form) = -3.163008393135476823679949552943
y[1] (numeric) = -3.1630083931354768236799495529435
absolute error = 5e-31
relative error = 1.5807735480093118490686262902366e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.8
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.8
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.81
y[1] (closed_form) = -3.154335287712480398585833080878
y[1] (numeric) = -3.1543352877124803985858330808783
absolute error = 3e-31
relative error = 9.5107200927127688558574322199549e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.81
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.81
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.82
y[1] (closed_form) = -3.145657982373358820925107716304
y[1] (numeric) = -3.145657982373358820925107716304
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.82
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.82
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.83
y[1] (closed_form) = -3.136976478881301163721408695055
y[1] (numeric) = -3.1369764788813011637214086950551
absolute error = 1e-31
relative error = 3.1877829073063910981928829179290e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.83
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.83
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.84
y[1] (closed_form) = -3.128290778998016693680003658292
y[1] (numeric) = -3.1282907789980166936800036582923
absolute error = 3e-31
relative error = 9.5899013612823169440982368282076e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.84
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.84
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.85
y[1] (closed_form) = -3.119600884483736733360391718174
y[1] (numeric) = -3.1196008844837367333603917181747
absolute error = 7e-31
relative error = 2.2438767839875231854981915090178e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.85
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.85
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.86
y[1] (closed_form) = -3.110906797097216520225761438238
y[1] (numeric) = -3.1109067970972165202257614382388
absolute error = 8e-31
relative error = 2.5715974543065033664751400745644e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.86
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.86
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.87
y[1] (closed_form) = -3.102208518595737062575852451105
y[1] (numeric) = -3.1022085185957370625758524511054
absolute error = 4e-31
relative error = 1.2894039765614022024710612792316e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.87
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.87
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.88
y[1] (closed_form) = -3.093506050735106992369748985215
y[1] (numeric) = -3.0935060507351069923697489852153
absolute error = 3e-31
relative error = 9.6977343855109407796588458239633e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.88
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.88
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=136.5MB, alloc=44.3MB, time=1.59
x[1] = 21.89
y[1] (closed_form) = -3.084799395269664414945117169599
y[1] (numeric) = -3.0847993952696644149451171695993
absolute error = 3e-31
relative error = 9.7251056409058602908166294029395e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.89
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.89
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.9
y[1] (closed_form) = -3.076088553952278755640381631053
y[1] (numeric) = -3.0760885539522787556403816310536
absolute error = 6e-31
relative error = 1.9505290224141842673717626732890e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.9
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.9
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.91
y[1] (closed_form) = -3.067373528534352603326320591356
y[1] (numeric) = -3.0673735285343526033263205913564
absolute error = 4e-31
relative error = 1.3040472452376132521825573168234e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.91
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.91
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.92
y[1] (closed_form) = -3.058654320765823550853542413169
y[1] (numeric) = -3.0586543207658235508535424131695
absolute error = 5e-31
relative error = 1.6347058136167881139360208060425e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.92
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.92
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.93
y[1] (closed_form) = -3.049930932395166032422290331855
y[1] (numeric) = -3.0499309323951660324222903318555
absolute error = 5e-31
relative error = 1.6393813862772982171774130858218e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.93
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.93
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.94
y[1] (closed_form) = -3.041203365169393157881005946447
y[1] (numeric) = -3.0412033651693931578810059464474
absolute error = 4e-31
relative error = 1.3152688326639420441955845574685e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.94
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.94
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.95
y[1] (closed_form) = -3.032471620834058543960065926284
y[1] (numeric) = -3.0324716208340585439600659262841
absolute error = 1e-31
relative error = 3.2976400937429301003346031026709e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.95
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.95
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.96
y[1] (closed_form) = -3.023735701133258142447090320197
y[1] (numeric) = -3.0237357011332581424470903201971
absolute error = 1e-31
relative error = 3.3071673546904663879392053229179e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.96
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.96
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.97
y[1] (closed_form) = -3.014995607809632065310204832462
y[1] (numeric) = -3.0149956078096320653102048324623
absolute error = 3e-31
relative error = 9.9502632515590089260319261848134e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.97
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.97
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.98
y[1] (closed_form) = -3.006251342604366406775623453846
y[1] (numeric) = -3.0062513426043664067756234538461
absolute error = 1e-31
relative error = 3.3264018408177510501625769959176e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.98
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.98
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 21.99
y[1] (closed_form) = -2.997502907257195062365901906825
y[1] (numeric) = -2.9975029072571950623659019068255
absolute error = 5e-31
relative error = 1.6680550960916831115957076414871e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 23.99
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.99
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22
y[1] (closed_form) = -2.988750303506401544905196481295
y[1] (numeric) = -2.9887503035064015449051964812958
absolute error = 8e-31
relative error = 2.6767040360027402867700312051431e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.01
y[1] (closed_form) = -2.979993533088820797497847000632
y[1] (numeric) = -2.9799935330888207974978470006322
absolute error = 2e-31
relative error = 6.7114239604639725812067496110450e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.01
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.01
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.02
y[1] (closed_form) = -2.9712325977398410034865868677
y[1] (numeric) = -2.9712325977398410034865868677006
absolute error = 6e-31
relative error = 2.0193639517027659169719273667850e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.02
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.02
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.03
y[1] (closed_form) = -2.962467499193405393396667396155
y[1] (numeric) = -2.9624674991934053933966673961549
absolute error = 1e-31
relative error = 3.3755644585882248789359412910729e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.03
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.03
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.04
y[1] (closed_form) = -2.953698239182014048872167933964
y[1] (numeric) = -2.953698239182014048872167933965
absolute error = 1.0e-30
relative error = 3.3855862008332177997349597679626e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.04
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.04
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.05
y[1] (closed_form) = -2.944924819436725703610747633435
y[1] (numeric) = -2.9449248194367257036107476334353
absolute error = 3e-31
relative error = 1.0187017271883390553285933455277e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.05
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.05
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.06
y[1] (closed_form) = -2.936147241687159541303079114852
y[1] (numeric) = -2.9361472416871595413030791148528
absolute error = 8e-31
relative error = 2.7246589974837452550908233618520e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.06
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.06
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.07
y[1] (closed_form) = -2.927365507661496990583188709183
y[1] (numeric) = -2.9273655076614969905831887091839
absolute error = 9e-31
relative error = 3.0744367167151530436320286921937e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.07
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.07
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.08
y[1] (closed_form) = -2.91857961908648351699591244878
y[1] (numeric) = -2.9185796190864835169959124487805
absolute error = 5e-31
relative error = 1.7131621036828187746244224758783e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.08
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.08
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.09
y[1] (closed_form) = -2.909789577687430411987661503701
y[1] (numeric) = -2.9097895776874304119876615037014
absolute error = 4e-31
relative error = 1.3746698492126085924215130826843e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.09
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.09
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.1
y[1] (closed_form) = -2.900995385188216578926675334856
y[1] (numeric) = -2.9009953851882165789266753348561
absolute error = 1e-31
relative error = 3.4470926948238492305416476930328e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.1
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.1
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.11
y[1] (closed_form) = -2.892197043311290316158925453588
y[1] (numeric) = -2.8921970433112903161589254535886
absolute error = 6e-31
relative error = 2.0745474496200200521818635590138e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.11
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.11
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.12
y[1] (closed_form) = -2.883394553777671097105817340383
y[1] (numeric) = -2.8833945537776710971058173403829
absolute error = 1e-31
relative error = 3.4681344552373273742828983770191e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.12
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.12
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.13
y[1] (closed_form) = -2.874587918306951347409822782953
y[1] (numeric) = -2.8745879183069513474098227829535
absolute error = 5e-31
relative error = 1.7393797448870008934788757660446e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.13
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.13
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.14
y[1] (closed_form) = -2.865777138617298219134159645919
y[1] (numeric) = -2.8657771386172982191341596459198
absolute error = 8e-31
relative error = 2.7915638980426441580256136969289e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.14
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.14
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.15
y[1] (closed_form) = -2.856962216425455362022620880422
y[1] (numeric) = -2.8569622164254553620226208804222
absolute error = 2e-31
relative error = 7.0004425977405450434069443260622e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.15
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.15
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.16
y[1] (closed_form) = -2.84814315344674469182563942226
y[1] (numeric) = -2.84814315344674469182563942226
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.16
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.16
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.17
y[1] (closed_form) = -2.83931995139506815569866051128
y[1] (numeric) = -2.8393199513950681556986605112808
absolute error = 8e-31
relative error = 2.8175760875660699400849683101672e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.17
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.17
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.18
y[1] (closed_form) = -2.830492611982909494678877892675
y[1] (numeric) = -2.8304926119829094946788778926752
absolute error = 2e-31
relative error = 7.0659078618788353636275093615920e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.18
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.18
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.19
y[1] (closed_form) = -2.82166113692133600324637533239
y[1] (numeric) = -2.8216611369213360032463753323904
absolute error = 4e-31
relative error = 1.4176046682786043025206082011091e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.19
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.19
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.2
y[1] (closed_form) = -2.812825527920000285975699893923
y[1] (numeric) = -2.8128255279200002859756998939235
absolute error = 5e-31
relative error = 1.7775720357946798520811658887637e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.2
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.2
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.21
y[1] (closed_form) = -2.803985786687142011283878482147
y[1] (numeric) = -2.8039857866871420112838784821474
absolute error = 4e-31
relative error = 1.4265407545898893214691501817921e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.21
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.21
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.22
y[1] (closed_form) = -2.795141914929589662280874261414
y[1] (numeric) = -2.7951419149295896622808742614147
absolute error = 7e-31
relative error = 2.5043451148620236641196365963737e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.22
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.22
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.23
y[1] (closed_form) = -2.786293914352762284728464699841
y[1] (numeric) = -2.7862939143527622847284646998409
absolute error = 1e-31
relative error = 3.5889968206469467533945836318412e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.23
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.23
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.24
y[1] (closed_form) = -2.777441786660671232113508179236
y[1] (numeric) = -2.7774417866606712321135081792359
absolute error = 1e-31
relative error = 3.6004354971641144034920821030364e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.24
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.24
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.25
y[1] (closed_form) = -2.768585533555921907841551340496
y[1] (numeric) = -2.7685855335559219078415513404967
absolute error = 7e-31
relative error = 2.5283668917424865608510364816525e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.25
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.25
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.26
y[1] (closed_form) = -2.759725156739715504556714607256
y[1] (numeric) = -2.7597251567397155045567146072567
absolute error = 7e-31
relative error = 2.5364844694424791882739521446098e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.26
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.26
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.27
y[1] (closed_form) = -2.750860657911850740593778646055
y[1] (numeric) = -2.7508606579118507405937786460557
absolute error = 7e-31
relative error = 2.5446581526647104099154256682769e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.27
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.27
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.28
y[1] (closed_form) = -2.741992038770725593568379879122
y[1] (numeric) = -2.7419920387707255935683798791226
absolute error = 6e-31
relative error = 2.1881901607161070245024503786853e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.28
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.28
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.29
y[1] (closed_form) = -2.733119301013339031111208565902
y[1] (numeric) = -2.7331193010133390311112085659025
absolute error = 5e-31
relative error = 1.8294115438525445554640817395147e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.29
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.29
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.3
y[1] (closed_form) = -2.724242446335292738752088411573
y[1] (numeric) = -2.7242424463352927387520884115734
absolute error = 4e-31
relative error = 1.4682980971025110845505191898108e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.3
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.3
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.31
y[1] (closed_form) = -2.71536147643079284495980214485
y[1] (numeric) = -2.71536147643079284495980214485
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.31
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.31
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.32
y[1] (closed_form) = -2.706476392992651643343513033219
y[1] (numeric) = -2.7064763929926516433435130332188
absolute error = 2e-31
relative error = 7.3896820425931208258009776642441e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.32
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.32
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.33
y[1] (closed_form) = -2.697587197712289312021617871263
y[1] (numeric) = -2.6975871977122893120216178712627
absolute error = 3e-31
relative error = 1.1121049219629209080351281174439e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.33
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.33
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.34
y[1] (closed_form) = -2.688693892279735630163852586762
y[1] (numeric) = -2.6886938922797356301638525867621
absolute error = 1e-31
relative error = 3.7192779842710281387865036047916e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.34
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.34
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.35
y[1] (closed_form) = -2.679796478383631691712457259684
y[1] (numeric) = -2.6797964783836316917124572596846
absolute error = 6e-31
relative error = 2.2389760000054219973545055329102e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.35
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.35
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.36
y[1] (closed_form) = -2.670894957711231616288193040846
y[1] (numeric) = -2.6708949577112316162881930408464
absolute error = 4e-31
relative error = 1.4976253515517201602255662047556e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.36
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.36
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.37
y[1] (closed_form) = -2.661989331948404257286989189816
y[1] (numeric) = -2.6619893319484042572869891898163
absolute error = 3e-31
relative error = 1.1269767177482239439615044881596e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.37
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.37
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.38
y[1] (closed_form) = -2.653079602779634907172984225403
y[1] (numeric) = -2.6530796027796349071729842254031
absolute error = 1e-31
relative error = 3.7692046591903941204912695402126e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.38
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.38
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.39
y[1] (closed_form) = -2.644165771888026999973710996683
y[1] (numeric) = -2.6441657718880269999737109966832
absolute error = 2e-31
relative error = 7.5638222885395340762748072507594e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.39
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.39
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.4
y[1] (closed_form) = -2.635247840955303810983161337853
y[1] (numeric) = -2.635247840955303810983161337853
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.4
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.4
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.41
y[1] (closed_form) = -2.626325811661810153678451866098
y[1] (numeric) = -2.626325811661810153678451866098
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.41
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.41
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.42
y[1] (closed_form) = -2.617399685686514073855798418023
y[1] (numeric) = -2.6173996856865140738557984180234
absolute error = 4e-31
relative error = 1.5282343089877943645930362673963e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.42
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.42
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.43
y[1] (closed_form) = -2.608469464707008540991492596858
y[1] (numeric) = -2.6084694647070085409914925968584
absolute error = 4e-31
relative error = 1.5334662928282706680931463675191e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.43
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.43
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.44
y[1] (closed_form) = -2.599535150399513136833559919494
y[1] (numeric) = -2.5995351503995131368335599194936
absolute error = 4e-31
relative error = 1.5387366465828532826582211846488e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.44
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.44
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.45
y[1] (closed_form) = -2.59059674443887574122976510931
y[1] (numeric) = -2.5905967444388757412297651093097
absolute error = 3e-31
relative error = 1.1580343434152663395627662485059e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.45
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.45
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.46
y[1] (closed_form) = -2.581654248498574215197616177573
y[1] (numeric) = -2.581654248498574215197616177573
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.46
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.46
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.47
y[1] (closed_form) = -2.572707664250718081242005072777
y[1] (numeric) = -2.5727076642507180812420050727766
absolute error = 4e-31
relative error = 1.5547821680567699346953560329510e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.47
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.47
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.48
y[1] (closed_form) = -2.563756993366050200926108853574
y[1] (numeric) = -2.563756993366050200926108853574
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.48
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.48
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.49
y[1] (closed_form) = -2.554802237513948449701161556738
y[1] (numeric) = -2.5548022375139484497011615567381
absolute error = 1e-31
relative error = 3.9141972921281360103514970898668e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.49
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.49
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.5
y[1] (closed_form) = -2.545843398362427389000693186776
y[1] (numeric) = -2.5458433983624273890006931867764
absolute error = 4e-31
relative error = 1.5711885509426602350087163669230e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.5
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.5
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.51
y[1] (closed_form) = -2.536880477578139935604818548292
y[1] (numeric) = -2.5368804775781399356048185482922
absolute error = 2e-31
relative error = 7.8836981784389045313266867185292e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.51
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.51
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=180.8MB, alloc=44.3MB, time=2.08
TOP MAIN SOLVE Loop
x[1] = 22.52
y[1] (closed_form) = -2.527913476826379028280144975788
y[1] (numeric) = -2.5279134768263790282801449757881
absolute error = 1e-31
relative error = 3.9558315945822283874834811366747e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.52
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.52
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.53
y[1] (closed_form) = -2.518942397771079291700854388229
y[1] (numeric) = -2.5189423977710792917008543882291
absolute error = 1e-31
relative error = 3.9699200779059644523579267294717e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.53
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.53
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.54
y[1] (closed_form) = -2.50996724207481869765650150719
y[1] (numeric) = -2.5099672420748186976565015071899
absolute error = 1e-31
relative error = 3.9841157415798312035907559938987e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.54
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.54
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.55
y[1] (closed_form) = -2.50098801139882022355205652768
y[1] (numeric) = -2.5009880113988202235520565276802
absolute error = 2e-31
relative error = 7.9968396125233159456450949108348e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.55
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.55
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.56
y[1] (closed_form) = -2.492004707402953508205707019647
y[1] (numeric) = -2.4920047074029535082057070196475
absolute error = 5e-31
relative error = 2.0064167556130973750215270805355e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.56
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.56
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.57
y[1] (closed_form) = -2.483017331745736504949920365566
y[1] (numeric) = -2.4830173317457365049499203655663
absolute error = 3e-31
relative error = 1.2082074344164114940701536184349e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.57
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.57
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.58
y[1] (closed_form) = -2.474025886084337132041254605322
y[1] (numeric) = -2.4740258860843371320412546053221
absolute error = 1e-31
relative error = 4.0419948943327708345920597817536e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.58
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.58
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.59
y[1] (closed_form) = -2.465030372074574920384392163651
y[1] (numeric) = -2.4650303720745749203843921636509
absolute error = 1e-31
relative error = 4.0567451473565326738360030720945e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.59
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.59
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.6
y[1] (closed_form) = -2.456030791370922658575857577585
y[1] (numeric) = -2.4560307913709226585758575775851
absolute error = 1e-31
relative error = 4.0716101911809246218862309445649e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.6
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.6
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.61
y[1] (closed_form) = -2.447027145626508035272867021555
y[1] (numeric) = -2.4470271456265080352728670215547
absolute error = 3e-31
relative error = 1.2259774091030425827719752879286e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.61
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.61
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.62
y[1] (closed_form) = -2.438019436493115278892744145878
y[1] (numeric) = -2.4380194364931152788927441458776
absolute error = 4e-31
relative error = 1.6406760094388999743941755484854e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.62
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.62
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.63
y[1] (closed_form) = -2.429007665621186794648323500223
y[1] (numeric) = -2.4290076656211867946483235002231
absolute error = 1e-31
relative error = 4.1169075509865183544158166387047e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.63
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.63
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.64
y[1] (closed_form) = -2.41999183465982479892474960712
y[1] (numeric) = -2.4199918346598247989247496071199
absolute error = 1e-31
relative error = 4.1322453475987398907945775344243e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.64
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.64
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.65
y[1] (closed_form) = -2.41097194525679295100306658159
y[1] (numeric) = -2.4109719452567929510030665815893
absolute error = 7e-31
relative error = 2.9033933861285262879544912234674e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.65
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.65
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.66
y[1] (closed_form) = -2.401947999058517982135980061388
y[1] (numeric) = -2.4019479990585179821359800613879
absolute error = 1e-31
relative error = 4.1632874666394361097907531310996e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.66
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.66
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.67
y[1] (closed_form) = -2.392919997710091321981160118026
y[1] (numeric) = -2.3929199977100913219811601180253
absolute error = 7e-31
relative error = 2.9252962935236703978052756796111e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.67
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.67
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.68
y[1] (closed_form) = -2.383887942855270722397440761555
y[1] (numeric) = -2.3838879428552707223974407615549
absolute error = 1e-31
relative error = 4.1948280454922014061677905852610e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.68
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.68
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.69
y[1] (closed_form) = -2.374851836136481878609258632007
y[1] (numeric) = -2.374851836136481878609258632007
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.69
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.69
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.7
y[1] (closed_form) = -2.365811679194820047744660487114
y[1] (numeric) = -2.3658116791948200477446604871139
absolute error = 1e-31
relative error = 4.2268791248014289674555608932923e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.7
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.7
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.71
y[1] (closed_form) = -2.356767473670051664752196149556
y[1] (numeric) = -2.3567674736700516647521961495559
absolute error = 1e-31
relative error = 4.2430999713466020839338075387152e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.71
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.71
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.72
y[1] (closed_form) = -2.347719221200615955702000667208
y[1] (numeric) = -2.3477192212006159557020006672079
absolute error = 1e-31
relative error = 4.2594531363448277268605700241060e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.72
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.72
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.73
y[1] (closed_form) = -2.338666923423626548476356566678
y[1] (numeric) = -2.338666923423626548476356566678
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.73
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.73
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.74
y[1] (closed_form) = -2.329610581974873080855014243676
y[1] (numeric) = -2.3296105819748730808550142436755
absolute error = 5e-31
relative error = 2.1462814595224608404941572732403e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.74
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.74
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.75
y[1] (closed_form) = -2.320550198488822806000535733316
y[1] (numeric) = -2.3205501984888228060005357333155
absolute error = 5e-31
relative error = 2.1546614260945853306274087561736e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.75
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.75
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.76
y[1] (closed_form) = -2.311485774598622195348914339239
y[1] (numeric) = -2.3114857745986221953489143392382
absolute error = 8e-31
relative error = 3.4609773886188676658375232469809e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.76
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.76
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.77
y[1] (closed_form) = -2.302417311936098538910709872281
y[1] (numeric) = -2.3024173119360985389107098722808
absolute error = 2e-31
relative error = 8.6865225935875353101563950755785e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.77
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.77
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.78
y[1] (closed_form) = -2.293344812131761542987926557266
y[1] (numeric) = -2.2933448121317615429879265572654
absolute error = 6e-31
relative error = 2.6162659745974896854368985715967e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.78
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.78
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.79
y[1] (closed_form) = -2.28426827681480492531184801015
y[1] (numeric) = -2.2842682768148049253118480101495
absolute error = 5e-31
relative error = 2.1888847517385413810927674136696e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.79
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.79
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.8
y[1] (closed_form) = -2.275187707613108007607031067206
y[1] (numeric) = -2.2751877076131080076070310672052
absolute error = 8e-31
relative error = 3.5161933994416548025535431039751e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.8
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.8
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.81
y[1] (closed_form) = -2.266103106153237305586647662934
y[1] (numeric) = -2.2661031061532373055866476629332
absolute error = 8e-31
relative error = 3.5302894993071104987865203233077e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.81
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.81
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.82
y[1] (closed_form) = -2.25701447406044811638435140397
y[1] (numeric) = -2.2570144740604481163843514039697
absolute error = 3e-31
relative error = 1.3291895264645312136387349931871e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.82
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.82
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.83
y[1] (closed_form) = -2.247921812958686103427832972187
y[1] (numeric) = -2.2479218129586861034278329721862
absolute error = 8e-31
relative error = 3.5588426402920579056446230169171e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.83
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.83
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.84
y[1] (closed_form) = -2.238825124470588878759216011405
y[1] (numeric) = -2.2388251244705888787592160114043
absolute error = 7e-31
relative error = 3.1266399163960061167597450060629e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.84
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.84
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.85
y[1] (closed_form) = -2.229724410217487582807432708537
y[1] (numeric) = -2.2297244102174875828074327085362
absolute error = 8e-31
relative error = 3.5878873475756939187791334125700e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.85
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.85
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.86
y[1] (closed_form) = -2.220619671819408461617705871402
y[1] (numeric) = -2.2206196718194084616177058714017
absolute error = 3e-31
relative error = 1.3509742519492435256037770121279e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.86
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.86
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.87
y[1] (closed_form) = -2.211510910895074441543251931852
y[1] (numeric) = -2.2115109108950744415432519318517
absolute error = 3e-31
relative error = 1.3565386384577216197186255269809e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.87
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.87
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.88
y[1] (closed_form) = -2.202398129061906701404306964037
y[1] (numeric) = -2.202398129061906701404306964037
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.88
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.88
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.89
y[1] (closed_form) = -2.193281327936026242119565503583
y[1] (numeric) = -2.1932813279360262421195655035828
absolute error = 2e-31
relative error = 9.1187572452553889467017001380281e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.89
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.89
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.9
y[1] (closed_form) = -2.184160509132255453815109683955
y[1] (numeric) = -2.1841605091322554538151096839548
absolute error = 2e-31
relative error = 9.1568361923848694921466131499257e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.9
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.9
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.91
y[1] (closed_form) = -2.175035674264119680415893971324
y[1] (numeric) = -2.1750356742641196804158939713234
absolute error = 6e-31
relative error = 2.7585754436096692432598147896514e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.91
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.91
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.92
y[1] (closed_form) = -2.165906824943848781724838578631
y[1] (numeric) = -2.1659068249438487817248385786304
absolute error = 6e-31
relative error = 2.7702022685835297796107093044353e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.92
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.92
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.93
y[1] (closed_form) = -2.156773962782378692994572473238
y[1] (numeric) = -2.1567739627823786929945724732374
absolute error = 6e-31
relative error = 2.7819326937068591776233420633354e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.93
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.93
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.94
y[1] (closed_form) = -2.147637089389352981996854760366
y[1] (numeric) = -2.1476370893893529819968547603652
absolute error = 8e-31
relative error = 3.7250241390991598503873088085400e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.94
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.94
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.95
y[1] (closed_form) = -2.138496206373124403594691126421
y[1] (numeric) = -2.1384962063731244035946911264202
absolute error = 8e-31
relative error = 3.7409465474656827848481337131365e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.95
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.95
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.96
y[1] (closed_form) = -2.129351315340756451822149962132
y[1] (numeric) = -2.1293513153407564518221499621316
absolute error = 4e-31
relative error = 1.8785063653809924907611827308205e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.96
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.96
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.97
y[1] (closed_form) = -2.120202417898024909476870755084
y[1] (numeric) = -2.1202024178980249094768707550836
absolute error = 4e-31
relative error = 1.8866123188207718863160918179702e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.97
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.97
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.98
y[1] (closed_form) = -2.111049515649419395230245344614
y[1] (numeric) = -2.1110495156494193952302453446136
absolute error = 4e-31
relative error = 1.8947921260717019436654400458651e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.98
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.98
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 22.99
y[1] (closed_form) = -2.101892610198144908260240669053
y[1] (numeric) = -2.1018926101981449082602406690529
absolute error = 1e-31
relative error = 4.7576169931237840059583851698965e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 24.99
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.99
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23
y[1] (closed_form) = -2.0927317031461233704118197058
y[1] (numeric) = -2.0927317031461233704118197057994
absolute error = 6e-31
relative error = 2.8670660414709905347226370241119e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.01
y[1] (closed_form) = -2.083566796093995165889905408628
y[1] (numeric) = -2.0835667960939951658899054086273
absolute error = 7e-31
relative error = 3.3596235134494875251053331555106e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.01
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.01
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.02
y[1] (closed_form) = -2.074397890641120678489820583855
y[1] (numeric) = -2.0743978906411206784898205838552
absolute error = 2e-31
relative error = 9.6413518786498235119208103413108e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.02
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.02
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.03
y[1] (closed_form) = -2.06522498838558182637012481739
y[1] (numeric) = -2.0652249883855818263701248173894
absolute error = 6e-31
relative error = 2.9052524706716300133649726171486e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.03
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.03
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.04
y[1] (closed_form) = -2.056048090924183594372757768151
y[1] (numeric) = -2.0560480909241835943727577681504
absolute error = 6e-31
relative error = 2.9182196790460427644228460881781e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.04
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.04
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.05
y[1] (closed_form) = -2.046867199852455563895386379848
y[1] (numeric) = -2.0468671998524555638953863798477
absolute error = 3e-31
relative error = 1.4656544402178358996158440234092e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.05
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.05
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.06
y[1] (closed_form) = -2.037682316764653440320841832406
y[1] (numeric) = -2.0376823167646534403208418324059
absolute error = 1e-31
relative error = 4.9075363307257731833851851957259e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.06
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.06
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.07
y[1] (closed_form) = -2.028493443253760578008520356445
y[1] (numeric) = -2.0284934432537605780085203564444
absolute error = 6e-31
relative error = 2.9578601892722074175824157314031e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.07
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.07
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.08
y[1] (closed_form) = -2.01930058091148950285261036898
y[1] (numeric) = -2.0193005809114895028526103689793
absolute error = 7e-31
relative error = 3.4665468163438446423639663521500e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.08
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.08
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.09
y[1] (closed_form) = -2.010103731328283432411996755837
y[1] (numeric) = -2.0101037313282834324119967558369
absolute error = 1e-31
relative error = 4.9748676370009848891375234037864e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.09
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.09
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.1
y[1] (closed_form) = -2.000902896093317793616681526048
y[1] (numeric) = -2.0009028960933177936166815260475
absolute error = 5e-31
relative error = 2.4988718891667848277092037858505e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.1
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.1
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.11
y[1] (closed_form) = -1.991698076794501738055548495616
y[1] (numeric) = -1.9916980767945017380555484956156
absolute error = 4e-31
relative error = 2.0083365278123475669073470789563e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.11
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.11
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.12
y[1] (closed_form) = -1.982489275018479654850288122441
y[1] (numeric) = -1.9824892750184796548502881224403
absolute error = 7e-31
relative error = 3.5309144358093689661551097397099e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.12
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.12
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.13
y[1] (closed_form) = -1.973276492350632681120287110681
y[1] (numeric) = -1.973276492350632681120287110681
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.13
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.13
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.14
y[1] (closed_form) = -1.964059730375080210043275931431
y[1] (numeric) = -1.9640597303750802100432759314301
absolute error = 9e-31
relative error = 4.5823453639473851125697603398564e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.14
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.14
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=225.0MB, alloc=44.3MB, time=2.56
TOP MAIN SOLVE Loop
x[1] = 23.15
y[1] (closed_form) = -1.954838990674681396516515967061
y[1] (numeric) = -1.9548389906746813965165159670605
absolute error = 5e-31
relative error = 2.5577554079143520712366566763221e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.15
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.15
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.16
y[1] (closed_form) = -1.945614274831036660423296578961
y[1] (numeric) = -1.9456142748310366604232965789608
absolute error = 2e-31
relative error = 1.0279529842438508882474556468687e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.16
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.16
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.17
y[1] (closed_form) = -1.936385584424489187509501022458
y[1] (numeric) = -1.9363855844244891875095010224573
absolute error = 7e-31
relative error = 3.6149824995110472873265773909085e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.17
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.17
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.18
y[1] (closed_form) = -1.927152921034126427874988788444
y[1] (numeric) = -1.9271529210341264278749887884433
absolute error = 7e-31
relative error = 3.6323012686734487391176702984776e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.18
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.18
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.19
y[1] (closed_form) = -1.917916286237781592084530638494
y[1] (numeric) = -1.917916286237781592084530638493
absolute error = 1.0e-30
relative error = 5.2139919097387594228846625556465e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.19
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.19
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.2
y[1] (closed_form) = -1.908675681612035144903021318936
y[1] (numeric) = -1.908675681612035144903021318936
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.2
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.2
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.21
y[1] (closed_form) = -1.8994311087322162966596836894
y[1] (numeric) = -1.8994311087322162966596836893993
absolute error = 7e-31
relative error = 3.6853139699666080507737232937188e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.21
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.21
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.22
y[1] (closed_form) = -1.890182569172404492245966782593
y[1] (numeric) = -1.8901825691724044922459667825921
absolute error = 9e-31
relative error = 4.7614448184973742204210172947027e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.22
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.22
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.23
y[1] (closed_form) = -1.880930064505430897751829124522
y[1] (numeric) = -1.8809300645054308977518291245217
absolute error = 3e-31
relative error = 1.5949556321163996999013738953788e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.23
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.23
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.24
y[1] (closed_form) = -1.871673596302879884745087487772
y[1] (numeric) = -1.8716735963028798847450874877713
absolute error = 7e-31
relative error = 3.7399683437470679685196629288590e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.24
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.24
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.25
y[1] (closed_form) = -1.862413166135090512198500124865
y[1] (numeric) = -1.8624131661350905121985001248647
absolute error = 3e-31
relative error = 1.6108133547109999322545096070672e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.25
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.25
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.26
y[1] (closed_form) = -1.853148775571158006069242433974
y[1] (numeric) = -1.8531487755711580060692424339734
absolute error = 6e-31
relative error = 3.2377324902857533209457434332636e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.26
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.26
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.27
y[1] (closed_form) = -1.8438804261789352365354219452
y[1] (numeric) = -1.8438804261789352365354219451999
absolute error = 1e-31
relative error = 5.4233451681695830581588580451878e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.27
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.27
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.28
y[1] (closed_form) = -1.834608119525034192894268482299
y[1] (numeric) = -1.8346081195250341928942684822981
absolute error = 9e-31
relative error = 4.9056798038864180800939653917869e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.28
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.28
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.29
y[1] (closed_form) = -1.825331857174827456126624351871
y[1] (numeric) = -1.8253318571748274561266243518706
absolute error = 4e-31
relative error = 2.1913823419435812760031170711316e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.29
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.29
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.3
y[1] (closed_form) = -1.816051640692449669132348439713
y[1] (numeric) = -1.8160516406924496691323484397127
absolute error = 3e-31
relative error = 1.6519354035858351893335896202193e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.3
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.3
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.31
y[1] (closed_form) = -1.806767471640799004641237151967
y[1] (numeric) = -1.8067674716407990046412371519667
absolute error = 3e-31
relative error = 1.6604239599662362856272468187440e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.31
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.31
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.32
y[1] (closed_form) = -1.797479351581538630804054227001
y[1] (numeric) = -1.7974793515815386308040542270011
absolute error = 1e-31
relative error = 5.5633462443957161443604466705572e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.32
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.32
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.33
y[1] (closed_form) = -1.788187282075098174468250562351
y[1] (numeric) = -1.7881872820750981744682505623507
absolute error = 3e-31
relative error = 1.6776766226178816701221438196325e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.33
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.33
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.34
y[1] (closed_form) = -1.778891264680675182142944349545
y[1] (numeric) = -1.7788912646806751821429443495441
absolute error = 9e-31
relative error = 5.0593311568234441806262807017419e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.34
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.34
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.35
y[1] (closed_form) = -1.769591300956236578657720988114
y[1] (numeric) = -1.7695913009562365786577209881139
absolute error = 1e-31
relative error = 5.6510223544816736598061628179288e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.35
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.35
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.36
y[1] (closed_form) = -1.760287392458520123519801458436
y[1] (numeric) = -1.7602873924585201235198014584351
absolute error = 9e-31
relative error = 5.1128014883013362116109768676199e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.36
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.36
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.37
y[1] (closed_form) = -1.750979540743035864974117071174
y[1] (numeric) = -1.7509795407430358649741170711736
absolute error = 4e-31
relative error = 2.2844356012878268223622032540435e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.37
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.37
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.38
y[1] (closed_form) = -1.74166774736406759177081777896
y[1] (numeric) = -1.7416677473640675917708177789596
absolute error = 4e-31
relative error = 2.2966492926413848455367296214722e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.38
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.38
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.39
y[1] (closed_form) = -1.732352013874674282644730533332
y[1] (numeric) = -1.7323520138746742826447305333313
absolute error = 7e-31
relative error = 4.0407491918131656301562220038229e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.39
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.39
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.4
y[1] (closed_form) = -1.723032341826691553511273496934
y[1] (numeric) = -1.7230323418266915535112734969337
absolute error = 3e-31
relative error = 1.7411164765598753872424509582051e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.4
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.4
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.41
y[1] (closed_form) = -1.713708732770733102383321277309
y[1] (numeric) = -1.7137087327707331023833212773081
absolute error = 9e-31
relative error = 5.2517676008155444609283950494191e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.41
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.41
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.42
y[1] (closed_form) = -1.704381188256192152013505734285
y[1] (numeric) = -1.7043811882561921520135057342847
absolute error = 3e-31
relative error = 1.7601696267660625901076263470223e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.42
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.42
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.43
y[1] (closed_form) = -1.695049709831242890266426327889
y[1] (numeric) = -1.6950497098312428902664263278889
absolute error = 1e-31
relative error = 5.8995319972035439412740334978193e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.43
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.43
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.44
y[1] (closed_form) = -1.685714299042841908225233417718
y[1] (numeric) = -1.6857142990428419082252334177179
absolute error = 1e-31
relative error = 5.9322033429259373499619012887746e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.44
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.44
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.45
y[1] (closed_form) = -1.676374957436729636037037397824
y[1] (numeric) = -1.6763749574367296360370373978234
absolute error = 6e-31
relative error = 3.5791515337203158024490354484367e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.45
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.45
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.46
y[1] (closed_form) = -1.667031686557431776501586053181
y[1] (numeric) = -1.667031686557431776501586053181
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.46
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.46
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.47
y[1] (closed_form) = -1.657684487948260736407642054727
y[1] (numeric) = -1.6576844879482607364076420547262
absolute error = 8e-31
relative error = 4.8260088443620002938083210701571e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.47
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.47
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.48
y[1] (closed_form) = -1.648333363151317055621482069615
y[1] (numeric) = -1.648333363151317055621482069615
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.48
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.48
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.49
y[1] (closed_form) = -1.638978313707490833931928551723
y[1] (numeric) = -1.6389783137074908339319285517227
absolute error = 3e-31
relative error = 1.8304085996194646984441528740222e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.49
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.49
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.5
y[1] (closed_form) = -1.629619341156463155656314894346
y[1] (numeric) = -1.6296193411564631556563148943453
absolute error = 7e-31
relative error = 4.2954816644679939299477777113711e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.5
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.5
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.51
y[1] (closed_form) = -1.620256447036707512011774272521
y[1] (numeric) = -1.6202564470367075120117742725207
absolute error = 3e-31
relative error = 1.8515587489170063984220784546753e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.51
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.51
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.52
y[1] (closed_form) = -1.610889632885491221256232176251
y[1] (numeric) = -1.6108896328854912212562321762505
absolute error = 5e-31
relative error = 3.1038749632051427643708587873417e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.52
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.52
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.53
y[1] (closed_form) = -1.601518900238876846603472338096
y[1] (numeric) = -1.6015189002388768466034723380958
absolute error = 2e-31
relative error = 1.2488144846131301565800284599395e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.53
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.53
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.54
y[1] (closed_form) = -1.592144250631723611916635489042
y[1] (numeric) = -1.5921442506317236119166354890417
absolute error = 3e-31
relative error = 1.8842513791132140903864073450842e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.54
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.54
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.55
y[1] (closed_form) = -1.582765685597688815184500135099
y[1] (numeric) = -1.582765685597688815184500135099
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.55
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.55
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.56
y[1] (closed_form) = -1.573383206669229239784884333742
y[1] (numeric) = -1.573383206669229239784884333742
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.56
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.56
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.57
y[1] (closed_form) = -1.563996815377602563539497263882
y[1] (numeric) = -1.5639968153776025635394972638812
absolute error = 8e-31
relative error = 5.1150999294512790640679760114203e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.57
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.57
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.58
y[1] (closed_form) = -1.554606513252868765564559225556
y[1] (numeric) = -1.5546065132528687655645592255555
absolute error = 5e-31
relative error = 3.2162479427272998649613881449243e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.58
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.58
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.59
y[1] (closed_form) = -1.545212301823891530921498575809
y[1] (numeric) = -1.5452123018238915309214985758085
absolute error = 5e-31
relative error = 3.2358013161675255780046610635766e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.59
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.59
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.6
y[1] (closed_form) = -1.535814182618339653072024005205
y[1] (numeric) = -1.5358141826183396530720240052045
absolute error = 5e-31
relative error = 3.2556021793442014705160348537845e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.6
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.6
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.61
y[1] (closed_form) = -1.526412157162688434141860485052
y[1] (numeric) = -1.5264121571626884341418604850515
absolute error = 5e-31
relative error = 3.2756552524411588371487185087092e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.61
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.61
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.62
y[1] (closed_form) = -1.517006226982221082997427168548
y[1] (numeric) = -1.5170062269822210829974271685478
absolute error = 2e-31
relative error = 1.3183861505819906419860323346403e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.62
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.62
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.63
y[1] (closed_form) = -1.507596393601030111139725509671
y[1] (numeric) = -1.5075963936010301111397255096706
absolute error = 4e-31
relative error = 2.6532300136680738728762812362969e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.63
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.63
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.64
y[1] (closed_form) = -1.498182658542018726419695871585
y[1] (numeric) = -1.4981826585420187264196958715847
absolute error = 3e-31
relative error = 2.0024260612651195008849662100583e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.64
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.64
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.65
y[1] (closed_form) = -1.488765023326902224579290931598
y[1] (numeric) = -1.488765023326902224579290931598
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.65
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.65
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.66
y[1] (closed_form) = -1.479343489476209378622504252126
y[1] (numeric) = -1.4793434894762093786225042521258
absolute error = 2e-31
relative error = 1.3519510608777811880925217647919e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.66
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.66
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.67
y[1] (closed_form) = -1.469918058509283826020582476673
y[1] (numeric) = -1.4699180585092838260205824766729
absolute error = 1e-31
relative error = 6.8031003103271563761922120937650e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.67
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.67
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.68
y[1] (closed_form) = -1.460488731944285453755639726417
y[1] (numeric) = -1.460488731944285453755639726417
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.68
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.68
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.69
y[1] (closed_form) = -1.451055511298191781206882916489
y[1] (numeric) = -1.4510555112981917812068829164883
absolute error = 7e-31
relative error = 4.8240745757117355447566193197996e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.69
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.69
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.7
y[1] (closed_form) = -1.441618398086799340883646881412
y[1] (numeric) = -1.4416183980867993408836468814118
absolute error = 2e-31
relative error = 1.3873296863124389021842684049179e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.7
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.7
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.71
y[1] (closed_form) = -1.43217739382472505700942839632
y[1] (numeric) = -1.4321773938247250570094283963201
absolute error = 1e-31
relative error = 6.9823752582034090012458192688871e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.71
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.71
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.72
y[1] (closed_form) = -1.422732500025407621961098404382
y[1] (numeric) = -1.4227325000254076219610984043813
absolute error = 7e-31
relative error = 4.9201097183588564345502839318132e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.72
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.72
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.73
y[1] (closed_form) = -1.413283718201108870567462011324
y[1] (numeric) = -1.413283718201108870567462011324
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.73
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.73
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.74
y[1] (closed_form) = -1.403831049862915152271326084908
y[1] (numeric) = -1.4038310498629151522713260849075
absolute error = 5e-31
relative error = 3.5616821557610174358092693023879e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.74
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.74
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.75
y[1] (closed_form) = -1.394374496520738701159224600592
y[1] (numeric) = -1.3943744965207387011592246005921
absolute error = 1e-31
relative error = 7.1716744855504238534621921304928e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.75
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.75
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.76
y[1] (closed_form) = -1.38491405968331900386294220443
y[1] (numeric) = -1.3849140596833190038629422044299
absolute error = 1e-31
relative error = 7.2206646543011104064433570033127e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.76
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.76
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=269.1MB, alloc=44.3MB, time=3.05
x[1] = 23.77
y[1] (closed_form) = -1.375449740858224165336966820242
y[1] (numeric) = -1.3754497408582241653369668202415
absolute error = 5e-31
relative error = 3.6351746279585652392257833118350e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.77
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.77
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.78
y[1] (closed_form) = -1.365981541551852272515992510383
y[1] (numeric) = -1.365981541551852272515992510383
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.78
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.78
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.79
y[1] (closed_form) = -1.356509463269432755856584207765
y[1] (numeric) = -1.3565094632694327558565842077643
absolute error = 7e-31
relative error = 5.1603031084860521259963410565676e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.79
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.79
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.8
y[1] (closed_form) = -1.347033507515027748767106371168
y[1] (numeric) = -1.3470335075150277487671063711679
absolute error = 1e-31
relative error = 7.4237203040685594796558475145404e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.8
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.8
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.81
y[1] (closed_form) = -1.337553675791533444930008076261
y[1] (numeric) = -1.3375536757915334449300080762603
absolute error = 7e-31
relative error = 5.2334348345740676885904270470651e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.81
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.81
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.82
y[1] (closed_form) = -1.328069969600681453520547540903
y[1] (numeric) = -1.3280699696006814535205475409033
absolute error = 3e-31
relative error = 2.2589171268604375594122129292012e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.82
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.82
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.83
y[1] (closed_form) = -1.31858239044304015232602959538
y[1] (numeric) = -1.3185823904430401523260295953799
absolute error = 1e-31
relative error = 7.5839022820864661917096348820888e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.83
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.83
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.84
y[1] (closed_form) = -1.30909093981801603876962014587
y[1] (numeric) = -1.3090909398180160387696201458701
absolute error = 1e-31
relative error = 7.6388887095881629329501574855310e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.84
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.84
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.85
y[1] (closed_form) = -1.299595619223855078842792242866
y[1] (numeric) = -1.2995956192238550788427922428659
absolute error = 1e-31
relative error = 7.6947012225019681688886118497324e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.85
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.85
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.86
y[1] (closed_form) = -1.290096430157644053950448955122
y[1] (numeric) = -1.2900964301576440539504489551219
absolute error = 1e-31
relative error = 7.7513585544749119365046866741850e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.86
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.86
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.87
y[1] (closed_form) = -1.28059337411531190567275886412
y[1] (numeric) = -1.2805933741153119056727588641193
absolute error = 7e-31
relative error = 5.4662160069630972613623305520968e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.87
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.87
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.88
y[1] (closed_form) = -1.271086452591631078447730633802
y[1] (numeric) = -1.2710864525916310784477306338013
absolute error = 7e-31
relative error = 5.5070998402411015410609002490356e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.88
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.88
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.89
y[1] (closed_form) = -1.261575667080218860178543775431
y[1] (numeric) = -1.2615756670802188601785437754306
absolute error = 4e-31
relative error = 3.1706381982283865797639604398732e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.89
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.89
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.9
y[1] (closed_form) = -1.252061019073538720769643417757
y[1] (numeric) = -1.2520610190735387207696434177568
absolute error = 2e-31
relative error = 1.5973662381725596476254264836538e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.9
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.9
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.91
y[1] (closed_form) = -1.242542510062901648595597608177
y[1] (numeric) = -1.2425425100629016485955976081766
absolute error = 4e-31
relative error = 3.2192057556224025291520322849305e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.91
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.91
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.92
y[1] (closed_form) = -1.233020141538467484906706411149
y[1] (numeric) = -1.2330201415384674849067064111486
absolute error = 4e-31
relative error = 3.2440670393340925811049065010107e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.92
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.92
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.93
y[1] (closed_form) = -1.223493914989246256175342835712
y[1] (numeric) = -1.2234939149892462561753428357117
absolute error = 3e-31
relative error = 2.4519942136584864973629436061787e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.93
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.93
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.94
y[1] (closed_form) = -1.213963831903099504386996414471
y[1] (numeric) = -1.2139638319030995043869964144702
absolute error = 8e-31
relative error = 6.5899821640143991849782301943119e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.94
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.94
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.95
y[1] (closed_form) = -1.204429893766741615279981071775
y[1] (numeric) = -1.2044298937667416152799810717745
absolute error = 5e-31
relative error = 4.1513416645305677302371199060829e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.95
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.95
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.96
y[1] (closed_form) = -1.194892102065741144537759758972
y[1] (numeric) = -1.1948921020657411445377597589713
absolute error = 7e-31
relative error = 5.8582695357165149759365518278979e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.96
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.96
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.97
y[1] (closed_form) = -1.185350458284522141937829199436
y[1] (numeric) = -1.1853504582845221419378291994351
absolute error = 9e-31
relative error = 7.5926912054558899366040248321224e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.97
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.97
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.98
y[1] (closed_form) = -1.175804963906365473461098975562
y[1] (numeric) = -1.1758049639063654734610989755617
absolute error = 3e-31
relative error = 2.5514435574698791707894349749916e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.98
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.98
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 23.99
y[1] (closed_form) = -1.166255620413410141365690103912
y[1] (numeric) = -1.1662556204134101413656901039122
absolute error = 2e-31
relative error = 1.7148899134917327287449956293568e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 25.99
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.99
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24
y[1] (closed_form) = -1.156702429286654602229069183183
y[1] (numeric) = -1.1567024292866546022290691831823
absolute error = 7e-31
relative error = 6.0516860886312328574250987686677e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.01
y[1] (closed_form) = -1.147145392005958082962425162551
y[1] (numeric) = -1.1471453920059580829624251625509
absolute error = 1e-31
relative error = 8.7172908244119605530007358461807e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.01
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.01
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.02
y[1] (closed_form) = -1.137584510050041894801186765162
y[1] (numeric) = -1.137584510050041894801186765162
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.02
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.02
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.03
y[1] (closed_form) = -1.128019784896490745275569612945
y[1] (numeric) = -1.1280197848964907452755696129451
absolute error = 1e-31
relative error = 8.8650927349803701732596652837594e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.03
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.03
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.04
y[1] (closed_form) = -1.118451218021754048165033134595
y[1] (numeric) = -1.1184512180217540481650331345945
absolute error = 5e-31
relative error = 4.4704676604882996615356312613078e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.04
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.04
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.05
y[1] (closed_form) = -1.108878810901147231440518398251
y[1] (numeric) = -1.108878810901147231440518398251
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.05
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.05
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.06
y[1] (closed_form) = -1.099302565008853043198329094166
y[1] (numeric) = -1.0993025650088530431983290941658
absolute error = 2e-31
relative error = 1.8193353346572909576446157787157e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.06
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.06
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.07
y[1] (closed_form) = -1.089722481817922855589509000323
y[1] (numeric) = -1.0897224818179228555895090003224
absolute error = 6e-31
relative error = 5.5059890018883860694904951698500e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.07
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.07
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.08
y[1] (closed_form) = -1.080138562800277966748560395559
y[1] (numeric) = -1.0801385628002779667485603955584
absolute error = 6e-31
relative error = 5.5548428753852615791333593893176e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.08
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.08
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.09
y[1] (closed_form) = -1.0705508094267109007253390401
y[1] (numeric) = -1.0705508094267109007253390400993
absolute error = 7e-31
relative error = 6.5386901194802325814250215640122e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.09
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.09
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.1
y[1] (closed_form) = -1.060959223166886705423952522522
y[1] (numeric) = -1.060959223166886705423952522522
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.1
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.1
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.11
y[1] (closed_form) = -1.05136380548934424855247997492
y[1] (numeric) = -1.0513638054893442485524799749203
absolute error = 3e-31
relative error = 2.8534366356693125779865359345691e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.11
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.11
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.12
y[1] (closed_form) = -1.041764557861497511587322384394
y[1] (numeric) = -1.0417645578614975115873223843939
absolute error = 1e-31
relative error = 9.5990979195219453303485738667739e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.12
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.12
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.13
y[1] (closed_form) = -1.032161481749636881755983978836
y[1] (numeric) = -1.0321614817496368817559839788357
absolute error = 3e-31
relative error = 2.9065219474327234175978741387482e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.13
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.13
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.14
y[1] (closed_form) = -1.022554578618930442042076438293
y[1] (numeric) = -1.0225545786189304420420764382933
absolute error = 3e-31
relative error = 2.9338287292711764552057458543109e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.14
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.14
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.15
y[1] (closed_form) = -1.012943849933425259216328979846
y[1] (numeric) = -1.012943849933425259216328979846
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.15
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.15
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.16
y[1] (closed_form) = -1.003329297156048669897378683905
y[1] (numeric) = -1.0033292971560486698973786839051
absolute error = 1e-31
relative error = 9.9668175028329621133080527992170e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.16
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.16
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.17
y[1] (closed_form) = -0.993710921748609564646106773036
y[1] (numeric) = -0.993710921748609564646106773036
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.17
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.17
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.18
y[1] (closed_form) = -0.984088725171799670097277920747
y[1] (numeric) = -0.9840887251717996700972779207468
absolute error = 2.0e-31
relative error = 2.0323370737235559336459483311164e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.18
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.18
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.19
y[1] (closed_form) = -0.974462708885194829132231057121
y[1] (numeric) = -0.97446270888519482913223105712078
absolute error = 2.2e-31
relative error = 2.2576543770636895624080401143500e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.19
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.19
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.2
y[1] (closed_form) = -0.964832874347256279096361550615
y[1] (numeric) = -0.96483287434725627909636155061476
absolute error = 2.4e-31
relative error = 2.4874774313879854832144050404574e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.2
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.2
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.21
y[1] (closed_form) = -0.955199223015331928065126080735
y[1] (numeric) = -0.95519922301533192806512608073525
absolute error = 2.5e-31
relative error = 2.6172550602670166050667933555022e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.21
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.21
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.22
y[1] (closed_form) = -0.945561756345657629162292974567
y[1] (numeric) = -0.94556175634565762916229297456709
absolute error = 9e-32
relative error = 9.5181514476458778612013567055222e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.22
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.22
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.23
y[1] (closed_form) = -0.935920475793358452934152261197
y[1] (numeric) = -0.93592047579335845293415226119705
absolute error = 5e-32
relative error = 5.3423342359954396504398535711513e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.23
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.23
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.24
y[1] (closed_form) = -0.926275382812449957783391201876
y[1] (numeric) = -0.92627538281244995778339120187613
absolute error = 1.3e-31
relative error = 1.4034703114454040458520342938569e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.24
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.24
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.25
y[1] (closed_form) = -0.916626478855839458466332580232
y[1] (numeric) = -0.91662647885583945846633258023151
absolute error = 4.9e-31
relative error = 5.3456889071285899517661395094430e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.25
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.25
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.26
y[1] (closed_form) = -0.906973765375327292657224585902
y[1] (numeric) = -0.906973765375327292657224585902
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.26
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.26
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.27
y[1] (closed_form) = -0.897317243821608085583262696561
y[1] (numeric) = -0.89731724382160808558326269656108
absolute error = 8e-32
relative error = 8.9154644637481710689184375804912e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.27
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.27
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.28
y[1] (closed_form) = -0.887656915644272012734015557341
y[1] (numeric) = -0.88765691564427201273401555734052
absolute error = 4.8e-31
relative error = 5.4074946247854133533575091788142e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.28
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.28
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.29
y[1] (closed_form) = -0.877992782291806060648918473107
y[1] (numeric) = -0.87799278229180606064891847310682
absolute error = 1.8e-31
relative error = 2.0501307485711874820905115781434e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.29
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.29
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.3
y[1] (closed_form) = -0.868324845211595285786489767804
y[1] (numeric) = -0.86832484521159528578648976780402
absolute error = 2e-32
relative error = 2.3032854709030416520402583195380e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.3
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.3
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.31
y[1] (closed_form) = -0.858653105849924071478916926092
y[1] (numeric) = -0.85865310584992407147891692609198
absolute error = 2e-32
relative error = 2.3292293318153574054744427458430e-30 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.31
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.31
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.32
y[1] (closed_form) = -0.848977565651977382975651115712
y[1] (numeric) = -0.84897756565197738297565111571153
absolute error = 4.7e-31
relative error = 5.5360709047601357752567249340607e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.32
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.32
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.33
y[1] (closed_form) = -0.839298226061842020579640394329
y[1] (numeric) = -0.83929822606184202057964039432906
absolute error = 6e-32
relative error = 7.1488295979764193292618730128825e-30 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.33
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.33
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.34
y[1] (closed_form) = -0.829615088522507870879823631987
y[1] (numeric) = -0.82961508852250787087982363198649
absolute error = 5.1e-31
relative error = 6.1474291759601169040992304692897e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.34
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.34
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.35
y[1] (closed_form) = -0.819928154475869156083498929641
y[1] (numeric) = -0.81992815447586915608349892964081
absolute error = 1.9e-31
relative error = 2.3172762023455042003320081300869e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.35
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.35
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.36
y[1] (closed_form) = -0.810237425362725681452172085554
y[1] (numeric) = -0.81023742536272568145217208555375
absolute error = 2.5e-31
relative error = 3.0855153338304563602517144584872e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.36
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.36
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.37
y[1] (closed_form) = -0.80054290262278408084448245442
y[1] (numeric) = -0.80054290262278408084448245442033
absolute error = 3.3e-31
relative error = 4.1222025567753492736906292664173e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.37
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.37
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.38
y[1] (closed_form) = -0.790844587694659060369795359039
y[1] (numeric) = -0.79084458769465906036979535903862
absolute error = 3.8e-31
relative error = 4.8049895758623564507558473472214e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.38
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.38
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.39
y[1] (closed_form) = -0.781142482015874640156042050956
y[1] (numeric) = -0.78114248201587464015604205095587
absolute error = 1.3e-31
relative error = 1.6642290362254052429229998283992e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.39
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.39
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=313.3MB, alloc=44.3MB, time=3.53
TOP MAIN SOLVE Loop
x[1] = 24.4
y[1] (closed_form) = -0.771436587022865394235380074813
y[1] (numeric) = -0.77143658702286539423538007481263
absolute error = 3.7e-31
relative error = 4.7962464604888281424366467871888e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.4
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.4
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.41
y[1] (closed_form) = -0.761726904150977688551238770981
y[1] (numeric) = -0.76172690415097768855123877098073
absolute error = 2.7e-31
relative error = 3.5445774401383725986879959188348e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.41
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.41
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.42
y[1] (closed_form) = -0.752013434834470917090306552488
y[1] (numeric) = -0.75201343483447091709030655248768
absolute error = 3.2e-31
relative error = 4.2552431270119083608819533712960e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.42
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.42
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.43
y[1] (closed_form) = -0.742296180506518736143008515074
y[1] (numeric) = -0.74229618050651873614300851507423
absolute error = 2.3e-31
relative error = 3.0984936476846141302083070784462e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.43
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.43
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.44
y[1] (closed_form) = -0.732575142599210296696014883478
y[1] (numeric) = -0.73257514259921029669601488347826
absolute error = 2.6e-31
relative error = 3.5491239721499154712474673160203e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.44
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.44
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.45
y[1] (closed_form) = -0.722850322543551474960312762612
y[1] (numeric) = -0.72285032254355147496031276261215
absolute error = 1.5e-31
relative error = 2.0751183934204103965787004935749e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.45
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.45
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.46
y[1] (closed_form) = -0.713121721769466101038365649138
y[1] (numeric) = -0.7131217217694661010383656491382
absolute error = 2.0e-31
relative error = 2.8045702983740390477071478436831e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.46
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.46
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.47
y[1] (closed_form) = -0.703389341705797185733877166983
y[1] (numeric) = -0.70338934170579718573387716698253
absolute error = 4.7e-31
relative error = 6.6819323542804595173481757182582e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.47
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.47
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.48
y[1] (closed_form) = -0.693653183780308145507667519499
y[1] (numeric) = -0.69365318378030814550766751949888
absolute error = 1.2e-31
relative error = 1.7299711557008589632800782549524e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.48
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.48
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.49
y[1] (closed_form) = -0.683913249419684025583163201236
y[1] (numeric) = -0.68391324941968402558316320123548
absolute error = 5.2e-31
relative error = 7.6033034956002365458429013838646e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.49
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.49
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.5
y[1] (closed_form) = -0.674169540049532721204992583507
y[1] (numeric) = -0.67416954004953272120499258350718
absolute error = 1.8e-31
relative error = 2.6699515375134718113510496239768e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.5
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.5
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.51
y[1] (closed_form) = -0.664422057094386197054172080168
y[1] (numeric) = -0.66442205709438619705417208016807
absolute error = 7e-32
relative error = 1.0535472032057474065349255107612e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.51
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.51
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.52
y[1] (closed_form) = -0.654670801977701704823359713053
y[1] (numeric) = -0.65467080197770170482335971305327
absolute error = 2.7e-31
relative error = 4.1242102012851992999662881353142e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.52
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.52
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.53
y[1] (closed_form) = -0.64491577612186299895564503045
y[1] (numeric) = -0.64491577612186299895564503045012
absolute error = 1.2e-31
relative error = 1.8607080869010227660320413686081e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.53
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.53
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.54
y[1] (closed_form) = -0.635156980948181550550336486605
y[1] (numeric) = -0.63515698094818155055033648660493
absolute error = 7e-32
relative error = 1.1020897526073299698716136685334e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.54
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.54
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.55
y[1] (closed_form) = -0.62539441787689775943919956561
y[1] (numeric) = -0.62539441787689775943919956561013
absolute error = 1.3e-31
relative error = 2.0786882051382351408832457853699e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.55
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.55
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.56
y[1] (closed_form) = -0.615628088327182164436591128986
y[1] (numeric) = -0.61562808832718216443659112898538
absolute error = 6.2e-31
relative error = 1.0071015467872777372605838948314e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.56
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.56
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.57
y[1] (closed_form) = -0.605857993717136651766927682802
y[1] (numeric) = -0.60585799371713665176692768280224
absolute error = 2.4e-31
relative error = 3.9613243117833870790984723005798e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.57
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.57
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.58
y[1] (closed_form) = -0.596084135463795661672917497245
y[1] (numeric) = -0.5960841354637956616729174972446
absolute error = 4.0e-31
relative error = 6.7104621009376751652089765224639e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.58
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.58
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.59
y[1] (closed_form) = -0.586306514983127393207978768984
y[1] (numeric) = -0.58630651498312739320797876898363
absolute error = 3.7e-31
relative error = 6.3106922837220695551859678110962e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.59
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.59
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.6
y[1] (closed_form) = -0.576525133690035007216258294615
y[1] (numeric) = -0.57652513369003500721625829461508
absolute error = 8e-32
relative error = 1.3876238055392651846996952199615e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.6
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.6
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.61
y[1] (closed_form) = -0.566739992998357827503657421598
y[1] (numeric) = -0.56673999299835782750365742159756
absolute error = 4.4e-31
relative error = 7.7637012639987616626264080815505e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.61
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.61
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.62
y[1] (closed_form) = -0.556951094320872540203264361581
y[1] (numeric) = -0.55695109432087254020326436158133
absolute error = 3.3e-31
relative error = 5.9251162869585689080339074445777e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.62
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.62
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.63
y[1] (closed_form) = -0.547158439069294391338584289667
y[1] (numeric) = -0.54715843906929439133858428966753
absolute error = 5.3e-31
relative error = 9.6864082166313553620827339797772e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.63
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.63
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.64
y[1] (closed_form) = -0.537362028654278382587951011927
y[1] (numeric) = -0.53736202865427838258795101192689
absolute error = 1.1e-31
relative error = 2.0470370836486940752218097912708e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.64
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.64
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.65
y[1] (closed_form) = -0.527561864485420465253496362374
y[1] (numeric) = -0.52756186448542046525349636237426
absolute error = 2.6e-31
relative error = 4.9283319645100177386284112958209e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.65
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.65
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.66
y[1] (closed_form) = -0.517757947971258732438045889481
y[1] (numeric) = -0.51775794797125873243804588948083
absolute error = 1.7e-31
relative error = 3.2833875494546125636075486260138e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.66
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.66
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.67
y[1] (closed_form) = -0.507950280519274609433301811149
y[1] (numeric) = -0.50795028051927460943330181114899
absolute error = 1e-32
relative error = 1.9686966192393984544152622171386e-30 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.67
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.67
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.68
y[1] (closed_form) = -0.498138863535894042322666655816
y[1] (numeric) = -0.49813886353589404232266665581627
absolute error = 2.7e-31
relative error = 5.4201753720535558972688630168229e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.68
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.68
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.69
y[1] (closed_form) = -0.488323698426488684802053465935
y[1] (numeric) = -0.48832369842648868480205346593444
absolute error = 5.6e-31
relative error = 1.1467803053680822506522494157740e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.69
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.69
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.7
y[1] (closed_form) = -0.478504786595377083222020918429
y[1] (numeric) = -0.47850478659537708322202091842854
absolute error = 4.6e-31
relative error = 9.6132789657750131869261319977390e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.7
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.7
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.71
y[1] (closed_form) = -0.468682129445825859854564214819
y[1] (numeric) = -0.46868212944582585985456421481891
absolute error = 9e-32
relative error = 1.9202780380471694761969153125913e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.71
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.71
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.72
y[1] (closed_form) = -0.458855728380050894387885111428
y[1] (numeric) = -0.45885572838005089438788511142813
absolute error = 1.3e-31
relative error = 2.8331345117767924973534291090669e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.72
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.72
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.73
y[1] (closed_form) = -0.449025584799218503652456997436
y[1] (numeric) = -0.44902558479921850365245699743561
absolute error = 3.9e-31
relative error = 8.6854739062226987519629484913123e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.73
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.73
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.74
y[1] (closed_form) = -0.439191700103446619581693485426
y[1] (numeric) = -0.43919170010344661958169348542605
absolute error = 5e-32
relative error = 1.1384550297335552462131851869766e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.74
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.74
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.75
y[1] (closed_form) = -0.429354075691805965410521555447
y[1] (numeric) = -0.42935407569180596541052155544644
absolute error = 5.6e-31
relative error = 1.3042848122442717849948686575082e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.75
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.75
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.76
y[1] (closed_form) = -0.419512712962321230115152889381
y[1] (numeric) = -0.41951271296232123011515288938105
absolute error = 5e-32
relative error = 1.1918589939011163668033716047255e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.76
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.76
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.77
y[1] (closed_form) = -0.409667613311972241097339647616
y[1] (numeric) = -0.40966761331197224109733964761631
absolute error = 3.1e-31
relative error = 7.5671102602862375978640745245541e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.77
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.77
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.78
y[1] (closed_form) = -0.399818778136695135116393574442
y[1] (numeric) = -0.39981877813669513511639357444139
absolute error = 6.1e-31
relative error = 1.5256912215149770487496078861818e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.78
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.78
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.79
y[1] (closed_form) = -0.389966208831383527472239972356
y[1] (numeric) = -0.38996620883138352747223997235567
absolute error = 3.3e-31
relative error = 8.4622716667917204026927065927128e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.79
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.79
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.8
y[1] (closed_form) = -0.380109906789889679442770758376
y[1] (numeric) = -0.3801099067898896794427707583758
absolute error = 2.0e-31
relative error = 5.2616360801812093875847257121696e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.8
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.8
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.81
y[1] (closed_form) = -0.370249873405025663978753507494
y[1] (numeric) = -0.37024987340502566397875350749395
absolute error = 5e-32
relative error = 1.3504393543790287912660395585469e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.81
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.81
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.82
y[1] (closed_form) = -0.360386110068564529659546099579
y[1] (numeric) = -0.36038611006856452965954609957877
absolute error = 2.3e-31
relative error = 6.3820439682384489153901841106816e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.82
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.82
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.83
y[1] (closed_form) = -0.350518618171241462912859316174
y[1] (numeric) = -0.35051861817124146291285931617424
absolute error = 2.4e-31
relative error = 6.8469972080841371499627701550931e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.83
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.83
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.84
y[1] (closed_form) = -0.340647399102754948501802482783
y[1] (numeric) = -0.34064739910275494850180248278244
absolute error = 5.6e-31
relative error = 1.6439285944205263165378763922790e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.84
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.84
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.85
y[1] (closed_form) = -0.330772454251767928282440020258
y[1] (numeric) = -0.33077245425176792828244002025785
absolute error = 1.5e-31
relative error = 4.5348395270492289759457886987228e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.85
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.85
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.86
y[1] (closed_form) = -0.320893785005908958235079555837
y[1] (numeric) = -0.32089378500590895823507955583648
absolute error = 5.2e-31
relative error = 1.6204738897963532932373758425341e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.86
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.86
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.87
y[1] (closed_form) = -0.311011392751773363772505050017
y[1] (numeric) = -0.31101139275177336377250505001689
absolute error = 1.1e-31
relative error = 3.5368479278761979757599886073710e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.87
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.87
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.88
y[1] (closed_form) = -0.301125278874924393328361219946
y[1] (numeric) = -0.30112527887492439332836121994638
absolute error = 3.8e-31
relative error = 1.2619332439301353575953708156667e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.88
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.88
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.89
y[1] (closed_form) = -0.291235444759894370228888383088
y[1] (numeric) = -0.29123544475989437022888838308799
absolute error = 1e-32
relative error = 3.4336479916599375925887795852761e-30 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.89
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.89
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.9
y[1] (closed_form) = -0.281341891790185842851199706697
y[1] (numeric) = -0.28134189179018584285119970669683
absolute error = 1.7e-31
relative error = 6.0424702101164365320764756297352e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.9
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.9
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.91
y[1] (closed_form) = -0.271444621348272733071285728963
y[1] (numeric) = -0.27144462134827273307128572896321
absolute error = 2.1e-31
relative error = 7.7363846429125894387205763685465e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.91
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.91
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.92
y[1] (closed_form) = -0.261543634815601483004923916528
y[1] (numeric) = -0.26154363481560148300492391652833
absolute error = 3.3e-31
relative error = 1.2617397484464224810795363391853e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.92
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.92
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.93
y[1] (closed_form) = -0.251638933572592200044663940392
y[1] (numeric) = -0.25163893357259220004466394039239
absolute error = 3.9e-31
relative error = 1.5498396629768490460878146757534e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.93
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.93
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.94
y[1] (closed_form) = -0.241730518998639800196052287959
y[1] (numeric) = -0.24173051899863980019605228795872
absolute error = 2.8e-31
relative error = 1.1583146437607058600298337837313e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.94
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.94
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.95
y[1] (closed_form) = -0.231818392472115149716252783038
y[1] (numeric) = -0.2318183924721151497162527830374
absolute error = 6.0e-31
relative error = 2.5882329421819819067730233370788e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.95
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.95
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.96
y[1] (closed_form) = -0.221902555370366205058212558012
y[1] (numeric) = -0.22190255537036620505821255801229
absolute error = 2.9e-31
relative error = 1.3068799478941368351156388165337e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.96
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.96
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.97
y[1] (closed_form) = -0.211983009069719151123516013003
y[1] (numeric) = -0.2119830090697191511235160130032
absolute error = 2.0e-31
relative error = 9.4347184181267067531756952838123e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.97
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.97
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.98
y[1] (closed_form) = -0.202059754945479537827062305675
y[1] (numeric) = -0.20205975494547953782706230567483
absolute error = 1.7e-31
relative error = 8.4133527750674540891165858761208e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.98
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.98
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 24.99
y[1] (closed_form) = -0.192132794371933414976694942303
y[1] (numeric) = -0.19213279437193341497669494230307
absolute error = 7e-32
relative error = 3.6433134816377571386581554910198e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 26.99
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.99
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25
y[1] (closed_form) = -0.182202128722348465470905085753
y[1] (numeric) = -0.1822021287223484654709050857532
absolute error = 2.0e-31
relative error = 1.0976820161348010165392646165194e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.01
y[1] (closed_form) = -0.1722677593689751368177232591
y[1] (numeric) = -0.17226775936897513681772325909956
absolute error = 4.4e-31
relative error = 2.5541633652851850405686323436540e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.01
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.01
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=357.3MB, alloc=44.3MB, time=4.03
TOP MAIN SOLVE Loop
x[1] = 25.02
y[1] (closed_form) = -0.16232968768304777097790720467
y[1] (numeric) = -0.16232968768304777097790720466962
absolute error = 3.8e-31
relative error = 2.3409149948095645052686373445715e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.02
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.02
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.03
y[1] (closed_form) = -0.152387915034785732535526757273
y[1] (numeric) = -0.15238791503478573253552675727314
absolute error = 1.4e-31
relative error = 9.1870802201107659008314314686706e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.03
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.03
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.04
y[1] (closed_form) = -0.142442442793394535199039707227
y[1] (numeric) = -0.14244244279339453519903970722677
absolute error = 2.3e-31
relative error = 1.6146872764152410335448088605287e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.04
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.04
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.05
y[1] (closed_form) = -0.132493272327066966635945763453
y[1] (numeric) = -0.13249327232706696663594576345295
absolute error = 5e-32
relative error = 3.7737765187482301837262879780241e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.05
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.05
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.06
y[1] (closed_form) = -0.122540405002984211644098879366
y[1] (numeric) = -0.12254040500298421164409887936619
absolute error = 1.9e-31
relative error = 1.5505089933020292613518622932837e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.06
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.06
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.07
y[1] (closed_form) = -0.112583842187316973662751374408
y[1] (numeric) = -0.11258384218731697366275137440834
absolute error = 3.4e-31
relative error = 3.0199715464880659283615176018497e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.07
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.07
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.08
y[1] (closed_form) = -0.102623585245226594626396471904
y[1] (numeric) = -0.1026235852452265946263964719034
absolute error = 6.0e-31
relative error = 5.8466092230772870594364375958716e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.08
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.08
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.09
y[1] (closed_form) = -0.092659635540866173164469079321
y[1] (numeric) = -0.092659635540866173164469079321062
absolute error = 6.2e-32
relative error = 6.6911551764798178370520581401701e-29 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.09
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.09
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.1
y[1] (closed_form) = -0.082691994437381681149957860014
y[1] (numeric) = -0.08269199443738168114995786001364
absolute error = 3.60e-31
relative error = 4.3535048640362539047408210912199e-28 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.1
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.1
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.11
y[1] (closed_form) = -0.072720663296913078599974885972
y[1] (numeric) = -0.072720663296913078599974885971574
absolute error = 4.26e-31
relative error = 5.8580323760342170243051123332326e-28 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.11
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.11
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.12
y[1] (closed_form) = -0.062745643480595426931322419077
y[1] (numeric) = -0.062745643480595426931322419077182
absolute error = 1.82e-31
relative error = 2.9005997851673144522658317620730e-28 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.12
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.12
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.13
y[1] (closed_form) = -0.052766936348560000574089643673
y[1] (numeric) = -0.052766936348560000574089643672549
absolute error = 4.51e-31
relative error = 8.5470188570519065628376155542929e-28 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.13
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.13
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.14
y[1] (closed_form) = -0.042784543259935396946305465945
y[1] (numeric) = -0.042784543259935396946305465944666
absolute error = 3.34e-31
relative error = 7.8065575684844725267207696163671e-28 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.14
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.14
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.15
y[1] (closed_form) = -0.032798465572848644792666805618
y[1] (numeric) = -0.032798465572848644792666805617665
absolute error = 3.35e-31
relative error = 1.0213892453472610683767315776639e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.15
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.15
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.16
y[1] (closed_form) = -0.022808704644426310890355132678
y[1] (numeric) = -0.022808704644426310890355132677443
absolute error = 5.57e-31
relative error = 2.4420501237719884360059365435532e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.16
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.16
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.17
y[1] (closed_form) = -0.012815261830795605124947346287
y[1] (numeric) = -0.012815261830795605124947346287236
absolute error = 2.36e-31
relative error = 1.8415542586331105803058638246352e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.17
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.17
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.18
y[1] (closed_form) = -0.002818138487085483939420454633
y[1] (numeric) = -0.0028181384870854839394204546332151
absolute error = 2.151e-31
relative error = 7.6326980020934389610692043163178e-27 %
Desired digits = 8
Estimated correct digits = 9
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.18
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.18
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.19
y[1] (closed_form) = 0.007182664032572247840757106883
y[1] (numeric) = 0.0071826640325722478407571068836212
absolute error = 6.212e-31
relative error = 8.6486016495127161170411256279011e-27 %
Desired digits = 8
Estimated correct digits = 9
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.19
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.19
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.2
y[1] (closed_form) = 0.017187144375041836803461285969
y[1] (numeric) = 0.01718714437504183680346128596928
absolute error = 2.80e-31
relative error = 1.6291246171562949143829537035474e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.2
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.2
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.21
y[1] (closed_form) = 0.027195301188182482363695706411
y[1] (numeric) = 0.027195301188182482363695706412396
absolute error = 1.396e-30
relative error = 5.1332397105666971179197489704586e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.21
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.21
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.22
y[1] (closed_form) = 0.037207133120847239792349368186
y[1] (numeric) = 0.037207133120847239792349368187404
absolute error = 1.404e-30
relative error = 3.7734699834030901565690152286736e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.22
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.22
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.23
y[1] (closed_form) = 0.047222638822881924856962232597
y[1] (numeric) = 0.047222638822881924856962232596173
absolute error = 8.27e-31
relative error = 1.7512786676361544862153822813727e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.23
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.23
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.24
y[1] (closed_form) = 0.05724181694512402007153870695
y[1] (numeric) = 0.057241816945124020071538706949316
absolute error = 6.84e-31
relative error = 1.1949306232814550400993886945776e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.24
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.24
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.25
y[1] (closed_form) = 0.067264666139401582552455563082
y[1] (numeric) = 0.067264666139401582552455563081237
absolute error = 7.63e-31
relative error = 1.1343251127103386517846719899721e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.25
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.25
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.26
y[1] (closed_form) = 0.077291185058532153477517327039
y[1] (numeric) = 0.077291185058532153477517327037794
absolute error = 1.206e-30
relative error = 1.5603331726466651955534625577493e-27 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.26
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.26
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.27
y[1] (closed_form) = 0.087321372356321669145218663622
y[1] (numeric) = 0.087321372356321669145218663621247
absolute error = 7.53e-31
relative error = 8.6233184348881369123463205318263e-28 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.27
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.27
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.28
y[1] (closed_form) = 0.097355226687563373631279749172
y[1] (numeric) = 0.097355226687563373631279749173076
absolute error = 1.076e-30
relative error = 1.1052308505768734770950664956081e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.28
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.28
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.29
y[1] (closed_form) = 0.10739274670803673303952707907
y[1] (numeric) = 0.10739274670803673303952707906998
absolute error = 2e-32
relative error = 1.8623231654902165369947477147799e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.29
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.29
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.3
y[1] (closed_form) = 0.117433931074506351344198592951
y[1] (numeric) = 0.1174339310745063513441985929507
absolute error = 3.0e-31
relative error = 2.5546279278487577330098780662595e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.3
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.3
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.31
y[1] (closed_form) = 0.127478778444720887820758420728
y[1] (numeric) = 0.12747877844472088782075842072952
absolute error = 1.52e-30
relative error = 1.1923553226226774963706980777355e-27 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.31
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.31
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.32
y[1] (closed_form) = 0.137527287477411976062312956035
y[1] (numeric) = 0.1375272874774119760623129560352
absolute error = 2.0e-31
relative error = 1.4542568509020349038711357034772e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.32
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.32
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.33
y[1] (closed_form) = 0.147579456832293144578726350889
y[1] (numeric) = 0.14757945683229314457872635088925
absolute error = 2.5e-31
relative error = 1.6940027112587619005829432840134e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.33
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.33
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.34
y[1] (closed_form) = 0.157635285170058738975539896254
y[1] (numeric) = 0.15763528517005873897553989625335
absolute error = 6.5e-31
relative error = 4.1234422819660750782442310262071e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.34
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.34
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.35
y[1] (closed_form) = 0.167694771152382845709806107581
y[1] (numeric) = 0.16769477115238284570980610758021
absolute error = 7.9e-31
relative error = 4.7109399689161062843664826954071e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.35
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.35
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.36
y[1] (closed_form) = 0.177757913441918217419954672742
y[1] (numeric) = 0.17775791344191821741995467274255
absolute error = 5.5e-31
relative error = 3.0940957246311883333389625904853e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.36
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.36
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.37
y[1] (closed_form) = 0.187824710702295199826813741739
y[1] (numeric) = 0.18782471070229519982681374173927
absolute error = 2.7e-31
relative error = 1.4375105330413833885038455021292e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.37
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.37
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.38
y[1] (closed_form) = 0.197895161598120660202916343434
y[1] (numeric) = 0.19789516159812066020291634343329
absolute error = 7.1e-31
relative error = 3.5877582567776261229939927813148e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.38
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.38
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.39
y[1] (closed_form) = 0.207969264794976917407228004308
y[1] (numeric) = 0.20796926479497691740722800430935
absolute error = 1.35e-30
relative error = 6.4913438114563482175805845439396e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.39
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.39
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.4
y[1] (closed_form) = 0.218047018959420673482437917899
y[1] (numeric) = 0.21804701895942067348243791789924
absolute error = 2.4e-31
relative error = 1.1006800328908181700298204144599e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.4
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.4
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.41
y[1] (closed_form) = 0.228128422758981946811962271154
y[1] (numeric) = 0.2281284227589819468119622711538
absolute error = 2.0e-31
relative error = 8.7669917488230008218524787547433e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.41
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.41
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.42
y[1] (closed_form) = 0.238213474862163006833814575692
y[1] (numeric) = 0.23821347486216300683381457569163
absolute error = 3.7e-31
relative error = 1.5532286753051747820040936632313e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.42
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.42
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.43
y[1] (closed_form) = 0.248302173938437310308504077571
y[1] (numeric) = 0.24830217393843731030850407757131
absolute error = 3.1e-31
relative error = 1.2484787993715258929312501428459e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.43
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.43
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.44
y[1] (closed_form) = 0.258394518658248439138129529063
y[1] (numeric) = 0.25839451865824843913812952906283
absolute error = 1.7e-31
relative error = 6.5790869281109373172417849555703e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.44
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.44
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.45
y[1] (closed_form) = 0.268490507693009039733841799882
y[1] (numeric) = 0.26849050769300903973384179988129
absolute error = 7.1e-31
relative error = 2.6444137861730706977482351567701e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.45
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.45
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.46
y[1] (closed_form) = 0.278590139715099763928854983539
y[1] (numeric) = 0.27859013971509976392885498353844
absolute error = 5.6e-31
relative error = 2.0101213940044111384685611560257e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.46
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.46
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.47
y[1] (closed_form) = 0.28869341339786821143419181691
y[1] (numeric) = 0.28869341339786821143419181691065
absolute error = 6.5e-31
relative error = 2.2515234842029124451762513612546e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.47
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.47
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.48
y[1] (closed_form) = 0.298800327415627873834355377862
y[1] (numeric) = 0.29880032741562787383435537786153
absolute error = 4.7e-31
relative error = 1.5729567770728554761985550514340e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.48
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.48
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.49
y[1] (closed_form) = 0.30891088044365708012012515684
y[1] (numeric) = 0.30891088044365708012012515683961
absolute error = 3.9e-31
relative error = 1.2625000435073148509564108549599e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.49
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.49
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.5
y[1] (closed_form) = 0.319025071158197943755681713842
y[1] (numeric) = 0.31902507115819794375568171384139
absolute error = 6.1e-31
relative error = 1.9120754296376713249773361022612e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.5
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.5
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.51
y[1] (closed_form) = 0.329142898236455311277270232033
y[1] (numeric) = 0.32914289823645531127727023203368
absolute error = 6.8e-31
relative error = 2.0659719642849166263793928817794e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.51
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.51
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.52
y[1] (closed_form) = 0.33926436035659571242061936371
y[1] (numeric) = 0.33926436035659571242061936371076
absolute error = 7.6e-31
relative error = 2.2401409897614218240707464726888e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.52
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.52
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.53
y[1] (closed_form) = 0.349389456197746311774337833167
y[1] (numeric) = 0.34938945619774631177433783316796
absolute error = 9.6e-31
relative error = 2.7476501736694146606151573032986e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.53
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.53
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.54
y[1] (closed_form) = 0.359518184439993861956517314547
y[1] (numeric) = 0.35951818443999386195651731454739
absolute error = 3.9e-31
relative error = 1.0847851843919560333731840281517e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.54
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.54
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.55
y[1] (closed_form) = 0.369650543764383658311776140801
y[1] (numeric) = 0.36965054376438365831177614079984
absolute error = 1.16e-30
relative error = 3.1380989953024048711494481808103e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.55
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.55
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.56
y[1] (closed_form) = 0.379786532852918495125984422651
y[1] (numeric) = 0.37978653285291849512598442265252
absolute error = 1.52e-30
relative error = 4.0022482855879902953897801400071e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.56
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.56
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.57
y[1] (closed_form) = 0.389926150388557623355917163922
y[1] (numeric) = 0.38992615038855762335591716392184
absolute error = 1.6e-31
relative error = 4.1033411029386347471784496623493e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.57
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.57
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.58
y[1] (closed_form) = 0.400069395055215709871087951706
y[1] (numeric) = 0.40006939505521570987108795170603
absolute error = 3e-32
relative error = 7.4986990684102541955953963930652e-30 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.58
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.58
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.59
y[1] (closed_form) = 0.41021626553776179820502177698
y[1] (numeric) = 0.41021626553776179820502177697999
absolute error = 1e-32
relative error = 2.4377385394240214719073970450955e-30 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.59
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.59
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.6
y[1] (closed_form) = 0.420366760522018270813231502936
y[1] (numeric) = 0.42036676052201827081323150293761
absolute error = 1.61e-30
relative error = 3.8299888364167420144726756152208e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.6
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.6
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.61
y[1] (closed_form) = 0.430520878694759812835168445129
y[1] (numeric) = 0.43052087869475981283516844512925
absolute error = 2.5e-31
relative error = 5.8069193010555595709105477279716e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.61
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.61
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.62
y[1] (closed_form) = 0.440678618743712377357423459068
y[1] (numeric) = 0.44067861874371237735742345906754
absolute error = 4.6e-31
relative error = 1.0438446079171461980354391315426e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.62
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.62
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.63
y[1] (closed_form) = 0.450839979357552152175460847568
y[1] (numeric) = 0.45083997935755215217546084756713
absolute error = 8.7e-31
relative error = 1.9297312568414001190344753849842e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.63
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.63
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=401.5MB, alloc=44.3MB, time=4.51
TOP MAIN SOLVE Loop
x[1] = 25.64
y[1] (closed_form) = 0.461004959225904528051173301687
y[1] (numeric) = 0.46100495922590452805117330168705
absolute error = 5e-32
relative error = 1.0845870309932758849846574875693e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.64
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.64
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.65
y[1] (closed_form) = 0.471173557039343068463551975801
y[1] (numeric) = 0.47117355703934306846355197580106
absolute error = 6e-32
relative error = 1.2734161139477950428494899503492e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.65
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.65
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.66
y[1] (closed_form) = 0.481345771489388480849771669074
y[1] (numeric) = 0.48134577148938848084977166907514
absolute error = 1.14e-30
relative error = 2.3683598517394099429028944512435e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.66
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.66
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.67
y[1] (closed_form) = 0.491521601268507589333996942526
y[1] (numeric) = 0.49152160126850758933399694252535
absolute error = 6.5e-31
relative error = 1.3224240772378976258738560109133e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.67
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.67
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.68
y[1] (closed_form) = 0.501701045070112308941220842906
y[1] (numeric) = 0.5017010450701123089412208429064
absolute error = 4.0e-31
relative error = 7.9728755586726020984876318062900e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.68
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.68
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.69
y[1] (closed_form) = 0.511884101588558621293453731985
y[1] (numeric) = 0.51188410158855862129345373198423
absolute error = 7.7e-31
relative error = 1.5042467574406312775000482797723e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.69
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.69
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.7
y[1] (closed_form) = 0.522070769519145551785585532318
y[1] (numeric) = 0.52207076951914555178558553231798
absolute error = 2e-32
relative error = 3.8308982551199035077777757700573e-30 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.7
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.7
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.71
y[1] (closed_form) = 0.53226104755811414823825049856
y[1] (numeric) = 0.53226104755811414823825049855916
absolute error = 8.4e-31
relative error = 1.5781729733064597816237301287588e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.71
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.71
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.72
y[1] (closed_form) = 0.542454934402646461025029406512
y[1] (numeric) = 0.54245493440264646102502940651277
absolute error = 7.7e-31
relative error = 1.4194727546315475468164097493724e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.72
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.72
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.73
y[1] (closed_form) = 0.552652428750864524671329820838
y[1] (numeric) = 0.55265242875086452467132982083738
absolute error = 6.2e-31
relative error = 1.1218624360366210048004030744488e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.73
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.73
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.74
y[1] (closed_form) = 0.562853529301829340922290856332
y[1] (numeric) = 0.5628535293018293409222908563313
absolute error = 7.0e-31
relative error = 1.2436628066777672717245823233395e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.74
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.74
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.75
y[1] (closed_form) = 0.573058234755539863277064587304
y[1] (numeric) = 0.57305823475553986327706458730288
absolute error = 1.12e-30
relative error = 1.9544261509090420523598353311176e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.75
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.75
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.76
y[1] (closed_form) = 0.583266543812931982986831984595
y[1] (numeric) = 0.58326654381293198298683198459459
absolute error = 4.1e-31
relative error = 7.0293762662906506068594582198891e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.76
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.76
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.77
y[1] (closed_form) = 0.593478455175877516513916970467
y[1] (numeric) = 0.59347845517587751651391697046682
absolute error = 1.8e-31
relative error = 3.0329660399661340110816776107216e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.77
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.77
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.78
y[1] (closed_form) = 0.603693967547183194449367877787
y[1] (numeric) = 0.603693967547183194449367877788
absolute error = 1.00e-30
relative error = 1.6564684322803714745757761216788e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.78
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.78
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.79
y[1] (closed_form) = 0.613913079630589651886381281864
y[1] (numeric) = 0.61391307963058965188638128186548
absolute error = 1.48e-30
relative error = 2.4107647305552789954148881228373e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.79
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.79
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.8
y[1] (closed_form) = 0.624135790130770420246948840827
y[1] (numeric) = 0.62413579013077042024694884082682
absolute error = 1.8e-31
relative error = 2.8839877931417131267280596301370e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.8
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.8
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.81
y[1] (closed_form) = 0.634362097753330920559113433765
y[1] (numeric) = 0.63436209775333092055911343376605
absolute error = 1.05e-30
relative error = 1.6552060782299262772189393781871e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.81
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.81
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.82
y[1] (closed_form) = 0.644592001204807458182226524945
y[1] (numeric) = 0.64459200120480745818222652494421
absolute error = 7.9e-31
relative error = 1.2255814507834573303520633463551e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.82
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.82
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.83
y[1] (closed_form) = 0.65482549919266621897760430722
y[1] (numeric) = 0.65482549919266621897760430721934
absolute error = 6.6e-31
relative error = 1.0079021064599857801945365766289e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.83
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.83
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.84
y[1] (closed_form) = 0.665062590425302266921985788618
y[1] (numeric) = 0.66506259042530226692198578861887
absolute error = 8.7e-31
relative error = 1.3081475526140207050359114588775e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.84
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.84
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.85
y[1] (closed_form) = 0.675303273612038543161201582599
y[1] (numeric) = 0.67530327361203854316120158259792
absolute error = 1.08e-30
relative error = 1.5992814520553613694380918112596e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.85
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.85
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.86
y[1] (closed_form) = 0.68554754746312486650146774509
y[1] (numeric) = 0.68554754746312486650146774509012
absolute error = 1.2e-31
relative error = 1.7504256334088149865508824303350e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.86
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.86
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.87
y[1] (closed_form) = 0.695795410689736935335724569994
y[1] (numeric) = 0.69579541068973693533572456999461
absolute error = 6.1e-31
relative error = 8.7669448609227162325918270145861e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.87
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.87
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.88
y[1] (closed_form) = 0.706046862003975331002445809294
y[1] (numeric) = 0.70604686200397533100244580929344
absolute error = 5.6e-31
relative error = 7.9314848650491838349400386734926e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.88
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.88
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.89
y[1] (closed_form) = 0.716301900118864522574349324597
y[1] (numeric) = 0.71630190011886452257434932459797
absolute error = 9.7e-31
relative error = 1.3541776167828625389660907878794e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.89
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.89
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.9
y[1] (closed_form) = 0.726560523748351873074445703622
y[1] (numeric) = 0.72656052374835187307444570362122
absolute error = 7.8e-31
relative error = 1.0735513071587648981669469229535e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.9
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.9
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.91
y[1] (closed_form) = 0.736822731607306647116866887905
y[1] (numeric) = 0.73682273160730664711686688790504
absolute error = 4e-32
relative error = 5.4287141647684940958188264548352e-30 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.91
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.91
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.92
y[1] (closed_form) = 0.747088522411519019969922357137
y[1] (numeric) = 0.74708852241151901996992235713659
absolute error = 4.1e-31
relative error = 5.4879708053413188866558371675553e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.92
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.92
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.93
y[1] (closed_form) = 0.757357894877699088038835900606
y[1] (numeric) = 0.75735789487769908803883590060709
absolute error = 1.09e-30
relative error = 1.4392138873471665214894611466541e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.93
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.93
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.94
y[1] (closed_form) = 0.767630847723475880765621477837
y[1] (numeric) = 0.76763084772347588076562147783702
absolute error = 2e-32
relative error = 2.6054190056734942415711428691401e-30 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.94
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.94
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.95
y[1] (closed_form) = 0.777907379667396373943562128156
y[1] (numeric) = 0.77790737966739637394356212815514
absolute error = 8.6e-31
relative error = 1.1055300701321323240825601558369e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.95
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.95
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.96
y[1] (closed_form) = 0.788187489428924504443761333113
y[1] (numeric) = 0.78818748942892450444376133311273
absolute error = 2.7e-31
relative error = 3.4255808880654339023066044915793e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.96
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.96
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.97
y[1] (closed_form) = 0.798471175728440186351241666078
y[1] (numeric) = 0.79847117572844018635124166607942
absolute error = 1.42e-30
relative error = 1.7783985736298408162552597878116e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.97
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.97
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.98
y[1] (closed_form) = 0.808758437287238328508070980239
y[1] (numeric) = 0.8087584372872383285080709802405
absolute error = 1.50e-30
relative error = 1.8546947158058031979939510101304e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.98
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.98
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 25.99
y[1] (closed_form) = 0.819049272827527853461001789537
y[1] (numeric) = 0.81904927282752785346100178953776
absolute error = 7.6e-31
relative error = 9.2790510316470030604288985592608e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 27.99
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.99
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26
y[1] (closed_form) = 0.829343681072430717811114886906
y[1] (numeric) = 0.82934368107243071781111488690478
absolute error = 1.22e-30
relative error = 1.4710427387864203410972527806917e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.01
y[1] (closed_form) = 0.839641660745980933962963620481
y[1] (numeric) = 0.83964166074598093396296362048183
absolute error = 8.3e-31
relative error = 9.8851693383411348891409569506151e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.01
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.01
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.02
y[1] (closed_form) = 0.849943210573123593270720611394
y[1] (numeric) = 0.8499432105731235932707206113939
absolute error = 1.0e-31
relative error = 1.1765491947699563337104248414756e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.02
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.02
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.03
y[1] (closed_form) = 0.860248329279713890578834046175
y[1] (numeric) = 0.860248329279713890578834046176
absolute error = 1.00e-30
relative error = 1.1624550329987856100758119130069e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.03
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.03
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.04
y[1] (closed_form) = 0.870557015592516150154706013072
y[1] (numeric) = 0.87055701559251615015470601307102
absolute error = 9.8e-31
relative error = 1.1257160443799250336482816587227e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.04
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.04
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.05
y[1] (closed_form) = 0.880869268239202853010910674246
y[1] (numeric) = 0.8808692682392028530109106742453
absolute error = 7.0e-31
relative error = 7.9466956702809249597516343711948e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.05
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.05
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.06
y[1] (closed_form) = 0.891185085948353665614475375504
y[1] (numeric) = 0.89118508594835366561447537550357
absolute error = 4.3e-31
relative error = 4.8250358626953003291023541210523e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.06
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.06
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.07
y[1] (closed_form) = 0.901504467449454469980753091375
y[1] (numeric) = 0.90150446744945446998075309137605
absolute error = 1.05e-30
relative error = 1.1647196857167780744673960598327e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.07
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.07
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.08
y[1] (closed_form) = 0.911827411472896395149419886533
y[1] (numeric) = 0.91182741147289639514941988653373
absolute error = 7.3e-31
relative error = 8.0059010160794982610727058056307e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.08
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.08
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.09
y[1] (closed_form) = 0.9221539167499748500401363444
y[1] (numeric) = 0.92215391674997485004013634440116
absolute error = 1.16e-30
relative error = 1.2579244949566404764181246630802e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.09
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.09
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.1
y[1] (closed_form) = 0.932483982012888557685417170616
y[1] (numeric) = 0.93248398201288855768541717061693
absolute error = 9.3e-31
relative error = 9.9733616656070964582588343735461e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.1
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.1
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.11
y[1] (closed_form) = 0.942817605994738590838258422678
y[1] (numeric) = 0.94281760599473859083825842267722
absolute error = 7.8e-31
relative error = 8.2730741878440569005747761566695e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.11
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.11
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.12
y[1] (closed_form) = 0.953154787429527408952077047727
y[1] (numeric) = 0.95315478742952740895207704772569
absolute error = 1.31e-30
relative error = 1.3743832767527869659949680189183e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.12
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.12
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.13
y[1] (closed_form) = 0.96349552505215789653052262806
y[1] (numeric) = 0.96349552505215789653052262805959
absolute error = 4.1e-31
relative error = 4.2553389127344939908125547376514e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.13
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.13
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.14
y[1] (closed_form) = 0.973839817598432402844726438545
y[1] (numeric) = 0.97383981759843240284472643854524
absolute error = 2.4e-31
relative error = 2.4644710111757329091021685868567e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.14
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.14
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.15
y[1] (closed_form) = 0.984187663805051783015558111811
y[1] (numeric) = 0.9841876638050517830155581118121
absolute error = 1.10e-30
relative error = 1.1176730215731380704719917319504e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.15
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.15
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.16
y[1] (closed_form) = 0.99453906240961444045846538586
y[1] (numeric) = 0.99453906240961444045846538586103
absolute error = 1.03e-30
relative error = 1.0356556508745560866259579161023e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.16
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.16
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.17
y[1] (closed_form) = 1.004894012150615370688477574616
y[1] (numeric) = 1.0048940121506153706884775746152
absolute error = 8e-31
relative error = 7.9610385804557319057239925488799e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.17
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.17
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.18
y[1] (closed_form) = 1.015252511767445206482958554998
y[1] (numeric) = 1.0152525117674452064829585549978
absolute error = 2e-31
relative error = 1.9699532646496146514324633705851e-29 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.18
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.18
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.19
y[1] (closed_form) = 1.025614560000389264399700204379
y[1] (numeric) = 1.0256145600003892643997002043776
absolute error = 1.4e-30
relative error = 1.3650352233683857221988013420318e-28 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.19
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.19
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.2
y[1] (closed_form) = 1.035980155590626592647952349712
y[1] (numeric) = 1.0359801555906265926479523497131
absolute error = 1.1e-30
relative error = 1.0617964003112345429032994653406e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.2
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.2
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.21
y[1] (closed_form) = 1.046349297280229020309990404493
y[1] (numeric) = 1.0463492972802290203099904044921
absolute error = 9e-31
relative error = 8.6013342039734333024182397960351e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.21
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.21
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.22
y[1] (closed_form) = 1.056721983812160207910826971634
y[1] (numeric) = 1.0567219838121602079108269716337
absolute error = 3e-31
relative error = 2.8389680975287357863727313416301e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.22
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.22
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.23
y[1] (closed_form) = 1.067098213930274699333678779937
y[1] (numeric) = 1.0670982139302746993336787799386
absolute error = 1.6e-30
relative error = 1.4993933820833343221984370581279e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.23
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.23
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.24
y[1] (closed_form) = 1.077477986379316975078805398465
y[1] (numeric) = 1.0774779863793169750788053984658
absolute error = 8e-31
relative error = 7.4247456571086436438953398780947e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.24
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.24
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.25
y[1] (closed_form) = 1.087861299904920506863341237432
y[1] (numeric) = 1.0878612999049205068633412374325
absolute error = 5e-31
relative error = 4.5961741634131133351513887286704e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.25
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.25
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=445.6MB, alloc=44.3MB, time=5.00
x[1] = 26.26
y[1] (closed_form) = 1.098248153253606813559747395891
y[1] (numeric) = 1.0982481532536068135597473958912
absolute error = 2e-31
relative error = 1.8210820515153292351444998023045e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.26
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.26
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.27
y[1] (closed_form) = 1.108638545172784518470514955594
y[1] (numeric) = 1.1086385451727845184705149555941
absolute error = 1e-31
relative error = 9.0200724515143672231745583952160e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.27
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.27
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.28
y[1] (closed_form) = 1.119032474410748407936756347125
y[1] (numeric) = 1.1190324744107484079367563471256
absolute error = 6e-31
relative error = 5.3617746912657152984883029887237e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.28
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.28
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.29
y[1] (closed_form) = 1.129429939716678491278326428614
y[1] (numeric) = 1.1294299397166784912783264286151
absolute error = 1.1e-30
relative error = 9.7394266020249020837624491263788e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.29
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.29
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.3
y[1] (closed_form) = 1.139830939840639062063119919167
y[1] (numeric) = 1.1398309398406390620631199191676
absolute error = 6e-31
relative error = 5.2639385283214598308020907291376e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.3
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.3
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.31
y[1] (closed_form) = 1.1502354735335777607031968186
y[1] (numeric) = 1.1502354735335777607031968185999
absolute error = 1e-31
relative error = 8.6938720202042866709773424191542e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.31
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.31
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.32
y[1] (closed_form) = 1.160643539547324638375392422185
y[1] (numeric) = 1.1606435395473246383753924221866
absolute error = 1.6e-30
relative error = 1.3785455615632286296933443048221e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.32
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.32
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.33
y[1] (closed_form) = 1.171055136634591222264073503933
y[1] (numeric) = 1.171055136634591222264073503932
absolute error = 1.0e-30
relative error = 8.5393075758484443965185539401437e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.33
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.33
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.34
y[1] (closed_form) = 1.18147026354896958212370719443
y[1] (numeric) = 1.1814702635489695821237071944301
absolute error = 1e-31
relative error = 8.4640302075495444559310858467120e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.34
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.34
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.35
y[1] (closed_form) = 1.191888919044931398158914019686
y[1] (numeric) = 1.1918889190449313981589140196859
absolute error = 1e-31
relative error = 8.3900436023963266750784192316385e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.35
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.35
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.36
y[1] (closed_form) = 1.202311101877827030219681495388
y[1] (numeric) = 1.2023111018778270302196814953881
absolute error = 1e-31
relative error = 8.3173148649975212968255000379394e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.36
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.36
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.37
y[1] (closed_form) = 1.212736810803884588309419587072
y[1] (numeric) = 1.2127368108038845883094195870707
absolute error = 1.3e-30
relative error = 1.0719555870809853823051844927486e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.37
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.37
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.38
y[1] (closed_form) = 1.223166044580209004403544250423
y[1] (numeric) = 1.2231660445802090044035442504232
absolute error = 2e-31
relative error = 1.6351009814750054387866321798676e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.38
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.38
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.39
y[1] (closed_form) = 1.233598801964781105576280157735
y[1] (numeric) = 1.2335988019647811055762801577352
absolute error = 2e-31
relative error = 1.6212726510552329721941304464453e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.39
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.39
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.4
y[1] (closed_form) = 1.244035081716456688433378596124
y[1] (numeric) = 1.2440350817164566884333785961228
absolute error = 1.2e-30
relative error = 9.6460302256452502146166795524190e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.4
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.4
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.41
y[1] (closed_form) = 1.254474882594965594848451390824
y[1] (numeric) = 1.2544748825949655948484513908238
absolute error = 2e-31
relative error = 1.5942925822977544204115382977934e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.41
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.41
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.42
y[1] (closed_form) = 1.26491820336091078900062656249
y[1] (numeric) = 1.2649182033609107890006265624885
absolute error = 1.5e-30
relative error = 1.1858474295132069251912122219580e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.42
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.42
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.43
y[1] (closed_form) = 1.27536504277576743571123627108
y[1] (numeric) = 1.2753650427757674357112362710807
absolute error = 7e-31
relative error = 5.4886246409615042096314484230290e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.43
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.43
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.44
y[1] (closed_form) = 1.285815399601881980077252430755
y[1] (numeric) = 1.2858153996018819800772524307559
absolute error = 9e-31
relative error = 6.9994495343473153215955810434951e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.44
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.44
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.45
y[1] (closed_form) = 1.296269272602471228399190199952
y[1] (numeric) = 1.2962692726024712283991901999535
absolute error = 1.5e-30
relative error = 1.1571669804287701944678182081554e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.45
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.45
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.46
y[1] (closed_form) = 1.306726660541621430401204358941
y[1] (numeric) = 1.3067266605416214304012043589411
absolute error = 1e-31
relative error = 7.6527098604195680364814418084862e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.46
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.46
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.47
y[1] (closed_form) = 1.317187562184287362741108383233
y[1] (numeric) = 1.317187562184287362741108383233
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.47
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.47
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.48
y[1] (closed_form) = 1.327651976296291413808050805688
y[1] (numeric) = 1.3276519762962914138080508056899
absolute error = 1.9e-30
relative error = 1.4310979337374013518699159034215e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.48
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.48
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.49
y[1] (closed_form) = 1.338119901644322669805588232737
y[1] (numeric) = 1.3381199016443226698055882327363
absolute error = 7e-31
relative error = 5.2312203049952293974172574852318e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.49
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.49
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.5
y[1] (closed_form) = 1.348591336995936002117899141032
y[1] (numeric) = 1.3485913369959360021178991410337
absolute error = 1.7e-30
relative error = 1.2605746109765518778126622513203e-28 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.5
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.5
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.51
y[1] (closed_form) = 1.359066281119551155956887330154
y[1] (numeric) = 1.3590662811195511559568873301549
absolute error = 9e-31
relative error = 6.6221935788047920104962198397923e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.51
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.51
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.52
y[1] (closed_form) = 1.369544732784451840287928644355
y[1] (numeric) = 1.3695447327844518402879286443554
absolute error = 4e-31
relative error = 2.9206786052672489803776090273723e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.52
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.52
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.53
y[1] (closed_form) = 1.380026690760784819032019302455
y[1] (numeric) = 1.3800266907607848190320193024543
absolute error = 7e-31
relative error = 5.0723656628271596740942819654739e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.53
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.53
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.54
y[1] (closed_form) = 1.390512153819559003542088889163
y[1] (numeric) = 1.3905121538195590035420888891641
absolute error = 1.1e-30
relative error = 7.9107542999781822752926245023565e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.54
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.54
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.55
y[1] (closed_form) = 1.401001120732644546351245763968
y[1] (numeric) = 1.4010011207326445463512457639686
absolute error = 6e-31
relative error = 4.2826518203371161472795800926154e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.55
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.55
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.56
y[1] (closed_form) = 1.411493590272771936190727334882
y[1] (numeric) = 1.4114935902727719361907273348816
absolute error = 4e-31
relative error = 2.8338775518116222782598010742786e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.56
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.56
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.57
y[1] (closed_form) = 1.421989561213531094275332324149
y[1] (numeric) = 1.4219895612135310942753323241502
absolute error = 1.2e-30
relative error = 8.4388805145370800716251656108023e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.57
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.57
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.58
y[1] (closed_form) = 1.432489032329370471854116821234
y[1] (numeric) = 1.4324890323293704718541168212346
absolute error = 6e-31
relative error = 4.1885137439714981718482394578410e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.58
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.58
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.59
y[1] (closed_form) = 1.44299200239559614902414057523
y[1] (numeric) = 1.4429920023955961490241405752305
absolute error = 5e-31
relative error = 3.4650226693558973556399926984809e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.59
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.59
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.6
y[1] (closed_form) = 1.453498470188370934805054624329
y[1] (numeric) = 1.4534984701883709348050546243295
absolute error = 5e-31
relative error = 3.4399761008018181719757260525462e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.6
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.6
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.61
y[1] (closed_form) = 1.464008434484713468472325993977
y[1] (numeric) = 1.4640084344847134684723259939777
absolute error = 7e-31
relative error = 4.7813932181775903000618118443184e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.61
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.61
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.62
y[1] (closed_form) = 1.474521894062497322146899818113
y[1] (numeric) = 1.4745218940624973221468998181136
absolute error = 6e-31
relative error = 4.0691155717391410759615702680119e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.62
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.62
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.63
y[1] (closed_form) = 1.485038847700450104639103849285
y[1] (numeric) = 1.4850388477004501046391038492843
absolute error = 7e-31
relative error = 4.7136814035803477992294887639005e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.63
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.63
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.64
y[1] (closed_form) = 1.495559294178152566544604923581
y[1] (numeric) = 1.4955592941781525665446049235815
absolute error = 5e-31
relative error = 3.3432308698583734253358053253470e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.64
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.64
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.65
y[1] (closed_form) = 1.506083232276037706590231535238
y[1] (numeric) = 1.5060832322760377065902315352377
absolute error = 3e-31
relative error = 1.9919217847384907866988762412948e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.65
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.65
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.66
y[1] (closed_form) = 1.516610660775389879227481253408
y[1] (numeric) = 1.5166106607753898792274812534092
absolute error = 1.2e-30
relative error = 7.9123800922412219863172740091341e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.66
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.66
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.67
y[1] (closed_form) = 1.527141578458343903471536280179
y[1] (numeric) = 1.5271415784583439034715362801787
absolute error = 3e-31
relative error = 1.9644544044361054650552533018506e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.67
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.67
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.68
y[1] (closed_form) = 1.537675984107884172983615004168
y[1] (numeric) = 1.5376759841078841729836150041682
absolute error = 2e-31
relative error = 1.3006641325417741100203589370608e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.68
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.68
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.69
y[1] (closed_form) = 1.548213876507843767394491948388
y[1] (numeric) = 1.5482138765078437673944919483892
absolute error = 1.2e-30
relative error = 7.7508671005244048407531931370292e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.69
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.69
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.7
y[1] (closed_form) = 1.558755254442903564867023044112
y[1] (numeric) = 1.5587552544429035648670230441106
absolute error = 1.4e-30
relative error = 8.9815254576341914654870481986712e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.7
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.7
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.71
y[1] (closed_form) = 1.569300116698591355895517684616
y[1] (numeric) = 1.5693001166985913558955176846167
absolute error = 7e-31
relative error = 4.4605871913947353240833971852052e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.71
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.71
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.72
y[1] (closed_form) = 1.579848462061280958339803523798
y[1] (numeric) = 1.5798484620612809583398035237983
absolute error = 3e-31
relative error = 1.8989163024444762153264838287689e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.72
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.72
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.73
y[1] (closed_form) = 1.590400289318191333691834484594
y[1] (numeric) = 1.590400289318191333691834484593
absolute error = 1.0e-30
relative error = 6.2877252143150863877699577350561e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.73
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.73
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.74
y[1] (closed_form) = 1.6009555972573857045726969314
y[1] (numeric) = 1.6009555972573857045726969314007
absolute error = 7e-31
relative error = 4.3723885984044626066753059248305e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.74
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.74
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.75
y[1] (closed_form) = 1.611514384667770673457873438776
y[1] (numeric) = 1.6115143846677706734578734387757
absolute error = 3e-31
relative error = 1.8616029919078129161660201796084e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.75
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.75
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.76
y[1] (closed_form) = 1.62207665033909534262862805597
y[1] (numeric) = 1.6220766503390953426286280559689
absolute error = 1.1e-30
relative error = 6.7814304568778846028717447005663e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.76
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.76
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.77
y[1] (closed_form) = 1.632642393061950435347381423295
y[1] (numeric) = 1.6326423930619504353473814232948
absolute error = 2e-31
relative error = 1.2250080045080087668755651818692e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.77
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.77
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.78
y[1] (closed_form) = 1.643211611627767418254948541851
y[1] (numeric) = 1.6432116116277674182549485418505
absolute error = 5e-31
relative error = 3.0428217307002802440082263853891e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.78
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.78
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.79
y[1] (closed_form) = 1.653784304828817624987516432862
y[1] (numeric) = 1.6537843048288176249875164328628
absolute error = 8e-31
relative error = 4.8373902065953370771813669801481e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.79
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.79
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.8
y[1] (closed_form) = 1.664360471458211381011243346895
y[1] (numeric) = 1.6643604714582113810112433468957
absolute error = 7e-31
relative error = 4.2058196646950079861370703975330e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.8
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.8
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.81
y[1] (closed_form) = 1.674940110309897129672365596364
y[1] (numeric) = 1.6749401103098971296723655963633
absolute error = 7e-31
relative error = 4.1792539069978216773669331421019e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.81
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.81
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.82
y[1] (closed_form) = 1.685523220178660559460702487274
y[1] (numeric) = 1.6855232201786605594607024872755
absolute error = 1.5e-30
relative error = 8.8993137682256573263656798723163e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.82
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.82
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.83
y[1] (closed_form) = 1.696109799860123732484454217937
y[1] (numeric) = 1.6961097998601237324844542179383
absolute error = 1.3e-30
relative error = 7.6645981298333960327378145011812e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.83
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.83
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.84
y[1] (closed_form) = 1.70669984815074421415419199346
y[1] (numeric) = 1.7066998481507442141541919934592
absolute error = 8e-31
relative error = 4.6874088661039127449783270348701e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.84
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.84
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.85
y[1] (closed_form) = 1.717293363847814204073943975404
y[1] (numeric) = 1.7172933638478142040739439754033
absolute error = 7e-31
relative error = 4.0761818262172804713418792485280e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.85
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.85
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.86
y[1] (closed_form) = 1.727890345749459668137285045838
y[1] (numeric) = 1.7278903457494596681372850458376
absolute error = 4e-31
relative error = 2.3149617160833371984109687340380e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.86
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.86
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.87
y[1] (closed_form) = 1.738490792654639471826342714314
y[1] (numeric) = 1.7384907926546394718263427143154
absolute error = 1.4e-30
relative error = 8.0529618328448490966230848021033e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.87
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.87
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.88
y[1] (closed_form) = 1.749094703363144514711635835124
y[1] (numeric) = 1.7490947033631445147116358351256
absolute error = 1.6e-30
relative error = 9.1475893039040911905685407294577e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.88
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.88
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=489.9MB, alloc=44.3MB, time=5.48
TOP MAIN SOLVE Loop
x[1] = 26.89
y[1] (closed_form) = 1.759702076675596866150667130385
y[1] (numeric) = 1.759702076675596866150667130384
absolute error = 1.0e-30
relative error = 5.6827801322436648370658092651985e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.89
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.89
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.9
y[1] (closed_form) = 1.77031291139344890218319483231
y[1] (numeric) = 1.7703129113934489021831948323105
absolute error = 5e-31
relative error = 2.8243594495757246811344634104661e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.9
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.9
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.91
y[1] (closed_form) = 1.780927206318982443621113065347
y[1] (numeric) = 1.7809272063189824436211130653463
absolute error = 7e-31
relative error = 3.9305368434841169768297761338805e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.91
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.91
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.92
y[1] (closed_form) = 1.791544960255307895330874885642
y[1] (numeric) = 1.7915449602553078953308748856418
absolute error = 2e-31
relative error = 1.1163549028180603289572021952634e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.92
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.92
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.93
y[1] (closed_form) = 1.802166172006363386706396181928
y[1] (numeric) = 1.802166172006363386706396181928
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.93
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.93
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.94
y[1] (closed_form) = 1.812790840376913913330382917888
y[1] (numeric) = 1.8127908403769139133303829178875
absolute error = 5e-31
relative error = 2.7581781023123463586098461619920e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.94
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.94
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.95
y[1] (closed_form) = 1.823418964172550479822028461908
y[1] (numeric) = 1.8234189641725504798220284619078
absolute error = 2e-31
relative error = 1.0968406270292248773155858692854e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.95
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.95
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.96
y[1] (closed_form) = 1.834050542199689243869032005549
y[1] (numeric) = 1.8340505421996892438690320055496
absolute error = 6e-31
relative error = 3.2714474666569614792142467950256e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.96
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.96
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.97
y[1] (closed_form) = 1.844685573265570661441893317222
y[1] (numeric) = 1.8446855732655706614418933172225
absolute error = 5e-31
relative error = 2.7104890245055186090139586289938e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.97
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.97
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.98
y[1] (closed_form) = 1.855324056178258633188443312471
y[1] (numeric) = 1.8553240561782586331884433124718
absolute error = 8e-31
relative error = 4.3119152006679764033116456589304e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.98
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.98
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 26.99
y[1] (closed_form) = 1.865965989746639652006574146954
y[1] (numeric) = 1.8659659897466396520065741469533
absolute error = 7e-31
relative error = 3.7514081384465416068071989096171e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 28.99
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.99
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27
y[1] (closed_form) = 1.876611372780421951793136752648
y[1] (numeric) = 1.8766113727804219517931367526489
absolute error = 9e-31
relative error = 4.7958784277564269161040388873120e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.01
y[1] (closed_form) = 1.88726020409013465736697794218
y[1] (numeric) = 1.8872602040901346573669779421811
absolute error = 1.1e-30
relative error = 5.8285550535959084883557291564376e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.01
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.01
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.02
y[1] (closed_form) = 1.897912482487126935564093400241
y[1] (numeric) = 1.8979124824871269355640934002395
absolute error = 1.5e-30
relative error = 7.9034202780220880066333770962919e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.02
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.02
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.03
y[1] (closed_form) = 1.908568206783567147502877065176
y[1] (numeric) = 1.9085682067835671475028770651766
absolute error = 6e-31
relative error = 3.1437178816425730330580293407056e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.03
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.03
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.04
y[1] (closed_form) = 1.919227375792442002017451577779
y[1] (numeric) = 1.9192273757924420020174515777794
absolute error = 4e-31
relative error = 2.0841720217482905330782002938800e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.04
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.04
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.05
y[1] (closed_form) = 1.929889988327555710257068638116
y[1] (numeric) = 1.9298899883275557102570686381171
absolute error = 1.1e-30
relative error = 5.6998067592094248165295504162260e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.05
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.05
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.06
y[1] (closed_form) = 1.940556043203529141449572265222
y[1] (numeric) = 1.9405560432035291414495722652207
absolute error = 1.3e-30
relative error = 6.6991108272962852662353401960839e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.06
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.06
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.07
y[1] (closed_form) = 1.951225539235798979826922098203
y[1] (numeric) = 1.9512255392357989798269220982039
absolute error = 9e-31
relative error = 4.6124857526848825060661999667446e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.07
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.07
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.08
y[1] (closed_form) = 1.961898475240616882710778011305
y[1] (numeric) = 1.9618984752406168827107780113058
absolute error = 8e-31
relative error = 4.0776829693080018502192268157469e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.08
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.08
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.09
y[1] (closed_form) = 1.972574850035048639756151439261
y[1] (numeric) = 1.9725748500350486397561514392612
absolute error = 2e-31
relative error = 1.0139032239838524105460380542451e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.09
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.09
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.1
y[1] (closed_form) = 1.983254662436973333351132923402
y[1] (numeric) = 1.9832546624369733333511329234007
absolute error = 1.3e-30
relative error = 6.5548818546711130465208543576622e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.1
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.1
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.11
y[1] (closed_form) = 1.993937911265082500170709492986
y[1] (numeric) = 1.9939379112650825001707094929877
absolute error = 1.7e-30
relative error = 8.5258422059963272507202639677864e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.11
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.11
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.12
y[1] (closed_form) = 2.004624595338879293882689590532
y[1] (numeric) = 2.0046245953388792938826895905318
absolute error = 2e-31
relative error = 9.9769303671638453992223681538698e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.12
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.12
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.13
y[1] (closed_form) = 2.01531471347867764900375733421
y[1] (numeric) = 2.0153147134786776490037573342106
absolute error = 6e-31
relative error = 2.9772024983846181583774991957734e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.13
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.13
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.14
y[1] (closed_form) = 2.026008264505601445903681985109
y[1] (numeric) = 2.0260082645056014459036819851095
absolute error = 5e-31
relative error = 2.4679070108433785968810608988274e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.14
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.14
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.15
y[1] (closed_form) = 2.036705247241583676955712551777
y[1] (numeric) = 2.0367052472415836769557125517762
absolute error = 8e-31
relative error = 3.9279125002671927890531649938999e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.15
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.15
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.16
y[1] (closed_form) = 2.047405660509365613831191519617
y[1] (numeric) = 2.0474056605093656138311915196177
absolute error = 7e-31
relative error = 3.4189609489789624092171639994549e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.16
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.16
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.17
y[1] (closed_form) = 2.058109503132495975936425737958
y[1] (numeric) = 2.0581095031324959759364257379579
absolute error = 1e-31
relative error = 4.8588279606987582367914584122197e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.17
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.17
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.18
y[1] (closed_form) = 2.068816773935330099989856533163
y[1] (numeric) = 2.0688167739353300999898565331624
absolute error = 6e-31
relative error = 2.9002085035238389815624409101633e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.18
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.18
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.19
y[1] (closed_form) = 2.079527471743029110737575142144
y[1] (numeric) = 2.0795274717430291107375751421421
absolute error = 1.9e-30
relative error = 9.1366910310997149544642876661193e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.19
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.19
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.2
y[1] (closed_form) = 2.090241595381559092805233576797
y[1] (numeric) = 2.0902415953815590928052335767959
absolute error = 1.1e-30
relative error = 5.2625495657079900191469892652685e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.2
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.2
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.21
y[1] (closed_form) = 2.100959143677690263684405036578
y[1] (numeric) = 2.1009591436776902636844050365777
absolute error = 3e-31
relative error = 1.4279192477529835659780097318860e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.21
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.21
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.22
y[1] (closed_form) = 2.111680115458996147851451983395
y[1] (numeric) = 2.1116801154589961478514519833935
absolute error = 1.5e-30
relative error = 7.1033486038862426632123801259328e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.22
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.22
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.23
y[1] (closed_form) = 2.12240450955385275201696398048
y[1] (numeric) = 2.1224045095538527520169639804787
absolute error = 1.3e-30
relative error = 6.1251283350941942496367905040585e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.23
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.23
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.24
y[1] (closed_form) = 2.133132324791437741503831374804
y[1] (numeric) = 2.1331323247914377415038313748043
absolute error = 3e-31
relative error = 1.4063825132335933792900147414574e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.24
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.24
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.25
y[1] (closed_form) = 2.143863560001729617752024870934
y[1] (numeric) = 2.1438635600017296177520248709321
absolute error = 1.9e-30
relative error = 8.8625042910774934087926545910567e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.25
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.25
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.26
y[1] (closed_form) = 2.154598214015506896948155003117
y[1] (numeric) = 2.1545982140155068969481550031182
absolute error = 1.2e-30
relative error = 5.5694838703294472273095413322738e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.26
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.26
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.27
y[1] (closed_form) = 2.165336285664347289777889461867
y[1] (numeric) = 2.1653362856643472897778894618671
absolute error = 1e-31
relative error = 4.6182203042572197312388805259467e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.27
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.27
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.28
y[1] (closed_form) = 2.176077773780626882299310171102
y[1] (numeric) = 2.1760777737806268822993101711004
absolute error = 1.6e-30
relative error = 7.3526783797815582944431733247602e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.28
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.28
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.29
y[1] (closed_form) = 2.186822677197519317935295942647
y[1] (numeric) = 2.1868226771975193179352959426466
absolute error = 4e-31
relative error = 1.8291377905071495429756573649483e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.29
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.29
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.3
y[1] (closed_form) = 2.197570994748994980583020455903
y[1] (numeric) = 2.1975709947489949805830204559023
absolute error = 7e-31
relative error = 3.1853350889351063244478900787073e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.3
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.3
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.31
y[1] (closed_form) = 2.208322725269820178838659222299
y[1] (numeric) = 2.2083227252698201788386592223
absolute error = 1.0e-30
relative error = 4.5283236392806521998771562022647e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.31
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.31
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.32
y[1] (closed_form) = 2.219077867595556331335403096651
y[1] (numeric) = 2.2190778675955563313354030966498
absolute error = 1.2e-30
relative error = 5.4076516084595056018941696679880e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.32
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.32
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.33
y[1] (closed_form) = 2.229836420562559153192879790547
y[1] (numeric) = 2.2298364205625591531928797905466
absolute error = 4e-31
relative error = 1.7938535594421994688956434820021e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.33
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.33
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.34
y[1] (closed_form) = 2.240598383007977843576088726862
y[1] (numeric) = 2.2405983830079778435760887268617
absolute error = 3e-31
relative error = 1.3389280393805042934114190913972e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.34
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.34
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.35
y[1] (closed_form) = 2.251363753769754274361958448901
y[1] (numeric) = 2.2513637537697542743619584489001
absolute error = 9e-31
relative error = 3.9975770174544726285833963664830e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.35
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.35
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.36
y[1] (closed_form) = 2.26213253168662217991163966313
y[1] (numeric) = 2.2621325316866221799116396631287
absolute error = 1.3e-30
relative error = 5.7467897295598931946024713131982e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.36
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.36
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.37
y[1] (closed_form) = 2.272904715598106347946650850484
y[1] (numeric) = 2.2729047155981063479466508504844
absolute error = 4e-31
relative error = 1.7598625989683931858283434275493e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.37
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.37
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.38
y[1] (closed_form) = 2.283680304344521811526997228188
y[1] (numeric) = 2.283680304344521811526997228189
absolute error = 1.0e-30
relative error = 4.3788966349518310680481845910462e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.38
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.38
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.39
y[1] (closed_form) = 2.294459296766973042129387681746
y[1] (numeric) = 2.2944592967669730421293876817468
absolute error = 8e-31
relative error = 3.4866602389819974342383799513121e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.39
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.39
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.4
y[1] (closed_form) = 2.30524169170735314382367811541
y[1] (numeric) = 2.3052416917073531438236781154108
absolute error = 8e-31
relative error = 3.4703519499835540836592050280776e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.4
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.4
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.41
y[1] (closed_form) = 2.316027488008343048545673488896
y[1] (numeric) = 2.3160274880083430485456734888965
absolute error = 5e-31
relative error = 2.1588690228800896040739740660645e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.41
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.41
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.42
y[1] (closed_form) = 2.326816684513410712464424618527
y[1] (numeric) = 2.3268166845134107124644246185265
absolute error = 5e-31
relative error = 2.1488585814595925360433498464107e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.42
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.42
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.43
y[1] (closed_form) = 2.337609280066810313442159622324
y[1] (numeric) = 2.3376092800668103134421596223239
absolute error = 1e-31
relative error = 4.2778748721061690168034618432712e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.43
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.43
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.44
y[1] (closed_form) = 2.348405273513581449584993680869
y[1] (numeric) = 2.3484052735135814495849936808699
absolute error = 9e-31
relative error = 3.8323879193707451094611619205825e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.44
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.44
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.45
y[1] (closed_form) = 2.359204663699548338882564569017
y[1] (numeric) = 2.3592046636995483388825645690171
absolute error = 1e-31
relative error = 4.2387166123682813502576725948642e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.45
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.45
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.46
y[1] (closed_form) = 2.370007449471319019934745187836
y[1] (numeric) = 2.3700074494713190199347451878355
absolute error = 5e-31
relative error = 2.1096980100696971275788037261577e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.46
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.46
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.47
y[1] (closed_form) = 2.380813629676284553763588091489
y[1] (numeric) = 2.3808136296762845537635880914881
absolute error = 9e-31
relative error = 3.7802202943637027562975966406698e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.47
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.47
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.48
y[1] (closed_form) = 2.391623203162618226708660760103
y[1] (numeric) = 2.3916232031626182267086607601033
absolute error = 3e-31
relative error = 1.2543781963784598898971823622965e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.48
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.48
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.49
y[1] (closed_form) = 2.402436168779274754403934117167
y[1] (numeric) = 2.4024361687792747544039341171684
absolute error = 1.4e-30
relative error = 5.8274180941563481306477192486744e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.49
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.49
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.5
y[1] (closed_form) = 2.413252525375989486834390528527
y[1] (numeric) = 2.4132525253759894868343905285259
absolute error = 1.1e-30
relative error = 4.5581636750949544241723681556645e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.5
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.5
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.51
y[1] (closed_form) = 2.424072271803277614470521249742
y[1] (numeric) = 2.4240722718032776144705212497421
absolute error = 1e-31
relative error = 4.1252895453323088051714617189536e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.51
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.51
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=534.2MB, alloc=44.3MB, time=5.97
TOP MAIN SOLVE Loop
x[1] = 27.52
y[1] (closed_form) = 2.434895406912433375478887009459
y[1] (numeric) = 2.4348954069124333754788870094588
absolute error = 2e-31
relative error = 8.2139051818086015843831513491446e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.52
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.52
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.53
y[1] (closed_form) = 2.445721929555529264006919128357
y[1] (numeric) = 2.4457219295555292640069191283569
absolute error = 1e-31
relative error = 4.0887722676704050403307963933379e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.53
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.53
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.54
y[1] (closed_form) = 2.456551838585415239540142276576
y[1] (numeric) = 2.456551838585415239540142276577
absolute error = 1.0e-30
relative error = 4.0707465818260184073075139607928e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.54
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.54
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.55
y[1] (closed_form) = 2.467385132855717937330003666889
y[1] (numeric) = 2.4673851328557179373300036668871
absolute error = 1.9e-30
relative error = 7.7004597891897236384505922439598e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.55
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.55
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.56
y[1] (closed_form) = 2.478221811220839879890497166579
y[1] (numeric) = 2.4782218112208398798904971665785
absolute error = 5e-31
relative error = 2.0175756574173895986851004364119e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.56
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.56
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.57
y[1] (closed_form) = 2.489061872535958689561774488033
y[1] (numeric) = 2.4890618725359586895617744880327
absolute error = 3e-31
relative error = 1.2052733735154106535472177898846e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.57
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.57
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.58
y[1] (closed_form) = 2.499905315657026302138939286162
y[1] (numeric) = 2.4999053156570263021389392861629
absolute error = 9e-31
relative error = 3.6001363506179895962809641477323e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.58
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.58
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.59
y[1] (closed_form) = 2.510752139440768181564223650512
y[1] (numeric) = 2.510752139440768181564223650511
absolute error = 1.0e-30
relative error = 3.9828702494812362371265950431806e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.59
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.59
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.6
y[1] (closed_form) = 2.521602342744682535680750130701
y[1] (numeric) = 2.5216023427446825356807501307023
absolute error = 1.3e-30
relative error = 5.1554520630124101007578157000259e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.6
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.6
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.61
y[1] (closed_form) = 2.532455924427039533046086076246
y[1] (numeric) = 2.5324559244270395330460860762463
absolute error = 3e-31
relative error = 1.1846208145473413895905693170184e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.61
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.61
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.62
y[1] (closed_form) = 2.54331288334688052080380070535
y[1] (numeric) = 2.5433128833468805208038007053486
absolute error = 1.4e-30
relative error = 5.5046314166335116179117802334393e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.62
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.62
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.63
y[1] (closed_form) = 2.554173218364017243611238942489
y[1] (numeric) = 2.554173218364017243611238942489
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.63
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.63
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.64
y[1] (closed_form) = 2.565036928339031063621729681044
y[1] (numeric) = 2.5650369283390310636217296810426
absolute error = 1.4e-30
relative error = 5.4580110895579140352430765124343e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.64
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.64
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.65
y[1] (closed_form) = 2.575904012133272181519449735208
y[1] (numeric) = 2.575904012133272181519449735209
absolute error = 1.0e-30
relative error = 3.8821322350899074449217445227409e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.65
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.65
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.66
y[1] (closed_form) = 2.586774468608858858605168344977
y[1] (numeric) = 2.5867744686088588586051683449757
absolute error = 1.3e-30
relative error = 5.0255637504383087915419390216052e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.66
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.66
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.67
y[1] (closed_form) = 2.597648296628676639931100688817
y[1] (numeric) = 2.5976482966286766399311006888156
absolute error = 1.4e-30
relative error = 5.3894901854764997098179104400504e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.67
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.67
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.68
y[1] (closed_form) = 2.608525495056377578483102441317
y[1] (numeric) = 2.608525495056377578483102441316
absolute error = 1.0e-30
relative error = 3.8335833860745424118540443395423e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.68
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.68
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.69
y[1] (closed_form) = 2.619406062756379460408440986987
y[1] (numeric) = 2.6194060627563794604084409869856
absolute error = 1.4e-30
relative error = 5.3447230649179742381327640592671e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.69
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.69
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.7
y[1] (closed_form) = 2.630289998593865031287382467111
y[1] (numeric) = 2.6302899985938650312873824671098
absolute error = 1.2e-30
relative error = 4.5622345849374470439953916623601e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.7
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.7
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.71
y[1] (closed_form) = 2.641177301434781223446837393743
y[1] (numeric) = 2.6411773014347812234468373937413
absolute error = 1.7e-30
relative error = 6.4365235877065113395022834970410e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.71
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.71
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.72
y[1] (closed_form) = 2.652067970145838384314311113755
y[1] (numeric) = 2.6520679701458383843143111137535
absolute error = 1.5e-30
relative error = 5.6559636362469033557798503783153e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.72
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.72
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.73
y[1] (closed_form) = 2.66296200359450950581040894636
y[1] (numeric) = 2.662962003594509505810408946361
absolute error = 1.0e-30
relative error = 3.7552169300582723480565469749063e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.73
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.73
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.74
y[1] (closed_form) = 2.673859400649029454778149349657
y[1] (numeric) = 2.6738594006490294547781493496562
absolute error = 8e-31
relative error = 2.9919299414390110943654772262797e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.74
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.74
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.75
y[1] (closed_form) = 2.684760160178394204447341995539
y[1] (numeric) = 2.6847601601783942044473419955384
absolute error = 6e-31
relative error = 2.2348365001070777661172965735182e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.75
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.75
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.76
y[1] (closed_form) = 2.695664281052360066932291147952
y[1] (numeric) = 2.6956642810523600669322911479512
absolute error = 8e-31
relative error = 2.9677286063518565914234264620672e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.76
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.76
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.77
y[1] (closed_form) = 2.706571762141442926761088246612
y[1] (numeric) = 2.7065717621414429267610882466124
absolute error = 4e-31
relative error = 1.4778843317404579183311063321112e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.77
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.77
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.78
y[1] (closed_form) = 2.717482602316917475434761097443
y[1] (numeric) = 2.7174826023169174754347610974418
absolute error = 1.2e-30
relative error = 4.4158516377506285308205316790379e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.78
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.78
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.79
y[1] (closed_form) = 2.728396800450816447014550561691
y[1] (numeric) = 2.7283968004508164470145505616903
absolute error = 7e-31
relative error = 2.5656092247445023996776890700409e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.79
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.79
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.8
y[1] (closed_form) = 2.739314355415929854735589118369
y[1] (numeric) = 2.7393143554159298547355891183682
absolute error = 8e-31
relative error = 2.9204388259358069561039281956213e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.8
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.8
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.81
y[1] (closed_form) = 2.750235266085804228645259148985
y[1] (numeric) = 2.7502352660858042286452591489844
absolute error = 6e-31
relative error = 2.1816315403952087888353841593932e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.81
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.81
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.82
y[1] (closed_form) = 2.761159531334741854264512259863
y[1] (numeric) = 2.7611595313347418542645122598635
absolute error = 5e-31
relative error = 1.8108334354672382231316715892713e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.82
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.82
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.83
y[1] (closed_form) = 2.772087150037800012270434415426
y[1] (numeric) = 2.7720871500378000122704344154265
absolute error = 5e-31
relative error = 1.8036950966465178784926149364988e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.83
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.83
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.84
y[1] (closed_form) = 2.783018121070790219198345105825
y[1] (numeric) = 2.7830181210707902191983451058253
absolute error = 3e-31
relative error = 1.0779663909790584230601721877625e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.84
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.84
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.85
y[1] (closed_form) = 2.793952443310277469161722214231
y[1] (numeric) = 2.7939524433102774691617222142301
absolute error = 9e-31
relative error = 3.2212430893550899451298267085683e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.85
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.85
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.86
y[1] (closed_form) = 2.804890115633579476588247682909
y[1] (numeric) = 2.8048901156335794765882476829094
absolute error = 4e-31
relative error = 1.4260808213859260078763430157882e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.86
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.86
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.87
y[1] (closed_form) = 2.815831136918765919970272503032
y[1] (numeric) = 2.8158311369187659199702725030306
absolute error = 1.4e-30
relative error = 4.9718890513156104904217834936620e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.87
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.87
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.88
y[1] (closed_form) = 2.826775506044657686628002970871
y[1] (numeric) = 2.8267755060446576866280029708704
absolute error = 6e-31
relative error = 2.1225597813373763506905924556769e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.88
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.88
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.89
y[1] (closed_form) = 2.837723221890826118483713562879
y[1] (numeric) = 2.8377232218908261184837135628779
absolute error = 1.1e-30
relative error = 3.8763470359418991469274197667371e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.89
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.89
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.9
y[1] (closed_form) = 2.848674283337592258845295183803
y[1] (numeric) = 2.8486742833375922588452951838028
absolute error = 2e-31
relative error = 7.0208096857487687016357798669165e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.9
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.9
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.91
y[1] (closed_form) = 2.859628689266026100197450935905
y[1] (numeric) = 2.8596286892660261001974509359055
absolute error = 5e-31
relative error = 1.7484787513736050003986973754042e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.91
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.91
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.92
y[1] (closed_form) = 2.870586438557945832998854943128
y[1] (numeric) = 2.8705864385579458329988549431266
absolute error = 1.4e-30
relative error = 4.8770522329343175937196901917712e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.92
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.92
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.93
y[1] (closed_form) = 2.881547530095917095483593142037
y[1] (numeric) = 2.8815475300959170954835931420361
absolute error = 9e-31
relative error = 3.1233217241779871151235319886541e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.93
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.93
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.94
y[1] (closed_form) = 2.892511962763252224465208321421
y[1] (numeric) = 2.8925119627632522244652083214213
absolute error = 3e-31
relative error = 1.0371607926330106281146490867620e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.94
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.94
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.95
y[1] (closed_form) = 2.903479735444009507141675054535
y[1] (numeric) = 2.9034797354440095071416750545338
absolute error = 1.2e-30
relative error = 4.1329718453037252584565649366085e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.95
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.95
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.96
y[1] (closed_form) = 2.914450847022992433899633522318
y[1] (numeric) = 2.9144508470229924338996335223183
absolute error = 3e-31
relative error = 1.0293534382521472180146968896946e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.96
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.96
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.97
y[1] (closed_form) = 2.925425296385748952116214572415
y[1] (numeric) = 2.9254252963857489521162145724136
absolute error = 1.4e-30
relative error = 4.7856289536076906357375043685080e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.97
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.97
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.98
y[1] (closed_form) = 2.936403082418570720956791697364
y[1] (numeric) = 2.9364030824185707209567916973632
absolute error = 8e-31
relative error = 2.7244216054325871615550300352560e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.98
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.98
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 27.99
y[1] (closed_form) = 2.947384204008492367166998946328
y[1] (numeric) = 2.9473842040084923671669989463282
absolute error = 2e-31
relative error = 6.7856779488740089384631694293189e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 29.99
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.99
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28
y[1] (closed_form) = 2.958368660043290741857357107675
y[1] (numeric) = 2.9583686600432907418573571076758
absolute error = 8e-31
relative error = 2.7041930601992428747194942322122e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.01
y[1] (closed_form) = 2.96935644941148417827885381514
y[1] (numeric) = 2.96935644941148417827885381514
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.01
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.01
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.02
y[1] (closed_form) = 2.980347571002331750587826537844
y[1] (numeric) = 2.980347571002331750587826537846
absolute error = 2.0e-30
relative error = 6.7106267049496263240486487695246e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.02
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.02
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.03
y[1] (closed_form) = 2.991342023705832533598500714368
y[1] (numeric) = 2.9913420237058325335985007143672
absolute error = 8e-31
relative error = 2.6743849204141415278765205215036e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.03
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.03
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.04
y[1] (closed_form) = 3.002339806412724863521538583175
y[1] (numeric) = 3.0023398064127248635215385831752
absolute error = 2e-31
relative error = 6.6614711490291066770622216300760e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.04
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.04
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.05
y[1] (closed_form) = 3.013340918014485599686957546354
y[1] (numeric) = 3.0133409180144855996869575463551
absolute error = 1.1e-30
relative error = 3.6504332895887491760675297771864e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.05
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.05
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.06
y[1] (closed_form) = 3.024345357403329387249780180327
y[1] (numeric) = 3.0243453574033293872497801803274
absolute error = 4e-31
relative error = 1.3226002745382085812146596357732e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.06
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.06
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.07
y[1] (closed_form) = 3.03535312347220792087678127655
y[1] (numeric) = 3.0353531234722079208767812765506
absolute error = 6e-31
relative error = 1.9767057590770416214670751694831e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.07
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.07
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.08
y[1] (closed_form) = 3.0463642151148092094127005568
y[1] (numeric) = 3.0463642151148092094127005568019
absolute error = 1.9e-30
relative error = 6.2369430108618648882634938089965e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.08
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.08
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.09
y[1] (closed_form) = 3.057378631225556841524292961671
y[1] (numeric) = 3.0573786312255568415242929616695
absolute error = 1.5e-30
relative error = 4.9061636811359597731425939750546e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.09
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.09
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.1
y[1] (closed_form) = 3.068396370699609252320591657351
y[1] (numeric) = 3.0683963706996092523205916573512
absolute error = 2e-31
relative error = 6.5180627219422447082751781712274e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.1
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.1
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.11
y[1] (closed_form) = 3.07941743243285899094776214477
y[1] (numeric) = 3.0794174324328589909477621447694
absolute error = 6e-31
relative error = 1.9484204826559573349637356391209e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.11
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.11
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.12
y[1] (closed_form) = 3.090441815321931989156929086395
y[1] (numeric) = 3.0904418153219319891569290863968
absolute error = 1.8e-30
relative error = 5.8244099308903947525972377341318e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.12
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.12
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.13
y[1] (closed_form) = 3.101469518264186830843360690058
y[1] (numeric) = 3.1014695182641868308433606900597
absolute error = 1.7e-30
relative error = 5.4812726354036409244710418145453e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.13
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.13
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=578.2MB, alloc=44.3MB, time=6.47
TOP MAIN SOLVE Loop
x[1] = 28.14
y[1] (closed_form) = 3.112500540157714022555398705372
y[1] (numeric) = 3.1125005401577140225553987053717
absolute error = 3e-31
relative error = 9.6385525441482702864529636753414e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.14
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.14
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.15
y[1] (closed_form) = 3.123534879901335264971525297364
y[1] (numeric) = 3.1235348799013352649715252973637
absolute error = 3e-31
relative error = 9.6045029601038505898288055476046e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.15
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.15
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.16
y[1] (closed_form) = 3.134572536394602725343961263341
y[1] (numeric) = 3.1345725363946027253439612633401
absolute error = 9e-31
relative error = 2.8712048917367962049609902448530e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.16
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.16
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.17
y[1] (closed_form) = 3.145613508537798310907193253025
y[1] (numeric) = 3.145613508537798310907193253026
absolute error = 1.0e-30
relative error = 3.1790300915411515922464142495749e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.17
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.17
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.18
y[1] (closed_form) = 3.156657795231932943249830838689
y[1] (numeric) = 3.1566577952319329432498308386903
absolute error = 1.3e-30
relative error = 4.1182797893506968649193092288577e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.18
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.18
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.19
y[1] (closed_form) = 3.167705395378745833648197461165
y[1] (numeric) = 3.1677053953787458336481974611642
absolute error = 8e-31
relative error = 2.5254873801303994612303615751580e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.19
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.19
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.2
y[1] (closed_form) = 3.178756307880703759360062449532
y[1] (numeric) = 3.1787563078807037593600624495328
absolute error = 8e-31
relative error = 2.5167075501090075224219269885654e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.2
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.2
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.21
y[1] (closed_form) = 3.189810531641000340876924476784
y[1] (numeric) = 3.1898105316410003408769244767857
absolute error = 1.7e-30
relative error = 5.3294701460698788506431873629050e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.21
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.21
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.22
y[1] (closed_form) = 3.200868065563555320133259970891
y[1] (numeric) = 3.2008680655635553201332599708895
absolute error = 1.5e-30
relative error = 4.6862287644333290720753540047532e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.22
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.22
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.23
y[1] (closed_form) = 3.211928908553013839671153150604
y[1] (numeric) = 3.2119289085530138396711531506059
absolute error = 1.9e-30
relative error = 5.9154484862367554989636468285867e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.23
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.23
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.24
y[1] (closed_form) = 3.22299305951474572275872749795
y[1] (numeric) = 3.2229930595147457227587274979489
absolute error = 1.1e-30
relative error = 3.4129766328619278842694022642283e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.24
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.24
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.25
y[1] (closed_form) = 3.234060517354844754460801614467
y[1] (numeric) = 3.2340605173548447544608016144687
absolute error = 1.7e-30
relative error = 5.2565497487673453128173677086705e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.25
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.25
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.26
y[1] (closed_form) = 3.24513128098012796366019553659
y[1] (numeric) = 3.2451312809801279636601955365884
absolute error = 1.6e-30
relative error = 4.9304630890518288223537981767591e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.26
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.26
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.27
y[1] (closed_form) = 3.256205349298134906028116706024
y[1] (numeric) = 3.2562053492981349060281167060232
absolute error = 8e-31
relative error = 2.4568475086266827451520691214049e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.27
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.27
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.28
y[1] (closed_form) = 3.267282721217126947942057904898
y[1] (numeric) = 3.267282721217126947942057904898
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.28
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.28
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.29
y[1] (closed_form) = 3.278363395646086551349642571566
y[1] (numeric) = 3.2783633956460865513496425715661
absolute error = 1e-31
relative error = 3.0503024811955724601271954566789e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.29
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.29
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.3
y[1] (closed_form) = 3.289447371494716559576856012344
y[1] (numeric) = 3.2894473714947165595768560123438
absolute error = 2e-31
relative error = 6.0800486347079177079733671687253e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.3
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.3
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.31
y[1] (closed_form) = 3.30053464767343948407910411642
y[1] (numeric) = 3.3005346476734394840791041164215
absolute error = 1.5e-30
relative error = 4.5447182354451458349550616179944e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.31
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.31
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.32
y[1] (closed_form) = 3.311625223093396792133544266125
y[1] (numeric) = 3.3116252230933967921335442661241
absolute error = 9e-31
relative error = 2.7176988317515830344698764566765e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.32
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.32
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.33
y[1] (closed_form) = 3.322719096666448195471136212477
y[1] (numeric) = 3.3227190966664481954711362124772
absolute error = 2e-31
relative error = 6.0191666578330993655104635228426e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.33
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.33
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.34
y[1] (closed_form) = 3.333816267305170939846863756718
y[1] (numeric) = 3.3338162673051709398468637567195
absolute error = 1.5e-30
relative error = 4.4993481335805509468338649066383e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.34
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.34
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.35
y[1] (closed_form) = 3.344916733922859095546581142001
y[1] (numeric) = 3.3449167339228590955465811420007
absolute error = 3e-31
relative error = 8.9688331239314682142613405828152e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.35
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.35
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.36
y[1] (closed_form) = 3.356020495433522848828941116035
y[1] (numeric) = 3.3560204954335228488289411160355
absolute error = 5e-31
relative error = 1.4898597928121746283508230144627e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.36
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.36
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.37
y[1] (closed_form) = 3.367127550751887794300864674969
y[1] (numeric) = 3.3671275507518877943008646749696
absolute error = 6e-31
relative error = 1.7819342776783687230284183389648e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.37
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.37
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.38
y[1] (closed_form) = 3.378237898793394228225015541171
y[1] (numeric) = 3.378237898793394228225015541171
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.38
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.38
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.39
y[1] (closed_form) = 3.389351538474196442757745463105
y[1] (numeric) = 3.3893515384741964427577454631033
absolute error = 1.7e-30
relative error = 5.0157087003294400606947914599690e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.39
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.39
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.4
y[1] (closed_form) = 3.400468468711162021115979453895
y[1] (numeric) = 3.4004684687111620211159794538958
absolute error = 8e-31
relative error = 2.3526170213341640444219347910345e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.4
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.4
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.41
y[1] (closed_form) = 3.411588688421871133671513106702
y[1] (numeric) = 3.4115886884218711336715131067015
absolute error = 5e-31
relative error = 1.4655928532559692557803546981982e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.41
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.41
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.42
y[1] (closed_form) = 3.422712196524615834971197139464
y[1] (numeric) = 3.4227121965246158349711971394632
absolute error = 8e-31
relative error = 2.3373276923847443704431980568398e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.42
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.42
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.43
y[1] (closed_form) = 3.433838991938399361681487329294
y[1] (numeric) = 3.433838991938399361681487329295
absolute error = 1.0e-30
relative error = 2.9121924538328478838772703793341e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.43
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.43
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.44
y[1] (closed_form) = 3.444969073582935431455840997357
y[1] (numeric) = 3.4449690735829354314558409973578
absolute error = 8e-31
relative error = 2.3222269428618152460042328834006e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.44
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.44
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.45
y[1] (closed_form) = 3.456102440378647542723444198876
y[1] (numeric) = 3.4561024403786475427234441988768
absolute error = 8e-31
relative error = 2.3147462026974892093534624017380e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.45
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.45
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.46
y[1] (closed_form) = 3.467239091246668275397756759838
y[1] (numeric) = 3.4672390912466682753977567598367
absolute error = 1.3e-30
relative error = 3.7493808929472371022386479440502e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.46
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.46
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.47
y[1] (closed_form) = 3.478379025108838592503365281913
y[1] (numeric) = 3.4783790251088385925033652819148
absolute error = 1.8e-30
relative error = 5.1748242126767020210627944297013e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.47
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.47
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.48
y[1] (closed_form) = 3.48952224088770714271963721039
y[1] (numeric) = 3.4895222408877071427196372103888
absolute error = 1.2e-30
relative error = 3.4388661746850749212806574147867e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.48
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.48
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.49
y[1] (closed_form) = 3.500668737506529563839672026106
y[1] (numeric) = 3.500668737506529563839672026105
absolute error = 1.0e-30
relative error = 2.8565970532598409469403618135656e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.49
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.49
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.5
y[1] (closed_form) = 3.511818513889267787143048582135
y[1] (numeric) = 3.511818513889267787143048582134
absolute error = 1.0e-30
relative error = 2.8475275588558825587885333541237e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.5
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.5
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.51
y[1] (closed_form) = 3.522971568960589342680870558484
y[1] (numeric) = 3.5229715689605893426808705584839
absolute error = 1e-31
relative error = 2.8385128305052942811469496431617e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.51
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.51
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.52
y[1] (closed_form) = 3.534127901645866665471614954216
y[1] (numeric) = 3.5341279016458666654716149542175
absolute error = 1.5e-30
relative error = 4.2443285634949434342867579535807e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.52
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.52
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.53
y[1] (closed_form) = 3.545287510871176402606291475531
y[1] (numeric) = 3.5452875108711764026062914755308
absolute error = 2e-31
relative error = 5.6412914153429096752516439652012e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.53
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.53
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.54
y[1] (closed_form) = 3.556450395563298721261423610831
y[1] (numeric) = 3.5564503955632987212614236108303
absolute error = 7e-31
relative error = 1.9682546419690143540050677572349e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.54
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.54
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.55
y[1] (closed_form) = 3.567616554649716617618365109599
y[1] (numeric) = 3.5676165546497166176183651095985
absolute error = 5e-31
relative error = 1.4014959072559076424589630276125e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.55
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.55
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.56
y[1] (closed_form) = 3.57878598705861522668746850089
y[1] (numeric) = 3.5787859870586152266874685008894
absolute error = 6e-31
relative error = 1.6765461868065956706251964216040e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.56
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.56
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.57
y[1] (closed_form) = 3.589958691718881133035625199659
y[1] (numeric) = 3.5899586917188811330356251996593
absolute error = 3e-31
relative error = 8.3566421165798778398422056633104e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.57
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.57
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.58
y[1] (closed_form) = 3.601134667560101682415699654837
y[1] (numeric) = 3.6011346675601016824156996548353
absolute error = 1.7e-30
relative error = 4.7207343155311966475908106906317e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.58
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.58
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.59
y[1] (closed_form) = 3.612313913512564294296382892065
y[1] (numeric) = 3.6123139135125642942963828920661
absolute error = 1.1e-30
relative error = 3.0451395596745775373485382983610e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.59
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.59
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.6
y[1] (closed_form) = 3.623496428507255775290993696513
y[1] (numeric) = 3.6234964285072557752909936965134
absolute error = 4e-31
relative error = 1.1039061522265249019044531547384e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.6
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.6
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.61
y[1] (closed_form) = 3.634682211475861633483758566832
y[1] (numeric) = 3.6346822114758616334837585668316
absolute error = 4e-31
relative error = 1.1005088663241899177984591309172e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.61
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.61
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.62
y[1] (closed_form) = 3.645871261350765393652104450683
y[1] (numeric) = 3.6458712613507653936521044506829
absolute error = 1e-31
relative error = 2.7428286089002171827588459873432e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.62
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.62
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.63
y[1] (closed_form) = 3.657063577065047913383501144742
y[1] (numeric) = 3.6570635770650479133835011447427
absolute error = 7e-31
relative error = 1.9141039942263742409027714951129e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.63
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.63
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.64
y[1] (closed_form) = 3.6682591575524867000853931082
y[1] (numeric) = 3.6682591575524867000853931082006
absolute error = 6e-31
relative error = 1.6356532464852573488349640216101e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.64
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.64
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.65
y[1] (closed_form) = 3.67945800174755522888676329826
y[1] (numeric) = 3.6794580017475552288867632982615
absolute error = 1.5e-30
relative error = 4.0766873797379297855831763228377e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.65
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.65
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.66
y[1] (closed_form) = 3.690660108585422261429874489117
y[1] (numeric) = 3.6906601085854222614298744891183
absolute error = 1.3e-30
relative error = 3.5224051030217236246554115162676e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.66
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.66
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.67
y[1] (closed_form) = 3.701865477001951165550736382326
y[1] (numeric) = 3.701865477001951165550736382327
absolute error = 1.0e-30
relative error = 2.7013407326996526721766544245597e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.67
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.67
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.68
y[1] (closed_form) = 3.71307410593369923584684965647
y[1] (numeric) = 3.7130741059336992358468496564693
absolute error = 7e-31
relative error = 1.8852303509950448085335583407039e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.68
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.68
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.69
y[1] (closed_form) = 3.724285994317917015130780937469
y[1] (numeric) = 3.7242859943179170151307809374701
absolute error = 1.1e-30
relative error = 2.9535862758076373087646384577170e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.69
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.69
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.7
y[1] (closed_form) = 3.735501141092547616768125497954
y[1] (numeric) = 3.7355011410925476167681254979527
absolute error = 1.3e-30
relative error = 3.4801220797372855080217955191042e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.7
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.7
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.71
y[1] (closed_form) = 3.746719545196226047898417314582
y[1] (numeric) = 3.7467195451962260478984173145834
absolute error = 1.4e-30
relative error = 3.7366020677874840358965293133936e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.71
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.71
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.72
y[1] (closed_form) = 3.757941205568278533537548926501
y[1] (numeric) = 3.757941205568278533537548926501
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.72
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.72
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.73
y[1] (closed_form) = 3.769166121148721841560266345651
y[1] (numeric) = 3.7691661211487218415602663456524
absolute error = 1.4e-30
relative error = 3.7143494210685640177705433629620e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.73
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.73
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.74
y[1] (closed_form) = 3.780394290878262608561307071192
y[1] (numeric) = 3.7803942908782626085613070711909
absolute error = 1.1e-30
relative error = 2.9097493948030685196756480353290e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.74
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.74
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.75
y[1] (closed_form) = 3.791625713698296666593752055045
y[1] (numeric) = 3.7916257136982966665937520550461
absolute error = 1.1e-30
relative error = 2.9011302355766439088768999841507e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.75
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.75
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.76
y[1] (closed_form) = 3.802860388550908370783165254365
y[1] (numeric) = 3.8028603885509083707831652543664
absolute error = 1.4e-30
relative error = 3.6814393823525935414201039337535e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.76
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.76
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=622.4MB, alloc=44.3MB, time=6.95
TOP MAIN SOLVE Loop
x[1] = 28.77
y[1] (closed_form) = 3.814098314378869927816097188779
y[1] (numeric) = 3.8140983143788699278160971887803
absolute error = 1.3e-30
relative error = 3.4084071590370276505902811510536e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.77
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.77
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.78
y[1] (closed_form) = 3.825339490125640725301531696337
y[1] (numeric) = 3.8253394901256407253015316963381
absolute error = 1.1e-30
relative error = 2.8755617712870530958825140633732e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.78
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.78
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.79
y[1] (closed_form) = 3.836583914735366662003857851601
y[1] (numeric) = 3.8365839147353666620038578516003
absolute error = 7e-31
relative error = 1.8245397873651967428000915849469e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.79
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.79
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.8
y[1] (closed_form) = 3.847831587152879478945951772642
y[1] (numeric) = 3.8478315871528794789459517726429
absolute error = 9e-31
relative error = 2.3389797074407191306892580335087e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.8
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.8
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.81
y[1] (closed_form) = 3.859082506323696091380955800778
y[1] (numeric) = 3.8590825063236960913809558007771
absolute error = 9e-31
relative error = 2.3321605550677202193644259527297e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.81
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.81
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.82
y[1] (closed_form) = 3.870336671194017921631345287545
y[1] (numeric) = 3.870336671194017921631345287545
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.82
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.82
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.83
y[1] (closed_form) = 3.881594080710730232793875968064
y[1] (numeric) = 3.8815940807107302327938759680629
absolute error = 1.1e-30
relative error = 2.8338872564402382462719107887760e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.83
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.83
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.84
y[1] (closed_form) = 3.892854733821401463309007638069
y[1] (numeric) = 3.8928547338214014633090076380709
absolute error = 1.9e-30
relative error = 4.8807369653243507030849725419924e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.84
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.84
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.85
y[1] (closed_form) = 3.904118629474282562393402584115
y[1] (numeric) = 3.9041186294742825623934025841145
absolute error = 5e-31
relative error = 1.2806987887745833393337350765120e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.85
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.85
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.86
y[1] (closed_form) = 3.91538576661830632633409994215
y[1] (numeric) = 3.9153857666183063263340999421494
absolute error = 6e-31
relative error = 1.5324160523733429387559444462546e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.86
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.86
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.87
y[1] (closed_form) = 3.926656144203086735642969879551
y[1] (numeric) = 3.9266561442030867356429698795508
absolute error = 2e-31
relative error = 5.0933922567999627708723853582432e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.87
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.87
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.88
y[1] (closed_form) = 3.937929761178918293070054209024
y[1] (numeric) = 3.9379297611789182930700542090235
absolute error = 5e-31
relative error = 1.2697026872574599388568003457521e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.88
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.88
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.89
y[1] (closed_form) = 3.949206616496775362474402750277
y[1] (numeric) = 3.9492066164967753624744027502771
absolute error = 1e-31
relative error = 2.5321541694545991803403079398434e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.89
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.89
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.9
y[1] (closed_form) = 3.960486709108311508551017456562
y[1] (numeric) = 3.9604867091083115085510174565638
absolute error = 1.8e-30
relative error = 4.5448959489255883432796697565275e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.9
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.9
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.91
y[1] (closed_form) = 3.971770037965858837412519018287
y[1] (numeric) = 3.9717700379658588374125190182871
absolute error = 1e-31
relative error = 2.5177691317500088269926210355563e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.91
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.91
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.92
y[1] (closed_form) = 3.983056602022427338024153344901
y[1] (numeric) = 3.9830566020224273380241533449012
absolute error = 2e-31
relative error = 5.0212693412001344928852675159256e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.92
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.92
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.93
y[1] (closed_form) = 3.99434640023170422449075800924
y[1] (numeric) = 3.9943464002317042244907580092408
absolute error = 8e-31
relative error = 2.0028308009380297218294462629735e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.93
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.93
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.94
y[1] (closed_form) = 4.00563943154805327919431141527
y[1] (numeric) = 4.0056394315480532791943114152708
absolute error = 8e-31
relative error = 1.9971842540276403176901188908589e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.94
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.94
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.95
y[1] (closed_form) = 4.016935694926514196780690121041
y[1] (numeric) = 4.0169356949265141967806901210412
absolute error = 2e-31
relative error = 4.9789196340037203180742368729507e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.95
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.95
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.96
y[1] (closed_form) = 4.028235189322801928994262413381
y[1] (numeric) = 4.0282351893228019289942624133818
absolute error = 8e-31
relative error = 1.9859813600766698893013920573033e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.96
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.96
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.97
y[1] (closed_form) = 4.039537913693306030358948889602
y[1] (numeric) = 4.039537913693306030358948889602
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.97
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.97
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.98
y[1] (closed_form) = 4.05084386699509000470438345418
y[1] (numeric) = 4.0508438669950900047043834541788
absolute error = 1.2e-30
relative error = 2.9623457220289219069916702386420e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.98
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.98
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 28.99
y[1] (closed_form) = 4.062153048185890652535810785142
y[1] (numeric) = 4.0621530481858906525358107851399
absolute error = 2.1e-30
relative error = 5.1696722774584652348005167610001e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 30.99
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.99
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29
y[1] (closed_form) = 4.073465456224117419246358965598
y[1] (numeric) = 4.0734654562241174192463589655976
absolute error = 4e-31
relative error = 9.8196487560441572240718823277131e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.01
y[1] (closed_form) = 4.08478109006885174417032861067
y[1] (numeric) = 4.0847810900688517441703286106684
absolute error = 1.6e-30
relative error = 3.9169785717281386047198713028327e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.01
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.01
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.02
y[1] (closed_form) = 4.096099948679846410476142448853
y[1] (numeric) = 4.0960999486798464104761424488534
absolute error = 4e-31
relative error = 9.7653867095923307041755384103073e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.02
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.02
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.03
y[1] (closed_form) = 4.107422031017524895897601939855
y[1] (numeric) = 4.1074220310175248958976019398548
absolute error = 2e-31
relative error = 4.8692342420546040005420018596933e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.03
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.03
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.04
y[1] (closed_form) = 4.118747336042980724302100127793
y[1] (numeric) = 4.1187473360429807243021001277918
absolute error = 1.2e-30
relative error = 2.9135071954981351520510239219076e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.04
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.04
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.05
y[1] (closed_form) = 4.130075862717976818094442539865
y[1] (numeric) = 4.1300758627179768180944425398642
absolute error = 8e-31
relative error = 1.9370104244853387680490627751648e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.05
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.05
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.06
y[1] (closed_form) = 4.141407610004944851454930545708
y[1] (numeric) = 4.1414076100049448514549305457088
absolute error = 8e-31
relative error = 1.9317103635665671602893040144299e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.06
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.06
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.07
y[1] (closed_form) = 4.152742576866984604410364192021
y[1] (numeric) = 4.1527425768669846044103641920221
absolute error = 1.1e-30
relative error = 2.6488518843609356914050350741530e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.07
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.07
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.08
y[1] (closed_form) = 4.164080762267863317736624120493
y[1] (numeric) = 4.1640807622678633177366241204934
absolute error = 4e-31
relative error = 9.6059616236201413159446354577245e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.08
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.08
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.09
y[1] (closed_form) = 4.175422165172015048691494764723
y[1] (numeric) = 4.175422165172015048691494764721
absolute error = 2.0e-30
relative error = 4.7899348158909002509008429287832e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.09
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.09
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.1
y[1] (closed_form) = 4.18676678454454002757639360359
y[1] (numeric) = 4.1867667845445400275763936035887
absolute error = 1.3e-30
relative error = 3.1050212894564684741260442347871e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.1
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.1
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.11
y[1] (closed_form) = 4.198114619351204015125673824573
y[1] (numeric) = 4.1981146193512040151256738245717
absolute error = 1.3e-30
relative error = 3.0966281721029045949939042880162e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.11
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.11
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.12
y[1] (closed_form) = 4.209465668558437660722170320636
y[1] (numeric) = 4.2094656685584376607221703206362
absolute error = 2e-31
relative error = 4.7511968441470022576566100205754e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.12
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.12
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.13
y[1] (closed_form) = 4.220819931133335861437661508815
y[1] (numeric) = 4.2208199311333358614376615088143
absolute error = 7e-31
relative error = 1.6584455423855109100977608443987e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.13
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.13
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.14
y[1] (closed_form) = 4.232177406043657121896922017181
y[1] (numeric) = 4.2321774060436571218969220171816
absolute error = 6e-31
relative error = 1.4177099455783321348064037358189e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.14
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.14
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.15
y[1] (closed_form) = 4.243538092257822914964043839862
y[1] (numeric) = 4.2435380922578229149640438398627
absolute error = 7e-31
relative error = 1.6495669056844898122687116574450e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.15
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.15
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.16
y[1] (closed_form) = 4.25490198874491704324970610685
y[1] (numeric) = 4.2549019887449170432497061068503
absolute error = 3e-31
relative error = 7.0506911979068176740311144716055e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.16
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.16
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.17
y[1] (closed_form) = 4.26626909447468500143807615686
y[1] (numeric) = 4.2662690944746850014380761568605
absolute error = 5e-31
relative error = 1.1719842066398441474366508952069e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.17
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.17
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.18
y[1] (closed_form) = 4.277639408417533339432027137177
y[1] (numeric) = 4.277639408417533339432027137178
absolute error = 1.0e-30
relative error = 2.3377379543310763479882243372770e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.18
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.18
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.19
y[1] (closed_form) = 4.289012929544529026315359884481
y[1] (numeric) = 4.2890129295445290263153598844818
absolute error = 8e-31
relative error = 1.8652310290073102187940391209397e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.19
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.19
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.2
y[1] (closed_form) = 4.300389656827398815130719365
y[1] (numeric) = 4.3003896568273988151307193650017
absolute error = 1.7e-30
relative error = 3.9531301478716943503859629458090e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.2
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.2
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.21
y[1] (closed_form) = 4.311769589238528608471898471052
y[1] (numeric) = 4.3117695892385286084718984710528
absolute error = 8e-31
relative error = 1.8553867117497862174075165074363e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.21
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.21
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.22
y[1] (closed_form) = 4.323152725750962824889224484039
y[1] (numeric) = 4.3231527257509628248892244840392
absolute error = 2e-31
relative error = 4.6262534008732841325717487087446e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.22
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.22
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.23
y[1] (closed_form) = 4.334539065338403766106726021433
y[1] (numeric) = 4.3345390653384037661067260214333
absolute error = 3e-31
relative error = 6.9211511415130956693588139485601e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.23
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.23
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.24
y[1] (closed_form) = 4.345928606975210985049780787025
y[1] (numeric) = 4.3459286069752109850497807870262
absolute error = 1.2e-30
relative error = 2.7612050461988750182823343019252e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.24
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.24
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.25
y[1] (closed_form) = 4.357321349636400654681946939931
y[1] (numeric) = 4.3573213496364006546819469399328
absolute error = 1.8e-30
relative error = 4.1309783134314895113913883313614e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.25
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.25
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.26
y[1] (closed_form) = 4.368717292297644937649683388427
y[1] (numeric) = 4.3687172922976449376496833884287
absolute error = 1.7e-30
relative error = 3.8913023806718261652919219766459e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.26
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.26
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.27
y[1] (closed_form) = 4.380116433935271356733666799715
y[1] (numeric) = 4.3801164339352713567336667997134
absolute error = 1.6e-30
relative error = 3.6528709319320449323587518683336e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.27
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.27
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.28
y[1] (closed_form) = 4.39151877352626216610541559615
y[1] (numeric) = 4.3915187735262621661054155961489
absolute error = 1.1e-30
relative error = 2.5048281852538499198410261981917e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.28
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.28
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.29
y[1] (closed_form) = 4.402924310048253723387933682429
y[1] (numeric) = 4.4029243100482537233879336824296
absolute error = 6e-31
relative error = 1.3627306711375747386269908978420e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.29
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.29
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.3
y[1] (closed_form) = 4.41433304247953586251908911651
y[1] (numeric) = 4.4143330424795358625190891165095
absolute error = 5e-31
relative error = 1.1326739400685305667510942960600e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.3
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.3
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.31
y[1] (closed_form) = 4.425744969799051267416445399966
y[1] (numeric) = 4.4257449697990512674164453999646
absolute error = 1.4e-30
relative error = 3.1633092497500286340509817570889e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.31
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.31
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.32
y[1] (closed_form) = 4.437160090986394846442265520811
y[1] (numeric) = 4.4371600909863948464422655208129
absolute error = 1.9e-30
relative error = 4.2820181400703618458495375169253e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.32
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.32
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.33
y[1] (closed_form) = 4.448578405021813107667411333667
y[1] (numeric) = 4.4485784050218131076674113336678
absolute error = 8e-31
relative error = 1.7983273018115486924736666233184e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.33
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.33
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.34
y[1] (closed_form) = 4.459999910886203534932863308473
y[1] (numeric) = 4.4599999108862035349328633084744
absolute error = 1.4e-30
relative error = 3.1390135156343972047844194713502e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.34
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.34
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.35
y[1] (closed_form) = 4.471424607561113964707588119989
y[1] (numeric) = 4.4714246075611139647075881199887
absolute error = 3e-31
relative error = 6.7092711234067183903313708536519e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.35
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.35
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.36
y[1] (closed_form) = 4.482852494028741963741483985621
y[1] (numeric) = 4.4828524940287419637414839856217
absolute error = 7e-31
relative error = 1.5615057620843322037720507260748e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.36
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.36
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.37
y[1] (closed_form) = 4.494283569271934207512136089291
y[1] (numeric) = 4.494283569271934207512136089292
absolute error = 1.0e-30
relative error = 2.2250487415550376309130829421415e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.37
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.37
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.38
y[1] (closed_form) = 4.505717832274185859464116853533
y[1] (numeric) = 4.5057178322741858594641168535332
absolute error = 2e-31
relative error = 4.4388043691376328088391756933769e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.38
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.38
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=666.6MB, alloc=44.3MB, time=7.44
x[1] = 29.39
y[1] (closed_form) = 4.517155282019639951039568241296
y[1] (numeric) = 4.5171552820196399510395682412953
absolute error = 7e-31
relative error = 1.5496478564425771254615231335841e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.39
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.39
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.4
y[1] (closed_form) = 4.528595917493086762498805682677
y[1] (numeric) = 4.5285959174930867624988056826777
absolute error = 7e-31
relative error = 1.5457329661408647902638483426599e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.4
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.4
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.41
y[1] (closed_form) = 4.540039737679963204529685630248
y[1] (numeric) = 4.5400397376799632045296856302476
absolute error = 4e-31
relative error = 8.8104955707812094857435401155988e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.41
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.41
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.42
y[1] (closed_form) = 4.551486741566352200644481149648
y[1] (numeric) = 4.551486741566352200644481149648
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.42
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.42
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.43
y[1] (closed_form) = 4.562936928138982070363012349895
y[1] (numeric) = 4.562936928138982070363012349895
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.43
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.43
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.44
y[1] (closed_form) = 4.57439029638522591318078085012
y[1] (numeric) = 4.57439029638522591318078085012
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.44
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.44
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.45
y[1] (closed_form) = 4.585846845293100993320859866544
y[1] (numeric) = 4.5858468452931009933208598665426
absolute error = 1.4e-30
relative error = 3.0528712519846921323781343274914e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.45
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.45
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.46
y[1] (closed_form) = 4.597306573851268125268293885176
y[1] (numeric) = 4.5973065738512681252682938851747
absolute error = 1.3e-30
relative error = 2.8277426774063502926332144467359e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.46
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.46
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.47
y[1] (closed_form) = 4.608769481049031060085764262175
y[1] (numeric) = 4.6087694810490310600857642621753
absolute error = 3e-31
relative error = 6.5093296862336258525133707070332e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.47
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.47
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.48
y[1] (closed_form) = 4.620235565876335872509279464906
y[1] (numeric) = 4.6202355658763358725092794649047
absolute error = 1.3e-30
relative error = 2.8137093476389110397771113131241e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.48
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.48
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.49
y[1] (closed_form) = 4.631704827323770348822651032587
y[1] (numeric) = 4.6317048273237703488226510325873
absolute error = 3e-31
relative error = 6.4770966886795759417568290039345e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.49
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.49
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.5
y[1] (closed_form) = 4.64317726438256337550951869609
y[1] (numeric) = 4.6431772643825633755095186960891
absolute error = 9e-31
relative error = 1.9383278922039593142516306989193e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.5
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.5
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.51
y[1] (closed_form) = 4.654652876044584328681690451673
y[1] (numeric) = 4.6546528760445843286816904516718
absolute error = 1.2e-30
relative error = 2.5780655012447073572773934437927e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.51
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.51
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.52
y[1] (closed_form) = 4.666131661302342464282565733704
y[1] (numeric) = 4.6661316613023424642825657337058
absolute error = 1.8e-30
relative error = 3.8575851061553850597241555092776e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.52
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.52
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.53
y[1] (closed_form) = 4.677613619148986309064412176225
y[1] (numeric) = 4.6776136191489863090644121762257
absolute error = 7e-31
relative error = 1.4964895713796756717983118934585e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.53
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.53
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.54
y[1] (closed_form) = 4.689098748578303052338268792909
y[1] (numeric) = 4.689098748578303052338268792909
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.54
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.54
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.55
y[1] (closed_form) = 4.700587048584717938495250739561
y[1] (numeric) = 4.7005870485847179384952507395606
absolute error = 4e-31
relative error = 8.5095754182540773158273431962527e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.55
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.55
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.56
y[1] (closed_form) = 4.712078518163293660298033152513
y[1] (numeric) = 4.7120785181632936602980331525114
absolute error = 1.6e-30
relative error = 3.3955291573190062057562436038112e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.56
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.56
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.57
y[1] (closed_form) = 4.723573156309729752941293880494
y[1] (numeric) = 4.7235731563097297529412938804951
absolute error = 1.1e-30
relative error = 2.3287455568050734798501401122147e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.57
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.57
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.58
y[1] (closed_form) = 4.73507096202036198887989724657
y[1] (numeric) = 4.7350709620203619888798972465706
absolute error = 6e-31
relative error = 1.2671404606447371126074127013920e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.58
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.58
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.59
y[1] (closed_form) = 4.746571934292161773423603290526
y[1] (numeric) = 4.7465719342921617734236032905241
absolute error = 1.9e-30
relative error = 4.0028888770719531429431492149482e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.59
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.59
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.6
y[1] (closed_form) = 4.758076072122735541097089250916
y[1] (numeric) = 4.7580760721227355410970892509175
absolute error = 1.5e-30
relative error = 3.1525347162656864612171699297617e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.6
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.6
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.61
y[1] (closed_form) = 4.769583374510324152764072349574
y[1] (numeric) = 4.7695833745103241527640723495746
absolute error = 6e-31
relative error = 1.2579715100621337319610928534187e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.61
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.61
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.62
y[1] (closed_form) = 4.781093840453802293514325239817
y[1] (numeric) = 4.7810938404538022935143252398166
absolute error = 4e-31
relative error = 8.3662863216680474272032929338891e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.62
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.62
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.63
y[1] (closed_form) = 4.792607468952677871312377773189
y[1] (numeric) = 4.7926074689526778713123777731898
absolute error = 8e-31
relative error = 1.6692374770571872742494159123805e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.63
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.63
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.64
y[1] (closed_form) = 4.804124259007091416406701027788
y[1] (numeric) = 4.8041242590070914164067010277867
absolute error = 1.3e-30
relative error = 2.7060082752078562688402190760236e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.64
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.64
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.65
y[1] (closed_form) = 4.815644209617815481498171824554
y[1] (numeric) = 4.8156442096178154814981718245544
absolute error = 4e-31
relative error = 8.3062614800553391680705648427854e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.65
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.65
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.66
y[1] (closed_form) = 4.827167319786254042666618236228
y[1] (numeric) = 4.8271673197862540426666182362289
absolute error = 9e-31
relative error = 1.8644474914116956927752848165189e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.66
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.66
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.67
y[1] (closed_form) = 4.838693588514441901054248866742
y[1] (numeric) = 4.8386935885144419010542488667407
absolute error = 1.3e-30
relative error = 2.6866755999714403690475280337667e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.67
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.67
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.68
y[1] (closed_form) = 4.850223014805044085304770947121
y[1] (numeric) = 4.8502230148050440853047709471198
absolute error = 1.2e-30
relative error = 2.4741130383841418002214425416806e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.68
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.68
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.69
y[1] (closed_form) = 4.861755597661355254757004557097
y[1] (numeric) = 4.8617555976613552547570045570977
absolute error = 7e-31
relative error = 1.4398091099781325925152127977749e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.69
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.69
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.7
y[1] (closed_form) = 4.873291336087299103391802539778
y[1] (numeric) = 4.8732913360872991033918025397773
absolute error = 7e-31
relative error = 1.4364008874585788750007283781057e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.7
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.7
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.71
y[1] (closed_form) = 4.884830229087427764531087929926
y[1] (numeric) = 4.8848302290874277645310879299257
absolute error = 3e-31
relative error = 6.1414621579600992295974586057509e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.71
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.71
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.72
y[1] (closed_form) = 4.896372275666921216287822964655
y[1] (numeric) = 4.896372275666921216287822964655
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.72
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.72
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.73
y[1] (closed_form) = 4.907917474831586687765725988508
y[1] (numeric) = 4.9079174748315866877657259885088
absolute error = 8e-31
relative error = 1.6300192578675168009468459353044e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.73
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.73
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.74
y[1] (closed_form) = 4.91946582558785806600755480327
y[1] (numeric) = 4.9194658255878580660075548032695
absolute error = 5e-31
relative error = 1.0163705120164176354368556853052e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.74
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.74
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.75
y[1] (closed_form) = 4.93101732694279530369077724617
y[1] (numeric) = 4.9310173269427953036907772461694
absolute error = 6e-31
relative error = 1.2167874501710518845556489234425e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.75
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.75
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.76
y[1] (closed_form) = 4.942571977904083827569452008626
y[1] (numeric) = 4.9425719779040838275694520086258
absolute error = 2e-31
relative error = 4.0464762252144428985701220379581e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.76
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.76
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.77
y[1] (closed_form) = 4.954129777480033947661144931151
y[1] (numeric) = 4.9541297774800339476611449311522
absolute error = 1.2e-30
relative error = 2.4222215684676544997134623016867e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.77
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.77
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.78
y[1] (closed_form) = 4.965690724679580267177708228728
y[1] (numeric) = 4.9656907246795802671777082287262
absolute error = 1.8e-30
relative error = 3.6248733555917300814406532308388e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.78
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.78
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.79
y[1] (closed_form) = 4.977254818512281093198752314637
y[1] (numeric) = 4.9772548185122810931987523146369
absolute error = 1e-31
relative error = 2.0091396491910042577457352550939e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.79
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.79
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.8
y[1] (closed_form) = 4.988822057988317848086642099704
y[1] (numeric) = 4.9888220579883178480866420997047
absolute error = 7e-31
relative error = 1.4031368364384327891934008500578e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.8
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.8
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.81
y[1] (closed_form) = 5.000392442118494481641851847771
y[1] (numeric) = 5.0003924421184944816418518477714
absolute error = 4e-31
relative error = 7.9993721418900021896694311580528e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.81
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.81
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.82
y[1] (closed_form) = 5.011965969914236883997514867516
y[1] (numeric) = 5.0119659699142368839975148675151
absolute error = 9e-31
relative error = 1.7957025354970646468411259846741e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.82
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.82
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.83
y[1] (closed_form) = 5.023542640387592299252006514963
y[1] (numeric) = 5.0235426403875922992520065149613
absolute error = 1.7e-30
relative error = 3.3840660300811863053242090439640e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.83
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.83
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.84
y[1] (closed_form) = 5.035122452551228739838401170559
y[1] (numeric) = 5.0351224525512287398384011705569
absolute error = 2.1e-30
relative error = 4.1707029367993985533179935889332e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.84
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.84
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.85
y[1] (closed_form) = 5.04670540541843440162964603935
y[1] (numeric) = 5.0467054054184344016296460393488
absolute error = 1.2e-30
relative error = 2.3777888812602588068578253240743e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.85
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.85
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.86
y[1] (closed_form) = 5.058291498003117079778296802692
y[1] (numeric) = 5.0582914980031170797782968026904
absolute error = 1.6e-30
relative error = 3.1631233601931377447353437867517e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.86
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.86
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.87
y[1] (closed_form) = 5.069880729319803585289662324984
y[1] (numeric) = 5.0698807293198035852896623249833
absolute error = 7e-31
relative error = 1.3807030921887484507128165777808e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.87
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.87
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.88
y[1] (closed_form) = 5.081473098383639162327207789276
y[1] (numeric) = 5.0814730983836391623272077892755
absolute error = 5e-31
relative error = 9.8396663786145894170252101789477e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.88
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.88
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.89
y[1] (closed_form) = 5.09306860421038690624906780108
y[1] (numeric) = 5.0930686042103869062490678010799
absolute error = 1e-31
relative error = 1.9634528370053966844339957776901e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.89
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.89
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.9
y[1] (closed_form) = 5.10466724581642718237452316057
y[1] (numeric) = 5.1046672458164271823745231605701
absolute error = 1e-31
relative error = 1.9589915499772455880337362741481e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.9
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.9
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.91
y[1] (closed_form) = 5.11626902221875704547929715936
y[1] (numeric) = 5.1162690222187570454792971593599
absolute error = 1e-31
relative error = 1.9545492929657029617054358268266e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.91
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.91
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.92
y[1] (closed_form) = 5.127873932434989660018529409394
y[1] (numeric) = 5.1278739324349896600185294093939
absolute error = 1e-31
relative error = 1.9501259453255442041256345487164e-30 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.92
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.92
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.93
y[1] (closed_form) = 5.139481975483353721076287358078
y[1] (numeric) = 5.1394819754833537210762873580786
absolute error = 6e-31
relative error = 1.1674328324569553522610225112487e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.93
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.93
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.94
y[1] (closed_form) = 5.15109315038269287604047778568
y[1] (numeric) = 5.1510931503826928760404777856808
absolute error = 8e-31
relative error = 1.5530684005210916807274197237493e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.94
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.94
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.95
y[1] (closed_form) = 5.162707456152465147002022718222
y[1] (numeric) = 5.1627074561524651470020227182213
absolute error = 7e-31
relative error = 1.3558777171574983590425649390061e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.95
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.95
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.96
y[1] (closed_form) = 5.174324891812742353877166321615
y[1] (numeric) = 5.1743248918127423538771663216137
absolute error = 1.3e-30
relative error = 2.5124050522165137859660280891468e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.96
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.96
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.97
y[1] (closed_form) = 5.185945456384209538251781470644
y[1] (numeric) = 5.1859454563842095382517814706458
absolute error = 1.8e-30
relative error = 3.4709196522383245758349679399900e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.97
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.97
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.98
y[1] (closed_form) = 5.197569148888164387946546809591
y[1] (numeric) = 5.1975691488881643879465468095922
absolute error = 1.2e-30
relative error = 2.3087715923061792215738710227135e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.98
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.98
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 29.99
y[1] (closed_form) = 5.20919596834651666230186723979
y[1] (numeric) = 5.2091959683465166623018672397889
absolute error = 1.1e-30
relative error = 2.1116502559782903528020083210481e-29 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 32
h = 0.005
Radius of convergence (given) for eq 1 = 31.99
Order of pole (given) = 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.99
Order of pole (three term test) = 1
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff ( y , x , 1 ) = ln ( 0.1 * x + 0.2 ) ;
Iterations = 2000
Total Elapsed Time = 7 Seconds
Elapsed Time(since restart) = 7 Seconds
Time to Timeout = 2 Minutes 52 Seconds
Percent Done = 100 %
> quit
memory used=709.7MB, alloc=44.3MB, time=7.91