|\^/| Maple 2016 (X86 64 LINUX)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2016
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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#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_complex := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> if vallen = 4 then
> printf("%-30s = %-20.4g %-20g %s \n",prelabel,Re(value), Im(value), postlabel);
> else
> printf("%-30s = %-20.12g %-20.12g %s \n",prelabel,Re(value),Im(value), postlabel);
> fi;# end if 0;
> fi;# end if -1;
> end;
omniout_complex := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then printf("%-30s = %-20.4g %-20g %s \n", prelabel,
Re(value), Im(value), postlabel)
else printf("%-30s = %-20.12g %-20.12g %s \n", prelabel, Re(value),
Im(value), postlabel)
end if
end if
end proc
# End Function number 6
# Begin Function number 7
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number -1
> if vallen = 5 then # if number 0
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;# end if 0;
> fi;# end if -1;
> 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 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 -1
> 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 0
> 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 1
> 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 2
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 3
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 3
> else
> fprintf(fd," 0.0 Seconds");
> fi;# end if 2
> 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 2
> 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 3
> 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 4
> 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 5
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 6
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 6
> else
> printf(" 0.0 Seconds\n");
> fi;# end if 5
> 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 5
> 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 6
> ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]);
> fi;# end if 6;
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 5;
> 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 5
> 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 6
> ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att);
> fi;# end if 6;
> iii_att := iii_att + 1;
> od;# end do number 1;
> ret_att := ret_att / c(mmm_att) ;
> fi;# end if 5;
> 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_complex := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g + %g I",Re(x),Im(x));
> fprintf(file," | ");
> end;
logitem_complex := proc(file, x)
fprintf(file, "");
fprintf(file, "%g + %g I", Re(x), Im(x));
fprintf(file, " | ")
end proc
# End Function number 19
# Begin Function number 20
> logitem_h_reason := proc(file)
> global glob_h_reason;
> fprintf(file,"");
> if (glob_h_reason = 1) then # if number 5
> fprintf(file,"Max H");
> elif
> (glob_h_reason = 2) then # if number 6
> fprintf(file,"Display Interval");
> elif
> (glob_h_reason = 3) then # if number 7
> fprintf(file,"Optimal");
> elif
> (glob_h_reason = 4) then # if number 8
> fprintf(file,"Pole Accuracy");
> elif
> (glob_h_reason = 5) then # if number 9
> fprintf(file,"Min H (Pole)");
> elif
> (glob_h_reason = 6) then # if number 10
> fprintf(file,"Pole");
> elif
> (glob_h_reason = 7) then # if number 11
> fprintf(file,"Opt Iter");
> else
> fprintf(file,"Impossible");
> fi;# end if 11
> 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 20
# Begin Function number 21
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
# End Function number 21
# Begin Function number 22
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file) fprintf(file, "\n") end proc
# End Function number 22
# Begin Function number 23
> chk_data := proc()
> global glob_max_iter,ALWAYS, ATS_MAX_TERMS;
> local errflag;
> errflag := false;
> if (glob_max_iter < 2) then # if number 11
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 11;
> if (errflag) then # if number 11
> quit;
> fi;# end if 11
> 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 23
# Begin Function number 24
> 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 11
> sec_left := glob__0;
> else
> if (sub2 > glob__0) then # if number 12
> rrr := (sub1/sub2);
> sec_left := rrr * c(ms2) - c(ms2);
> else
> sec_left := glob__0;
> fi;# end if 12
> fi;# end if 11;
> 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 24
# Begin Function number 25
> 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 11
> rrr := (glob__100*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 11;
> 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 25
# Begin Function number 26
> 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 11
> ret := float_abs(term1 * glob_h / term2);
> else
> ret := glob_larger_float;
> fi;# end if 11;
> 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 26
# Begin Function number 27
> 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 11
> 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 11;
> 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 27
# Begin Function number 28
> c := proc(in_val)
> #To Force Conversion when needed
> local ret;
> ret := evalc(in_val);
> ret;
> #End Conversion
> end;
c := proc(in_val) local ret; ret := evalc(in_val); ret end proc
# End Function number 28
# Begin Function number 29
> 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 11
> ret := float_abs((term2*glob_h*term1)/(temp));
> else
> ret := glob_larger_float;
> fi;# end if 11;
> 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 29
# Begin Function number 30
> 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 30
# Begin Function number 31
> 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 11
> 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 12
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> else
> if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0) then # if number 13
> 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 14
> if (rcs > glob__0) then # if number 15
> rad_c := float_abs( sqrt(rcs) * float_abs(glob_h));
> 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
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 13
> fi;# end if 12
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 11;
> 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 := float_abs(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 31
# Begin Function number 32
> 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 32
# Begin Function number 33
> 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 33
# Begin Function number 34
> factorial_1 := proc(nnn)
> global ATS_MAX_TERMS,array_fact_1;
> local ret;
> if (nnn <= ATS_MAX_TERMS) then # if number 11
> if (array_fact_1[nnn] = 0) then # if number 12
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 12;
> else
> ret := factorial_2(nnn);
> fi;# end if 11;
> 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 34
# Begin Function number 35
> 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 11
> if (array_fact_2[mmm,nnn] = 0) then # if number 12
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 12;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 11;
> 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 35
# Begin Function number 36
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
# End Function number 36
# Begin Function number 37
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
# End Function number 37
# Begin Function number 38
> float_abs := proc(x)
> abs(x);
> end;
float_abs := proc(x) abs(x) end proc
# End Function number 38
# Begin Function number 39
> expt := proc(x,y)
> x^y;
> end;
expt := proc(x, y) x^y end proc
# End Function number 39
# Begin Function number 40
> neg := proc(x)
> -x;
> end;
neg := proc(x) -x end proc
# End Function number 40
# Begin Function number 41
> int_trunc := proc(x)
> trunc(x);
> end;
int_trunc := proc(x) trunc(x) end proc
# End Function number 41
# Begin Function number 42
> 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 42
#END ATS LIBRARY BLOCK
#BEGIN USER FUNCTION BLOCK
#BEGIN BLOCK 3
#BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return(c(2.0)*expt(c(x),c(1.5))/c(3.0));
> end;
exact_soln_y := proc(x) return c(2.0)*expt(c(x), c(1.5))/c(3.0) end proc
> next_delta := proc()
> global glob_nxt, x_delta;
> x_delta := [ 0.001 + 0.00004 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.000 + 0.000 * I ];
> glob_nxt := glob_nxt + 1;
> it := x_delta[glob_nxt];
> return it;
> end;
Warning, `it` is implicitly declared local to procedure `next_delta`
next_delta := proc()
local it;
global glob_nxt, x_delta;
x_delta := [0.001 + 0.00004*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0. + 0.*I];
glob_nxt := glob_nxt + 1;
it := x_delta[glob_nxt];
return it
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 := float_abs(array_x[1] - (array_given_rad_poles[1,1] + array_given_rad_poles[1,2] * I ));
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," ");
> omniout_complex(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," ");
> if ((float_abs(rad_given) < float_abs(glob_least_given_sing)) and
> (float_abs(rad_given) > 0.0)) 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 ((float_abs(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_complex(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 ((float_abs(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_complex(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 ((float_abs(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_complex(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 := float_abs(array_x[1] - array_given_rad_poles[1, 1]
- array_given_rad_poles[1, 2]*I);
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 1 ", 4,
rad_given, 4, " ");
omniout_complex(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles[1, 1], 4, " ");
if float_abs(rad_given) < float_abs(glob_least_given_sing) and
0. < float_abs(rad_given) 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 float_abs(array_rad_test_poles[1, 1]) < glob_least_ratio_sing
then glob_least_ratio_sing := array_rad_test_poles[1, 1]
end if;
omniout_complex(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 float_abs(array_rad_test_poles[1, 2]) < glob_least_3_sing then
glob_least_3_sing := array_rad_test_poles[1, 2]
end if;
omniout_complex(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 float_abs(array_rad_test_poles[1, 3]) < glob_least_6_sing then
glob_least_6_sing := array_rad_test_poles[1, 3]
end if;
omniout_complex(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_h,
> glob_nxt,
> 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_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,
#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_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_h, glob_nxt, 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_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_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_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_h,
> glob_nxt,
> 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_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,
#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_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_h, glob_nxt, 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_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_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_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_h,
> glob_nxt,
> 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_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,
#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_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_h, glob_nxt, 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_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_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_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_h,
> glob_nxt,
> 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_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,
#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_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_h, glob_nxt, 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_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_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_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_h,
> glob_nxt,
> 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_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,
#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_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
> ind_var := array_x[1];
> omniout_complex(ALWAYS,"x[1] ",33,ind_var,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> omniout_complex(ALWAYS,"h ",33,glob_h,20," ");
> omniout_complex(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> closed_form_val_y := evalf(exact_soln_y(ind_var));
> omniout_complex(ALWAYS,"y[1] (closed_form) ",33,closed_form_val_y,20," ");
> abserr := float_abs(numeric_val - closed_form_val_y);
> if (float_abs(closed_form_val_y) > 0.0) then # if number 3
> relerr := abserr/float_abs(closed_form_val_y);
> if (float_abs(c(relerr)) > 0.0) then # if number 4
> glob_good_digits := round(-log10(relerr));
> else
> relerr := 0.0 ;
> glob_good_digits := Digits - 2;
> fi;# end if 4;
> else
> ;
> relerr := glob__m1 ;
> glob_good_digits := -16;
> fi;# end if 3;
> if (glob_good_digits < glob_min_good_digits) then # if number 3
> glob_min_good_digits := glob_good_digits;
> fi;# end if 3;
> omniout_float(ALWAYS,"absolute error ",4,abserr,4," ");
> omniout_float(ALWAYS,"relative error ",4,relerr * glob__100 ,4,"%");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> #BOTTOM DISPLAY ALOT
> 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_h, glob_nxt, 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_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_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_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;
ind_var := array_x[1];
omniout_complex(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
omniout_complex(ALWAYS, "h ", 33, glob_h,
20, " ");
omniout_complex(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
closed_form_val_y := evalf(exact_soln_y(ind_var));
omniout_complex(ALWAYS, "y[1] (closed_form) ", 33,
closed_form_val_y, 20, " ");
abserr := float_abs(numeric_val - closed_form_val_y);
if 0. < float_abs(closed_form_val_y) then
relerr := abserr/float_abs(closed_form_val_y);
if 0. < float_abs(c(relerr)) then
glob_good_digits := round(-log10(relerr))
else relerr := 0.; glob_good_digits := Digits - 2
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;
omniout_float(ALWAYS, "absolute error ", 4, abserr, 4,
" ");
omniout_float(ALWAYS, "relative error ", 4,
relerr*glob__100, 4, "%");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ")
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_h,
> glob_nxt,
> 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_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,
#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_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));
> 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;
> #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_h, glob_nxt, 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_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_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_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);
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
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_h,
> glob_nxt,
> 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_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,
#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_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
> ;
> if (true) 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_h, glob_nxt, 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_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_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_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;
display_poles()
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_h,
> glob_nxt,
> 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_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,
#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_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 sqrt 1 $eq_no = 1
> array_tmp1[1] := sqrt(array_x[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp2[1] := array_const_0D0[1] + array_tmp1[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_tmp2[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 sqrt 2 $eq_no = 1
> array_tmp1[2] := array_x[2] / array_tmp1[1]/glob__2;
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[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_tmp2[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 sqrt ID_LINEAR iii = 3 $eq_no = 1
> array_tmp1[3] := 0;
> array_tmp1[3] := neg(ats(3,array_tmp1,array_tmp1,2)) / array_tmp1[1] /glob__2;
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp2[3] := array_tmp1[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_tmp2[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 sqrt ID_LINEAR iii = 4 $eq_no = 1
> array_tmp1[4] := 0;
> array_tmp1[4] := neg(ats(4,array_tmp1,array_tmp1,2)) / array_tmp1[1] /glob__2;
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp2[4] := array_tmp1[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_tmp2[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 sqrt ID_LINEAR iii = 5 $eq_no = 1
> array_tmp1[5] := 0;
> array_tmp1[5] := neg(ats(5,array_tmp1,array_tmp1,2)) / array_tmp1[1] /glob__2;
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp2[5] := array_tmp1[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_tmp2[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 sqrt LINEAR $eq_no = 1
> array_tmp1[kkk] := 0;
> array_tmp1[kkk] := neg(ats(kkk,array_tmp1,array_tmp1,2)) /array_tmp1[1] / glob__2;
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp2[kkk] := array_tmp1[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_tmp2[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_h, glob_nxt, 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_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_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_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] := sqrt(array_x[1]);
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
if not array_y_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[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_x[2]/(array_tmp1[1]*glob__2);
array_tmp2[2] := array_tmp1[2];
if not array_y_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[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_tmp1[3] := 0;
array_tmp1[3] :=
neg(ats(3, array_tmp1, array_tmp1, 2))/(array_tmp1[1]*glob__2);
array_tmp2[3] := array_tmp1[3];
if not array_y_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[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_tmp1[4] := 0;
array_tmp1[4] :=
neg(ats(4, array_tmp1, array_tmp1, 2))/(array_tmp1[1]*glob__2);
array_tmp2[4] := array_tmp1[4];
if not array_y_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[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_tmp1[5] := 0;
array_tmp1[5] :=
neg(ats(5, array_tmp1, array_tmp1, 2))/(array_tmp1[1]*glob__2);
array_tmp2[5] := array_tmp1[5];
if not array_y_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[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_tmp1[kkk] := 0;
array_tmp1[kkk] := neg(ats(kkk, array_tmp1, array_tmp1, 2))/(
array_tmp1[1]*glob__2);
array_tmp2[kkk] := array_tmp1[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_tmp2[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_h,
> glob_nxt,
> 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_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,
> #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_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 := 40;
> # before first input block
> #BEGIN FIRST INPUT BLOCK
> #BEGIN BLOCK 1
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=40;
> #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..(40),[]);
> array_norms:= Array(0..(40),[]);
> array_fact_1:= Array(0..(40),[]);
> 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..(40),[]);
> array_x:= Array(0..(40),[]);
> array_tmp0:= Array(0..(40),[]);
> array_tmp1:= Array(0..(40),[]);
> array_tmp2:= Array(0..(40),[]);
> array_m1:= Array(0..(40),[]);
> array_y_higher := Array(0..(2) ,(0..40+ 1),[]);
> array_y_higher_work := Array(0..(2) ,(0..40+ 1),[]);
> array_y_higher_work2 := Array(0..(2) ,(0..40+ 1),[]);
> array_y_set_initial := Array(0..(2) ,(0..40+ 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..(40) ,(0..40+ 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 <= 40) do # do number 1
> array_y_init[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_norms[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) 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 <= 40) do # do number 1
> array_y[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_x[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp0[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) 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 <= 40) 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 <= 40) 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 <= 40) 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 <= 40) 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 <=40) do # do number 1
> term := 1;
> while (term <= 40) 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_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_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_h := 0.1;
> glob_nxt := 1;
> 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_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 := 10000;
> 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;
> array_y_set_initial[1,31] := false;
> array_y_set_initial[1,32] := false;
> array_y_set_initial[1,33] := false;
> array_y_set_initial[1,34] := false;
> array_y_set_initial[1,35] := false;
> array_y_set_initial[1,36] := false;
> array_y_set_initial[1,37] := false;
> array_y_set_initial[1,38] := false;
> array_y_set_initial[1,39] := false;
> array_y_set_initial[1,40] := false;
> # before generate init omniout const
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> ATS_MAX_TERMS := 40;
> 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 := 10000;
> glob_max_hours := (0.0);
> glob_max_minutes := (15.0);
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/sqrt_tonepostcpx.cpx#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = sqrt ( x ) ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=40;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := 0.5 + 0.1 * I;");
> omniout_str(ALWAYS,"x_end := 99.0 + 99.0 * I;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_h := c(0.01);");
> 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(0.0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_rad_poles[1,2] := c(0.0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_ord_poles[1,1] := c(1.5);");
> 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:=10000;");
> omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);");
> omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);");
> omniout_str(ALWAYS,"glob_look_poles:=true;");
> omniout_str(ALWAYS,"glob_h:=c(0.001);");
> omniout_str(ALWAYS,"glob_display_interval:=c(0.01);");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"return(c(2.0)*expt(c(x),c(1.5))/c(3.0));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"next_delta := proc()");
> omniout_str(ALWAYS,"global glob_nxt, x_delta;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"x_delta := [ 0.001 + 0.00004 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.000 + 0.000 * I ];");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_nxt := glob_nxt + 1;");
> omniout_str(ALWAYS,"it := x_delta[glob_nxt];");
> omniout_str(ALWAYS,"return it;");
> omniout_str(ALWAYS,"end;");
> 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 := 0.5 + 0.1 * I;
> x_end := 99.0 + 99.0 * I;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_max_h := c(0.01);
> glob_min_h := c(0.001);
> glob_type_given_pole := 1;
> array_given_rad_poles[1,1] := c(0.0);
> array_given_rad_poles[1,2] := c(0.0);
> array_given_ord_poles[1,1] := c(1.5);
> 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:=10000;
> glob_upper_ratio_limit:=c(1.000001);
> glob_lower_ratio_limit:=c(0.999999);
> glob_look_poles:=true;
> glob_h:=c(0.001);
> glob_display_interval:=c(0.01);
> #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
> found_h := true;
> glob_h := next_delta();
> #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
> #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
> found_h := true;
> 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;
> found_h := true;
> glob_h := next_delta();
> #START ADJUST ALL SERIES
> if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 10
> 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 11
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> h_new := glob_min_h;
> glob_h_reason := 5;
> fi;# end if 11;
> 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 10;
> #BOTTOM ADJUST ALL SERIES
> #END OPTIMIZE CODE
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_iter < glob_max_iter) and ((glob_iter < 10) or ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0))))) do # do number 1
> #left paren 0001C
> if (true) then # if number 10
> omniout_str(INFO," ");
> fi;# end if 10;
> found_h := true;
> glob_h := next_delta();
> #START ADJUST ALL SERIES
> if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 10
> 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 11
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> h_new := glob_min_h;
> glob_h_reason := 5;
> fi;# end if 11;
> term := 1;
> ratio := c(1.0);
> while (term <= ATS_MAX_TERMS) do # do number 2
> 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 2;
> glob_h := h_new;
> fi;# end if 10;
> #BOTTOM ADJUST ALL SERIES
> #END OPTIMIZE CODE
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> atomall();
> if ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0))) then # if number 10
> display_alot(current_iter);
> fi;# end if 10;
> if ((glob_look_poles) and ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0)))) then # if number 10
> check_for_pole();
> fi;# end if 10;
> if (true) 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 ) = sqrt ( x ) ; ");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 10
> logstart(html_log_file);
> logitem_str(html_log_file,"2017-11-26T16:31:56-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"sqrt_tone")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = sqrt ( x ) ; ")
> ;
> logitem_complex(html_log_file,x_start)
> ;
> logitem_complex(html_log_file,x_end)
> ;
> logitem_complex(html_log_file,array_x[1])
> ;
> logitem_complex(html_log_file,glob_h)
> ;
> logitem_h_reason(html_log_file)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> glob_desired_digits_correct := 0.0;
> 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
> glob_least_ratio_sing := 0;
> 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
> glob_least_6_sing := 0.0;
> 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," 309 | ")
> ;
> logitem_str(html_log_file,"sqrt_tone diffeq.mxt")
> ;
> logitem_str(html_log_file,"sqrt_tone 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
> ;
> ;;
> end;
> # End Function number 12
> #END OUTFILEMAIN
> end;
Warning, `h_new` is implicitly declared local to procedure `main`
Warning, `ratio` is implicitly declared local to procedure `main`
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, h_new,
ratio;
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_h, glob_nxt, 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_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_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_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 := 40;
Digits := 32;
max_terms := 40;
glob_html_log := true;
array_y_init := Array(0 .. 40, []);
array_norms := Array(0 .. 40, []);
array_fact_1 := Array(0 .. 40, []);
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 .. 40, []);
array_x := Array(0 .. 40, []);
array_tmp0 := Array(0 .. 40, []);
array_tmp1 := Array(0 .. 40, []);
array_tmp2 := Array(0 .. 40, []);
array_m1 := Array(0 .. 40, []);
array_y_higher := Array(0 .. 2, 0 .. 41, []);
array_y_higher_work := Array(0 .. 2, 0 .. 41, []);
array_y_higher_work2 := Array(0 .. 2, 0 .. 41, []);
array_y_set_initial := Array(0 .. 2, 0 .. 41, []);
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 .. 40, 0 .. 41, []);
term := 1;
while term <= 40 do array_y_init[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 40 do array_norms[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 40 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 <= 40 do array_y[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_x[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp0[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp1[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_m1[term] := c(0.); term := term + 1 end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 40 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 <= 40 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 <= 40 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 <= 40 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 <= 40 do
term := 1;
while term <= 40 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_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_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_h := 0.1;
glob_nxt := 1;
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_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 := 10000;
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;
array_y_set_initial[1, 31] := false;
array_y_set_initial[1, 32] := false;
array_y_set_initial[1, 33] := false;
array_y_set_initial[1, 34] := false;
array_y_set_initial[1, 35] := false;
array_y_set_initial[1, 36] := false;
array_y_set_initial[1, 37] := false;
array_y_set_initial[1, 38] := false;
array_y_set_initial[1, 39] := false;
array_y_set_initial[1, 40] := false;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
ATS_MAX_TERMS := 40;
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 := 10000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/sqrt_tonepostcpx.cpx#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = sqrt ( x ) ; ");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=40;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := 0.5 + 0.1 * I;");
omniout_str(ALWAYS, "x_end := 99.0 + 99.0 * I;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_h := c(0.01);");
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(0.0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_rad_poles[1,2] := c(0.0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_ord_poles[1,1] := c(1.5);");
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:=10000;");
omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);");
omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);");
omniout_str(ALWAYS, "glob_look_poles:=true;");
omniout_str(ALWAYS, "glob_h:=c(0.001);");
omniout_str(ALWAYS, "glob_display_interval:=c(0.01);");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "return(c(2.0)*expt(c(x),c(1.5))/c(3.0));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "next_delta := proc()");
omniout_str(ALWAYS, "global glob_nxt, x_delta;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "x_delta := [ 0.001 + 0.00004 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
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omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.000 + 0.000 * I ];");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_nxt := glob_nxt + 1;");
omniout_str(ALWAYS, "it := x_delta[glob_nxt];");
omniout_str(ALWAYS, "return it;");
omniout_str(ALWAYS, "end;");
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 := 0.5 + 0.1*I;
x_end := 99.0 + 99.0*I;
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_h := c(0.01);
glob_min_h := c(0.001);
glob_type_given_pole := 1;
array_given_rad_poles[1, 1] := c(0.);
array_given_rad_poles[1, 2] := c(0.);
array_given_ord_poles[1, 1] := c(1.5);
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 := 10000;
glob_upper_ratio_limit := c(1.000001);
glob_lower_ratio_limit := c(0.999999);
glob_look_poles := true;
glob_h := c(0.001);
glob_display_interval := c(0.01);
glob_last_good_h := glob_h;
glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours;
found_h := true;
glob_h := next_delta();
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 glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT)
end if;
found_h := true;
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;
found_h := true;
glob_h := next_delta();
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;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_iter < glob_max_iter and
(glob_iter < 10 or not (Re(glob_h) = 0. and Im(glob_h) = 0.)) do
omniout_str(INFO, " ");
found_h := true;
glob_h := next_delta();
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;
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
atomall();
if not (Re(glob_h) = 0. and Im(glob_h) = 0.) then
display_alot(current_iter)
end if;
if
glob_look_poles and not (Re(glob_h) = 0. and Im(glob_h) = 0.)
then check_for_pole()
end if;
glob_next_display := glob_next_display + glob_display_interval;
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 ) = sqrt ( x ) ; ");
omniout_int(INFO, "Iterations ", 32, glob_iter,
4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2017-11-26T16:31:56-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"sqrt_tone");
logitem_str(html_log_file,
"diff ( y , x , 1 ) = sqrt ( x ) ; ");
logitem_complex(html_log_file, x_start);
logitem_complex(html_log_file, x_end);
logitem_complex(html_log_file, array_x[1]);
logitem_complex(html_log_file, glob_h);
logitem_h_reason(html_log_file);
logitem_integer(html_log_file, Digits);
glob_desired_digits_correct := 0.;
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
glob_least_ratio_sing := 0;
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
glob_least_6_sing := 0.;
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, " 309 | ");
logitem_str(html_log_file, "sqrt_tone diffeq.mxt");
logitem_str(html_log_file, "sqrt_tone 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();
memory used=3.9MB, alloc=40.3MB, time=0.08
##############ECHO OF PROBLEM#################
##############temp/sqrt_tonepostcpx.cpx#################
diff ( y , x , 1 ) = sqrt ( x ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=40;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.5 + 0.1 * I;
x_end := 99.0 + 99.0 * I;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_h := c(0.01);
glob_min_h := c(0.001);
glob_type_given_pole := 1;
array_given_rad_poles[1,1] := c(0.0);
array_given_rad_poles[1,2] := c(0.0);
array_given_ord_poles[1,1] := c(1.5);
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:=10000;
glob_upper_ratio_limit:=c(1.000001);
glob_lower_ratio_limit:=c(0.999999);
glob_look_poles:=true;
glob_h:=c(0.001);
glob_display_interval:=c(0.01);
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return(c(2.0)*expt(c(x),c(1.5))/c(3.0));
end;
next_delta := proc()
global glob_nxt, x_delta;
x_delta := [ 0.001 + 0.00004 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.000 + 0.000 * I ];
glob_nxt := glob_nxt + 1;
it := x_delta[glob_nxt];
return it;
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = 0.5 0.1
h = 0.0001 0.005
y[1] (numeric) = 0.232175463989 0.0708276583663
y[1] (closed_form) = 0.232175463989 0.0708276583663
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 0.5099
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6373
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5001 0.105
h = 0.0001 0.003
y[1] (numeric) = 0.23188777788 0.0743887015357
y[1] (closed_form) = 0.231886041062 0.0743889137137
absolute error = 1.750e-06
relative error = 0.0007185 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.511
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3067
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5002 0.108
h = 0.001 0.001
y[1] (numeric) = 0.231732185632 0.0765299782958
y[1] (closed_form) = 0.231732526726 0.076529899063
absolute error = 3.502e-07
relative error = 0.0001435 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.5117
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2411
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=30.0MB, alloc=40.3MB, time=0.38
x[1] = 0.5012 0.109
h = 0.001 0.003
y[1] (numeric) = 0.232366688958 0.0773183907935
y[1] (closed_form) = 0.232367995829 0.0773178209002
absolute error = 1.426e-06
relative error = 0.0005822 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.5129
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.147
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5022 0.112
h = 0.0001 0.004
y[1] (numeric) = 0.232848615463 0.0795326293854
y[1] (closed_form) = 0.232847917363 0.0795329788968
absolute error = 7.807e-07
relative error = 0.0003173 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.5145
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.651
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5023 0.116
h = 0.003 0.006
y[1] (numeric) = 0.232601795272 0.0823944290204
y[1] (closed_form) = 0.232599545783 0.0823937263119
absolute error = 2.357e-06
relative error = 0.000955 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.5155
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8643
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5053 0.122
h = 0.0001 0.005
y[1] (numeric) = 0.234246421477 0.086923916373
y[1] (closed_form) = 0.234243977247 0.0869314255798
absolute error = 7.897e-06
relative error = 0.003161 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.5198
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3875
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5054 0.127
h = 0.0001 0.003
y[1] (numeric) = 0.233882434132 0.0905186951815
y[1] (closed_form) = 0.233880994945 0.0905209905126
absolute error = 2.709e-06
relative error = 0.00108 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.5211
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3128
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5055 0.13
h = 0.001 0.001
y[1] (numeric) = 0.23368305578 0.0926777356294
y[1] (closed_form) = 0.233683668046 0.0926797022612
absolute error = 2.060e-06
relative error = 0.0008193 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.5219
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2459
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5065 0.131
h = 0.001 0.003
y[1] (numeric) = 0.234308254099 0.0934863595907
y[1] (closed_form) = 0.234309812958 0.0934878218671
absolute error = 2.137e-06
relative error = 0.0008472 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.5232
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.17
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5075 0.134
h = 0.0001 0.004
y[1] (numeric) = 0.234751401803 0.0957316611887
y[1] (closed_form) = 0.234750993528 0.0957340721664
absolute error = 2.445e-06
relative error = 0.0009645 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.5249
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6641
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5076 0.138
h = 0.003 0.006
y[1] (numeric) = 0.234446355352 0.0986168608362
y[1] (closed_form) = 0.234444391364 0.0986182599016
absolute error = 2.411e-06
relative error = 0.0009481 %
Correct digits = 5
memory used=75.3MB, alloc=44.3MB, time=0.94
Radius of convergence (given) for eq 1 = 0.526
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8819
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5106 0.144
h = 0.0001 0.005
y[1] (numeric) = 0.236019648991 0.103223574628
y[1] (closed_form) = 0.236017647695 0.103233104804
absolute error = 9.738e-06
relative error = 0.00378 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.5305
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3955
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5107 0.149
h = 0.0001 0.003
y[1] (numeric) = 0.235583495811 0.106847746617
y[1] (closed_form) = 0.235582391822 0.106852098329
absolute error = 4.490e-06
relative error = 0.001736 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.532
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3193
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5108 0.152
h = 0.001 0.001
y[1] (numeric) = 0.235341118122 0.109025198701
y[1] (closed_form) = 0.235342037884 0.109029187077
absolute error = 4.093e-06
relative error = 0.001578 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.5329
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2511
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5118 0.153
h = 0.001 0.003
y[1] (numeric) = 0.235957489692 0.109854001251
y[1] (closed_form) = 0.235959336714 0.109857473076
absolute error = 3.933e-06
relative error = 0.001511 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.5342
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.194
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5128 0.156
h = 0.0001 0.004
y[1] (numeric) = 0.236362843594 0.112130777735
y[1] (closed_form) = 0.236362761742 0.112135224536
absolute error = 4.448e-06
relative error = 0.0017 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.536
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6782
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5129 0.16
h = 0.003 0.006
y[1] (numeric) = 0.236000613266 0.115040224626
y[1] (closed_form) = 0.235998973728 0.115043698774
absolute error = 3.842e-06
relative error = 0.001463 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.5373
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9008
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5159 0.166
h = 0.0001 0.005
y[1] (numeric) = 0.237504761205 0.119724679657
y[1] (closed_form) = 0.237503232313 0.119736198145
absolute error = 1.162e-05
relative error = 0.004369 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.5419
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.404
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.516 0.171
h = 0.0001 0.003
y[1] (numeric) = 0.236997743222 0.123379252883
y[1] (closed_form) = 0.236997009303 0.12338563295
absolute error = 6.422e-06
relative error = 0.002404 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.5436
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3263
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=120.6MB, alloc=44.3MB, time=1.48
x[1] = 0.5161 0.174
h = 0.001 0.001
y[1] (numeric) = 0.236713162965 0.125575700755
y[1] (closed_form) = 0.236714424159 0.125581685466
absolute error = 6.116e-06
relative error = 0.002282 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.5446
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2566
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5171 0.175
h = 0.001 0.003
y[1] (numeric) = 0.237321168781 0.126424624078
y[1] (closed_form) = 0.237323337887 0.126430081473
absolute error = 5.873e-06
relative error = 0.002184 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.5459
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.221
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5181 0.178
h = 0.0001 0.004
y[1] (numeric) = 0.237689704472 0.128733220606
y[1] (closed_form) = 0.237689983098 0.128739676359
absolute error = 6.462e-06
relative error = 0.00239 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.5478
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6932
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5182 0.182
h = 0.003 0.006
y[1] (numeric) = 0.237271344419 0.131667678355
y[1] (closed_form) = 0.237270065515 0.131673199515
absolute error = 5.667e-06
relative error = 0.002089 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.5492
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9208
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5212 0.188
h = 0.0001 0.005
y[1] (numeric) = 0.238708489237 0.136430255603
y[1] (closed_form) = 0.238707459469 0.136443729526
absolute error = 1.351e-05
relative error = 0.004915 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.5541
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4131
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5213 0.193
h = 0.0001 0.003
y[1] (numeric) = 0.23813191755 0.140116136564
y[1] (closed_form) = 0.238131585914 0.140124516017
absolute error = 8.386e-06
relative error = 0.003035 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.5559
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3336
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5214 0.196
h = 0.001 0.001
y[1] (numeric) = 0.237805935391 0.142332103261
y[1] (closed_form) = 0.237807569566 0.142340057886
absolute error = 8.121e-06
relative error = 0.00293 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.557
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2624
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5224 0.197
h = 0.0001 0.004
y[1] (numeric) = 0.238406017981 0.143201067492
y[1] (closed_form) = 0.238408540832 0.143208485386
absolute error = 7.835e-06
relative error = 0.002817 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.5583
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.58
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=166.1MB, alloc=44.3MB, time=2.04
x[1] = 0.5225 0.201
h = 0.003 0.006
y[1] (numeric) = 0.237942500031 0.146156404937
y[1] (closed_form) = 0.237940848395 0.146163467663
absolute error = 7.253e-06
relative error = 0.002597 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.5598
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9386
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5255 0.207
h = 0.0001 0.005
y[1] (numeric) = 0.239322711599 0.150985674022
y[1] (closed_form) = 0.239321421978 0.151000609144
absolute error = 1.499e-05
relative error = 0.005297 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.5648
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4211
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5256 0.212
h = 0.0001 0.003
y[1] (numeric) = 0.238686935429 0.154698348332
y[1] (closed_form) = 0.238686264413 0.154708228364
absolute error = 9.903e-06
relative error = 0.003482 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.5667
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3402
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5257 0.215
h = 0.001 0.001
y[1] (numeric) = 0.238325716177 0.156931010449
y[1] (closed_form) = 0.238326985721 0.156940441899
absolute error = 9.517e-06
relative error = 0.003335 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.568
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2676
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5267 0.216
h = 0.001 0.003
y[1] (numeric) = 0.238919081333 0.157817058933
y[1] (closed_form) = 0.238921223253 0.157825946337
absolute error = 9.142e-06
relative error = 0.003193 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.5693
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.273
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5277 0.219
h = 0.0001 0.004
y[1] (numeric) = 0.239221264159 0.160185162358
y[1] (closed_form) = 0.239221586357 0.160195084915
absolute error = 9.928e-06
relative error = 0.003448 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.5713
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7229
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5278 0.223
h = 0.003 0.006
y[1] (numeric) = 0.238700958144 0.16316728225
y[1] (closed_form) = 0.238699727605 0.163176337548
absolute error = 9.139e-06
relative error = 0.003161 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.573
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9606
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5308 0.229
h = 0.0001 0.005
y[1] (numeric) = 0.240018005257 0.168075089098
y[1] (closed_form) = 0.240017258098 0.168091918907
absolute error = 1.685e-05
relative error = 0.005749 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.5781
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.431
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=211.6MB, alloc=44.3MB, time=2.58
x[1] = 0.5309 0.234
h = 0.0001 0.003
y[1] (numeric) = 0.239315103515 0.171820520392
y[1] (closed_form) = 0.239314888268 0.171832344647
absolute error = 1.183e-05
relative error = 0.004014 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.5802
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3482
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.531 0.237
h = 0.001 0.001
y[1] (numeric) = 0.238913960313 0.174073532455
y[1] (closed_form) = 0.238915655693 0.174084883133
absolute error = 1.148e-05
relative error = 0.003882 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.5815
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.274
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.532 0.238
h = 0.001 0.003
y[1] (numeric) = 0.239500175631 0.17497942875
y[1] (closed_form) = 0.239502724605 0.174990228247
absolute error = 1.110e-05
relative error = 0.003741 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.5828
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.303
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.533 0.241
h = 0.0001 0.004
y[1] (numeric) = 0.239768234283 0.17738002343
y[1] (closed_form) = 0.239769001073 0.177391874071
absolute error = 1.188e-05
relative error = 0.003982 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.585
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7401
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5331 0.245
h = 0.003 0.006
y[1] (numeric) = 0.23919480735 0.180388924546
y[1] (closed_form) = 0.239194026472 0.180399942084
absolute error = 1.105e-05
relative error = 0.003687 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.5867
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9836
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5361 0.251
h = 0.0001 0.005
y[1] (numeric) = 0.24045066463 0.185375329219
y[1] (closed_form) = 0.240450479691 0.185394021337
absolute error = 1.869e-05
relative error = 0.006157 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.5919
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4413
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5362 0.256
h = 0.0001 0.003
y[1] (numeric) = 0.239681932465 0.189154162307
y[1] (closed_form) = 0.23968219807 0.189167900535
absolute error = 1.374e-05
relative error = 0.0045 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.5942
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3566
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5363 0.259
h = 0.001 0.001
y[1] (numeric) = 0.239241651068 0.191427890943
y[1] (closed_form) = 0.239243797331 0.191441132833
absolute error = 1.341e-05
relative error = 0.004378 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.5956
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2806
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5373 0.26
h = 0.001 0.003
y[1] (numeric) = 0.23982110341 0.192353506794
y[1] (closed_form) = 0.239824084842 0.192366191463
absolute error = 1.303e-05
relative error = 0.004238 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.5969
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.335
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=257.0MB, alloc=44.3MB, time=3.13
x[1] = 0.5383 0.263
h = 0.0001 0.004
y[1] (numeric) = 0.2400559366 0.194786724008
y[1] (closed_form) = 0.240057172747 0.194800473573
absolute error = 1.381e-05
relative error = 0.004465 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.5991
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7581
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5384 0.267
h = 0.003 0.006
y[1] (numeric) = 0.239430424848 0.197822885931
y[1] (closed_form) = 0.239430119714 0.197835835093
absolute error = 1.295e-05
relative error = 0.00417 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.601
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.008
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5414 0.273
h = 0.0001 0.005
y[1] (numeric) = 0.240626998551 0.20288785798
y[1] (closed_form) = 0.240627393495 0.202908380508
absolute error = 2.053e-05
relative error = 0.006521 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.6063
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.452
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5415 0.278
h = 0.0001 0.003
y[1] (numeric) = 0.239793712978 0.206700657603
y[1] (closed_form) = 0.239794482256 0.206716279524
absolute error = 1.564e-05
relative error = 0.00494 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.6087
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3653
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5416 0.281
h = 0.001 0.001
y[1] (numeric) = 0.239315066705 0.208995421899
y[1] (closed_form) = 0.239317686792 0.209010526827
absolute error = 1.533e-05
relative error = 0.004825 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.6102
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2875
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5426 0.282
h = 0.001 0.003
y[1] (numeric) = 0.239888123337 0.209940616896
y[1] (closed_form) = 0.239891560583 0.209955159563
absolute error = 1.494e-05
relative error = 0.004687 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.6115
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.367
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5436 0.285
h = 0.0001 0.004
y[1] (numeric) = 0.240090603009 0.212406544187
y[1] (closed_form) = 0.240092331109 0.212422163442
absolute error = 1.571e-05
relative error = 0.004902 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.6138
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7766
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5437 0.289
h = 0.003 0.006
y[1] (numeric) = 0.239414025666 0.215470384584
y[1] (closed_form) = 0.239414220011 0.215485234678
absolute error = 1.485e-05
relative error = 0.004611 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.6157
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.032
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=302.2MB, alloc=44.3MB, time=3.68
x[1] = 0.5467 0.295
h = 0.0001 0.005
y[1] (numeric) = 0.240553151398 0.220613813393
y[1] (closed_form) = 0.24055414196 0.220636135017
absolute error = 2.234e-05
relative error = 0.006845 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.6212
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4631
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5468 0.3
h = 0.0001 0.003
y[1] (numeric) = 0.239656566798 0.224461070325
y[1] (closed_form) = 0.239657860439 0.224478545796
absolute error = 1.752e-05
relative error = 0.005336 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.6237
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3743
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5469 0.303
h = 0.001 0.001
y[1] (numeric) = 0.239140313996 0.226777145584
y[1] (closed_form) = 0.239143428854 0.226794085373
absolute error = 1.722e-05
relative error = 0.005226 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.6252
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2946
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5479 0.304
h = 0.0001 0.004
y[1] (numeric) = 0.239707322944 0.227741769253
y[1] (closed_form) = 0.239711237407 0.227758142651
absolute error = 1.683e-05
relative error = 0.005091 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.6266
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.773
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.548 0.308
h = 0.003 0.006
y[1] (numeric) = 0.238989682869 0.230828437799
y[1] (closed_form) = 0.238989643156 0.230844763091
absolute error = 1.633e-05
relative error = 0.004913 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.6286
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.054
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.551 0.314
h = 0.0001 0.005
y[1] (numeric) = 0.240079842934 0.236038601025
y[1] (closed_form) = 0.240080677343 0.236062311148
absolute error = 2.372e-05
relative error = 0.007046 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.6342
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4728
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5511 0.319
h = 0.0001 0.003
y[1] (numeric) = 0.239129340056 0.239915124437
y[1] (closed_form) = 0.239130419343 0.239934035141
absolute error = 1.894e-05
relative error = 0.005592 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.6368
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3822
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5512 0.322
h = 0.001 0.001
y[1] (numeric) = 0.238581053596 0.242249297195
y[1] (closed_form) = 0.238583929112 0.242267657254
absolute error = 1.858e-05
relative error = 0.005465 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.6384
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3008
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=347.7MB, alloc=44.3MB, time=4.24
x[1] = 0.5522 0.323
h = 0.001 0.003
y[1] (numeric) = 0.239142892433 0.243230450877
y[1] (closed_form) = 0.239146552868 0.243248241457
absolute error = 1.816e-05
relative error = 0.005325 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.6397
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.43
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5532 0.326
h = 0.0001 0.004
y[1] (numeric) = 0.239287003028 0.245756983533
y[1] (closed_form) = 0.239289019159 0.245775867981
absolute error = 1.899e-05
relative error = 0.005537 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.6421
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8125
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5533 0.33
h = 0.003 0.006
y[1] (numeric) = 0.238517707777 0.248872666433
y[1] (closed_form) = 0.238518206293 0.248890836145
absolute error = 1.818e-05
relative error = 0.005273 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.6442
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.08
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5563 0.336
h = 0.0001 0.005
y[1] (numeric) = 0.239553647503 0.254160919674
y[1] (closed_form) = 0.239555102594 0.254186372574
absolute error = 2.549e-05
relative error = 0.007299 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.6499
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4845
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5564 0.341
h = 0.0001 0.003
y[1] (numeric) = 0.238542103914 0.258072651323
y[1] (closed_form) = 0.238543741227 0.258093360483
absolute error = 2.077e-05
relative error = 0.005911 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.6526
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3917
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5565 0.344
h = 0.001 0.001
y[1] (numeric) = 0.237957573569 0.260428551766
y[1] (closed_form) = 0.237960978255 0.260448694894
absolute error = 2.043e-05
relative error = 0.005791 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.6542
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3082
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5575 0.345
h = 0.001 0.003
y[1] (numeric) = 0.238513964961 0.261428837249
y[1] (closed_form) = 0.238518137928 0.26144840825
absolute error = 2.001e-05
relative error = 0.005654 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.6556
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.466
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5585 0.348
h = 0.0001 0.004
y[1] (numeric) = 0.238628058701 0.263988137308
y[1] (closed_form) = 0.23863062092 0.264008808916
absolute error = 2.083e-05
relative error = 0.005853 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.658
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8326
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5586 0.352
h = 0.003 0.006
y[1] (numeric) = 0.237810491837 0.267132406247
y[1] (closed_form) = 0.237811546371 0.267152390316
absolute error = 2.001e-05
relative error = 0.005595 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.6603
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.107
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=393.1MB, alloc=44.3MB, time=4.79
x[1] = 0.5616 0.358
h = 0.0001 0.005
y[1] (numeric) = 0.238793842349 0.272498459628
y[1] (closed_form) = 0.238795929213 0.272525626011
absolute error = 2.725e-05
relative error = 0.007519 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.666
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4965
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5617 0.363
h = 0.0001 0.003
y[1] (numeric) = 0.237722431545 0.276445710733
y[1] (closed_form) = 0.23772464225 0.276468189238
absolute error = 2.259e-05
relative error = 0.006195 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.6688
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4014
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5618 0.366
h = 0.001 0.001
y[1] (numeric) = 0.237102363947 0.278823508402
y[1] (closed_form) = 0.23710631369 0.278845407071
absolute error = 2.225e-05
relative error = 0.006079 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.6705
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3159
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5628 0.367
h = 0.001 0.003
y[1] (numeric) = 0.237653604177 0.279842755896
y[1] (closed_form) = 0.237658306082 0.279864080471
absolute error = 2.184e-05
relative error = 0.005948 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.6719
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.502
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5638 0.37
h = 0.0001 0.004
y[1] (numeric) = 0.237738441343 0.282434781506
y[1] (closed_form) = 0.237741565059 0.282457212005
absolute error = 2.265e-05
relative error = 0.006134 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.6744
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8533
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5639 0.374
h = 0.003 0.006
y[1] (numeric) = 0.236873533474 0.285607859516
y[1] (closed_form) = 0.236875160015 0.285629628329
absolute error = 2.183e-05
relative error = 0.005883 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.6767
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.134
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5669 0.38
h = 0.0001 0.005
y[1] (numeric) = 0.237805855593 0.29105137627
y[1] (closed_form) = 0.237808583973 0.291080227632
absolute error = 2.898e-05
relative error = 0.00771 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.6825
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5088
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.567 0.385
h = 0.0001 0.003
y[1] (numeric) = 0.236675718918 0.29503440593
y[1] (closed_form) = 0.236678516785 0.295058625204
absolute error = 2.438e-05
relative error = 0.006445 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.6854
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4114
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=438.5MB, alloc=44.3MB, time=5.34
x[1] = 0.5671 0.388
h = 0.001 0.001
y[1] (numeric) = 0.236020800558 0.297434239832
y[1] (closed_form) = 0.236025309705 0.297457866922
absolute error = 2.405e-05
relative error = 0.006335 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.6871
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3237
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5681 0.389
h = 0.001 0.003
y[1] (numeric) = 0.236567169196 0.298472275646
y[1] (closed_form) = 0.23657241491 0.298495327286
absolute error = 2.364e-05
relative error = 0.006207 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.6885
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.54
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5691 0.392
h = 0.0001 0.004
y[1] (numeric) = 0.236623480756 0.301096960469
y[1] (closed_form) = 0.236627179828 0.301121122071
absolute error = 2.444e-05
relative error = 0.006383 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.691
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8744
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5692 0.396
h = 0.003 0.006
y[1] (numeric) = 0.235712135956 0.304299030837
y[1] (closed_form) = 0.23571434883 0.304322555313
absolute error = 2.363e-05
relative error = 0.006138 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.6934
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.163
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5722 0.402
h = 0.0001 0.005
y[1] (numeric) = 0.236594921868 0.30981963412
y[1] (closed_form) = 0.236598300287 0.309850142757
absolute error = 3.070e-05
relative error = 0.007873 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.6993
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5213
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5723 0.407
h = 0.0001 0.003
y[1] (numeric) = 0.235407167602 0.313838654252
y[1] (closed_form) = 0.235410564931 0.313864586311
absolute error = 2.615e-05
relative error = 0.006666 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.7023
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4215
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5724 0.41
h = 0.001 0.001
y[1] (numeric) = 0.234718064389 0.316260635821
y[1] (closed_form) = 0.234723145859 0.316285964687
absolute error = 2.583e-05
relative error = 0.006559 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.7041
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3317
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5734 0.411
h = 0.0001 0.004
y[1] (numeric) = 0.235259825103 0.317317283507
y[1] (closed_form) = 0.235265628073 0.317342036113
absolute error = 2.542e-05
relative error = 0.006436 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.7055
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.996
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=484.0MB, alloc=44.3MB, time=5.89
x[1] = 0.5735 0.415
h = 0.003 0.006
y[1] (numeric) = 0.234311110833 0.320543104205
y[1] (closed_form) = 0.234313190827 0.320568025553
absolute error = 2.501e-05
relative error = 0.006298 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.7079
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.187
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5765 0.421
h = 0.0001 0.005
y[1] (numeric) = 0.235151490108 0.326129166019
y[1] (closed_form) = 0.235154787305 0.326160988783
absolute error = 3.199e-05
relative error = 0.007957 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.7139
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5322
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5766 0.426
h = 0.0001 0.003
y[1] (numeric) = 0.233914571047 0.330178633613
y[1] (closed_form) = 0.233917845806 0.330205926674
absolute error = 2.749e-05
relative error = 0.006793 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.7169
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4303
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5767 0.429
h = 0.001 0.001
y[1] (numeric) = 0.233196294866 0.332619352559
y[1] (closed_form) = 0.233201231036 0.332646033622
absolute error = 2.713e-05
relative error = 0.006679 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.7188
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3386
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5777 0.43
h = 0.001 0.003
y[1] (numeric) = 0.233734070022 0.333691827165
y[1] (closed_form) = 0.233739715143 0.33371793149
absolute error = 2.671e-05
relative error = 0.006555 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.7202
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.61
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5787 0.433
h = 0.0001 0.004
y[1] (numeric) = 0.233738762987 0.336376714773
y[1] (closed_form) = 0.23374291743 0.336403933956
absolute error = 2.753e-05
relative error = 0.006722 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.7228
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9145
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5788 0.437
h = 0.003 0.006
y[1] (numeric) = 0.232742974359 0.339632571658
y[1] (closed_form) = 0.232745663704 0.339659196298
absolute error = 2.676e-05
relative error = 0.006499 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.7252
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.216
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5818 0.443
h = 0.0001 0.005
y[1] (numeric) = 0.233536423907 0.34529494846
y[1] (closed_form) = 0.233540384451 0.345328379179
absolute error = 3.366e-05
relative error = 0.008075 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.7313
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5452
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5819 0.448
h = 0.0001 0.003
y[1] (numeric) = 0.232243858727 0.349380703001
y[1] (closed_form) = 0.232247752654 0.349409658596
absolute error = 2.922e-05
relative error = 0.006964 %
Correct digits = 4
memory used=529.5MB, alloc=44.3MB, time=6.44
Radius of convergence (given) for eq 1 = 0.7344
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4408
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.582 0.451
h = 0.001 0.001
y[1] (numeric) = 0.231492580856 0.351843720163
y[1] (closed_form) = 0.231498110268 0.351872054954
absolute error = 2.887e-05
relative error = 0.006854 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.7363
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3469
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.583 0.452
h = 0.001 0.003
y[1] (numeric) = 0.232026201338 0.352934477001
y[1] (closed_form) = 0.232032425592 0.352962235112
absolute error = 2.845e-05
relative error = 0.006735 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.7377
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.65
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.584 0.455
h = 0.0001 0.004
y[1] (numeric) = 0.232004304274 0.355651732775
y[1] (closed_form) = 0.232009066502 0.355680606795
absolute error = 2.926e-05
relative error = 0.006891 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.7403
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9367
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5841 0.459
h = 0.003 0.006
y[1] (numeric) = 0.230964514181 0.358936929784
y[1] (closed_form) = 0.230967823154 0.358965230428
absolute error = 2.849e-05
relative error = 0.006675 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.7429
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.245
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5871 0.465
h = 0.0001 0.005
y[1] (numeric) = 0.231712342221 0.364675160807
y[1] (closed_form) = 0.23171697174 0.364710174078
absolute error = 3.532e-05
relative error = 0.008174 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.7489
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5583
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5872 0.47
h = 0.0001 0.003
y[1] (numeric) = 0.230365143554 0.368797302984
y[1] (closed_form) = 0.230369665384 0.368827895
absolute error = 3.092e-05
relative error = 0.007111 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.7521
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4514
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5873 0.473
h = 0.001 0.001
y[1] (numeric) = 0.229581470902 0.371282665077
y[1] (closed_form) = 0.229587602973 0.37131262852
absolute error = 3.058e-05
relative error = 0.007006 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.7541
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3553
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5883 0.474
h = 0.001 0.003
y[1] (numeric) = 0.230111159413 0.372391524663
y[1] (closed_form) = 0.230117972725 0.372420911871
absolute error = 3.017e-05
relative error = 0.006891 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.7555
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.689
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=574.9MB, alloc=44.3MB, time=6.99
x[1] = 0.5893 0.477
h = 0.0001 0.004
y[1] (numeric) = 0.230063296 0.375141013774
y[1] (closed_form) = 0.230068674945 0.375171517115
absolute error = 3.097e-05
relative error = 0.007038 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.7582
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9593
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5894 0.481
h = 0.003 0.006
y[1] (numeric) = 0.228980304044 0.378455613965
y[1] (closed_form) = 0.228984241735 0.378485564018
absolute error = 3.021e-05
relative error = 0.006829 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.7608
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.275
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5924 0.487
h = 0.0001 0.005
y[1] (numeric) = 0.229683759156 0.384269218464
y[1] (closed_form) = 0.229689062451 0.384305789673
absolute error = 3.695e-05
relative error = 0.008254 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.7669
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5717
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5925 0.492
h = 0.0001 0.003
y[1] (numeric) = 0.228282906452 0.388427817588
y[1] (closed_form) = 0.228288063882 0.388460020608
absolute error = 3.261e-05
relative error = 0.007238 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.7701
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4623
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5926 0.495
h = 0.001 0.001
y[1] (numeric) = 0.227467425612 0.390935553166
y[1] (closed_form) = 0.227474168725 0.390967120787
absolute error = 3.228e-05
relative error = 0.007136 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.7721
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3638
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5936 0.496
h = 0.001 0.003
y[1] (numeric) = 0.227993392075 0.392062336368
y[1] (closed_form) = 0.228000803319 0.392093328545
absolute error = 3.187e-05
relative error = 0.007026 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.7735
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.73
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5946 0.499
h = 0.0001 0.004
y[1] (numeric) = 0.227920160219 0.394843911889
y[1] (closed_form) = 0.227926163786 0.394876019685
absolute error = 3.266e-05
relative error = 0.007164 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.7762
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9822
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5947 0.503
h = 0.003 0.006
y[1] (numeric) = 0.226794739378 0.398187954627
y[1] (closed_form) = 0.226799313796 0.398219528199
absolute error = 3.190e-05
relative error = 0.006962 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.7789
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.306
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=620.3MB, alloc=44.3MB, time=7.54
x[1] = 0.5977 0.509
h = 0.0001 0.005
y[1] (numeric) = 0.227455013142 0.404076435698
y[1] (closed_form) = 0.227460994267 0.404114541008
absolute error = 3.857e-05
relative error = 0.008318 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.7851
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5853
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5978 0.514
h = 0.0001 0.003
y[1] (numeric) = 0.226001453242 0.408271532992
y[1] (closed_form) = 0.226007253017 0.408305322296
absolute error = 3.428e-05
relative error = 0.007346 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.7884
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4732
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5979 0.517
h = 0.001 0.001
y[1] (numeric) = 0.225154730895 0.41080165439
y[1] (closed_form) = 0.225162092483 0.410834802332
absolute error = 3.396e-05
relative error = 0.007248 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.7904
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3724
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5989 0.518
h = 0.0001 0.004
y[1] (numeric) = 0.22567717322 0.411946182961
y[1] (closed_form) = 0.225685190309 0.411978756551
absolute error = 3.355e-05
relative error = 0.007141 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.7918
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.24
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.599 0.522
h = 0.003 0.006
y[1] (numeric) = 0.224517563581 0.415314253616
y[1] (closed_form) = 0.224522077287 0.415347145932
absolute error = 3.320e-05
relative error = 0.007032 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.7945
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.332
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.602 0.528
h = 0.0001 0.005
y[1] (numeric) = 0.22514069725 0.421266282111
y[1] (closed_form) = 0.225146651152 0.421305631305
absolute error = 3.980e-05
relative error = 0.008331 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8007
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.597
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6021 0.533
h = 0.0001 0.003
y[1] (numeric) = 0.223642067617 0.425492196491
y[1] (closed_form) = 0.223647811027 0.425527273463
absolute error = 3.554e-05
relative error = 0.007394 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8041
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4826
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6022 0.536
h = 0.001 0.001
y[1] (numeric) = 0.222768625964 0.428041222332
y[1] (closed_form) = 0.222775911245 0.428075653164
absolute error = 3.519e-05
relative error = 0.007293 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8062
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3798
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6032 0.537
h = 0.001 0.003
y[1] (numeric) = 0.223287976161 0.429200844811
y[1] (closed_form) = 0.223295906425 0.429234702305
absolute error = 3.477e-05
relative error = 0.007187 %
Correct digits = 4
memory used=666.0MB, alloc=44.3MB, time=8.10
Radius of convergence (given) for eq 1 = 0.8076
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.806
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6042 0.54
h = 0.0001 0.004
y[1] (numeric) = 0.223168669107 0.432041414062
y[1] (closed_form) = 0.223175238885 0.432076384825
absolute error = 3.558e-05
relative error = 0.007317 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8103
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.025
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6043 0.544
h = 0.003 0.006
y[1] (numeric) = 0.221965915595 0.435439791559
y[1] (closed_form) = 0.221971078659 0.435474261189
absolute error = 3.485e-05
relative error = 0.007131 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8131
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.363
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6073 0.55
h = 0.0001 0.005
y[1] (numeric) = 0.222547948723 0.44146575289
y[1] (closed_form) = 0.222554586526 0.441506593858
absolute error = 4.138e-05
relative error = 0.008369 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8193
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6108
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6074 0.555
h = 0.0001 0.003
y[1] (numeric) = 0.220998289665 0.445728187804
y[1] (closed_form) = 0.22100468601 0.445764806976
absolute error = 3.717e-05
relative error = 0.007471 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8228
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4938
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6075 0.558
h = 0.001 0.001
y[1] (numeric) = 0.220094609908 0.448299591382
y[1] (closed_form) = 0.220102525508 0.44833555986
absolute error = 3.683e-05
relative error = 0.007374 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8249
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3886
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6085 0.559
h = 0.001 0.003
y[1] (numeric) = 0.220610776823 0.449476633418
y[1] (closed_form) = 0.220619325621 0.449512030124
absolute error = 3.641e-05
relative error = 0.007272 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8263
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.848
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6095 0.562
h = 0.0001 0.004
y[1] (numeric) = 0.220467680462 0.452348823536
y[1] (closed_form) = 0.220474892843 0.452385331311
absolute error = 3.721e-05
relative error = 0.007395 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8291
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.049
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6096 0.566
h = 0.003 0.006
y[1] (numeric) = 0.219224567898 0.455776655121
y[1] (closed_form) = 0.219230385728 0.455812678203
absolute error = 3.649e-05
relative error = 0.007214 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8318
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.395
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=711.3MB, alloc=44.3MB, time=8.65
x[1] = 0.6126 0.572
h = 0.0001 0.005
y[1] (numeric) = 0.219766543579 0.461876022697
y[1] (closed_form) = 0.219773867575 0.461918333705
absolute error = 4.294e-05
relative error = 0.008394 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8381
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6248
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6127 0.577
h = 0.0001 0.003
y[1] (numeric) = 0.218166713201 0.466174954204
y[1] (closed_form) = 0.218173766951 0.46621309283
absolute error = 3.879e-05
relative error = 0.007535 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8416
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5052
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6128 0.58
h = 0.001 0.001
y[1] (numeric) = 0.217233308059 0.468768710414
y[1] (closed_form) = 0.217241859112 0.468806194445
absolute error = 3.845e-05
relative error = 0.007441 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8438
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3975
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6138 0.581
h = 0.001 0.003
y[1] (numeric) = 0.217746459139 0.469962998362
y[1] (closed_form) = 0.217755632039 0.469999912397
absolute error = 3.804e-05
relative error = 0.007343 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8452
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.89
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6148 0.584
h = 0.0001 0.004
y[1] (numeric) = 0.217580081343 0.472866630757
y[1] (closed_form) = 0.217587941034 0.472904653202
absolute error = 3.883e-05
relative error = 0.007459 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.848
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.073
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6149 0.588
h = 0.003 0.006
y[1] (numeric) = 0.216297285979 0.476323885651
y[1] (closed_form) = 0.216303763233 0.476361439024
absolute error = 3.811e-05
relative error = 0.007284 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8508
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.426
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6179 0.594
h = 0.0001 0.005
y[1] (numeric) = 0.216800200275 0.482496127528
y[1] (closed_form) = 0.216808212258 0.482539887536
absolute error = 4.449e-05
relative error = 0.00841 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8571
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.639
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.618 0.599
h = 0.0001 0.003
y[1] (numeric) = 0.215151027324 0.486831513669
y[1] (closed_form) = 0.215158742292 0.486871149674
absolute error = 4.038e-05
relative error = 0.007586 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8607
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5166
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=756.8MB, alloc=44.3MB, time=9.20
x[1] = 0.6181 0.602
h = 0.001 0.001
y[1] (numeric) = 0.214188391732 0.489447587111
y[1] (closed_form) = 0.214197582704 0.489486565218
absolute error = 4.005e-05
relative error = 0.007495 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8628
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4065
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6191 0.603
h = 0.001 0.003
y[1] (numeric) = 0.214698685043 0.490658949542
y[1] (closed_form) = 0.214708486926 0.490697359608
absolute error = 3.964e-05
relative error = 0.007401 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8642
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.932
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6201 0.606
h = 0.0001 0.004
y[1] (numeric) = 0.214509512788 0.493593840625
y[1] (closed_form) = 0.214518023841 0.493633356041
absolute error = 4.042e-05
relative error = 0.00751 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.867
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.097
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6202 0.61
h = 0.003 0.006
y[1] (numeric) = 0.213187687593 0.497080474566
y[1] (closed_form) = 0.213194828248 0.497119535758
absolute error = 3.971e-05
relative error = 0.007341 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8699
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.458
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6232 0.616
h = 0.0001 0.005
y[1] (numeric) = 0.213652491963 0.503325055411
y[1] (closed_form) = 0.213661193279 0.503370244049
absolute error = 4.602e-05
relative error = 0.008415 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8763
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6533
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6233 0.621
h = 0.0001 0.003
y[1] (numeric) = 0.211954776823 0.507696838227
y[1] (closed_form) = 0.211963156227 0.507737950197
absolute error = 4.196e-05
relative error = 0.007626 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8799
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5281
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6234 0.624
h = 0.001 0.001
y[1] (numeric) = 0.210963388561 0.510335184401
y[1] (closed_form) = 0.210973223301 0.51037563571
absolute error = 4.163e-05
relative error = 0.007538 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.882
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4156
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6244 0.625
h = 0.0001 0.004
y[1] (numeric) = 0.21147097338 0.511563452298
y[1] (closed_form) = 0.211481408497 0.51160333768
absolute error = 4.123e-05
relative error = 0.007447 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8835
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.5
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6245 0.629
h = 0.003 0.006
y[1] (numeric) = 0.210117652797 0.515074011662
y[1] (closed_form) = 0.210124784127 0.51511431888
memory used=802.4MB, alloc=52.3MB, time=9.77
absolute error = 4.093e-05
relative error = 0.007358 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8864
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.486
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6275 0.635
h = 0.0001 0.005
y[1] (numeric) = 0.21054952999 0.521379990143
y[1] (closed_form) = 0.210558243268 0.521426358577
absolute error = 4.718e-05
relative error = 0.00839 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8927
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6655
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6276 0.64
h = 0.0001 0.003
y[1] (numeric) = 0.208810219008 0.525782478959
y[1] (closed_form) = 0.208818589794 0.525824810358
absolute error = 4.315e-05
relative error = 0.007627 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8964
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.538
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6277 0.643
h = 0.001 0.001
y[1] (numeric) = 0.207794186921 0.528439619891
y[1] (closed_form) = 0.207803995775 0.528481288412
absolute error = 4.281e-05
relative error = 0.007538 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.8986
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4234
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6287 0.644
h = 0.001 0.003
y[1] (numeric) = 0.208299354919 0.529682276074
y[1] (closed_form) = 0.208309755361 0.529723380475
absolute error = 4.240e-05
relative error = 0.007449 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.012
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6297 0.647
h = 0.0001 0.004
y[1] (numeric) = 0.208068629073 0.532674571841
y[1] (closed_form) = 0.208077778275 0.532716775242
absolute error = 4.318e-05
relative error = 0.007551 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9028
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.142
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6298 0.651
h = 0.003 0.006
y[1] (numeric) = 0.206675491854 0.536215268043
y[1] (closed_form) = 0.206683292629 0.536257043083
absolute error = 4.250e-05
relative error = 0.007395 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9058
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.519
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6328 0.657
h = 0.0001 0.005
y[1] (numeric) = 0.207070925183 0.542592596172
y[1] (closed_form) = 0.207080329468 0.542640357047
absolute error = 4.868e-05
relative error = 0.008381 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9122
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.68
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6329 0.662
h = 0.0001 0.003
y[1] (numeric) = 0.20528449037 0.547031346132
y[1] (closed_form) = 0.205293530413 0.54707511537
absolute error = 4.469e-05
relative error = 0.007649 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9159
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5497
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=847.7MB, alloc=52.3MB, time=10.31
x[1] = 0.633 0.665
h = 0.001 0.001
y[1] (numeric) = 0.204240551892 0.54971066156
y[1] (closed_form) = 0.204251010467 0.549753766042
absolute error = 4.436e-05
relative error = 0.007563 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9181
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4326
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.634 0.666
h = 0.001 0.003
y[1] (numeric) = 0.204743269613 0.55096991721
y[1] (closed_form) = 0.204754309939 0.551012459926
absolute error = 4.395e-05
relative error = 0.007477 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9195
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.056
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.635 0.669
h = 0.0001 0.004
y[1] (numeric) = 0.204491038001 0.553992932317
y[1] (closed_form) = 0.204500847272 0.554036570074
absolute error = 4.473e-05
relative error = 0.007573 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9224
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.167
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6351 0.673
h = 0.003 0.006
y[1] (numeric) = 0.203060618668 0.557562826531
y[1] (closed_form) = 0.203069091236 0.557606048801
absolute error = 4.404e-05
relative error = 0.007422 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9254
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.551
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6381 0.679
h = 0.0001 0.005
y[1] (numeric) = 0.203420444536 0.564010967433
y[1] (closed_form) = 0.20343054011 0.564060102164
absolute error = 5.016e-05
relative error = 0.008365 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9318
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6946
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6382 0.684
h = 0.0001 0.003
y[1] (numeric) = 0.201587610854 0.568485883966
y[1] (closed_form) = 0.201597321946 0.568531071414
absolute error = 4.622e-05
relative error = 0.007662 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9355
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5615
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6383 0.687
h = 0.001 0.001
y[1] (numeric) = 0.200516198247 0.571187308679
y[1] (closed_form) = 0.20052730892 0.571231829904
absolute error = 4.589e-05
relative error = 0.007579 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9378
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4418
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6393 0.688
h = 0.001 0.003
y[1] (numeric) = 0.201016592766 0.572463002358
y[1] (closed_form) = 0.201028275706 0.572506964273
absolute error = 4.549e-05
relative error = 0.007497 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9392
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.1
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=893.2MB, alloc=52.3MB, time=10.85
x[1] = 0.6403 0.691
h = 0.0001 0.004
y[1] (numeric) = 0.200743270633 0.575516542033
y[1] (closed_form) = 0.200753741996 0.575561594795
absolute error = 4.625e-05
relative error = 0.007588 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9421
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.192
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6404 0.695
h = 0.003 0.006
y[1] (numeric) = 0.199276140084 0.579115550819
y[1] (closed_form) = 0.199285286325 0.579160200353
absolute error = 4.558e-05
relative error = 0.007441 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9451
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.584
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6434 0.701
h = 0.0001 0.005
y[1] (numeric) = 0.19960115874 0.585633969603
y[1] (closed_form) = 0.199611945582 0.585684460188
absolute error = 5.163e-05
relative error = 0.008344 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9515
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7094
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6435 0.706
h = 0.0001 0.003
y[1] (numeric) = 0.19772262667 0.590144948238
y[1] (closed_form) = 0.197733010192 0.590191534859
absolute error = 4.773e-05
relative error = 0.007668 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9553
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5734
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6436 0.709
h = 0.001 0.001
y[1] (numeric) = 0.196624157457 0.592868411475
y[1] (closed_form) = 0.196635922177 0.592914330779
absolute error = 4.740e-05
relative error = 0.007588 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9575
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4511
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6446 0.71
h = 0.001 0.003
y[1] (numeric) = 0.197122349031 0.594160384593
y[1] (closed_form) = 0.197134676872 0.594205747128
absolute error = 4.701e-05
relative error = 0.007509 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.959
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.144
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6456 0.713
h = 0.0001 0.004
y[1] (numeric) = 0.196828335186 0.597244252896
y[1] (closed_form) = 0.196839470248 0.597290701879
absolute error = 4.777e-05
relative error = 0.007595 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9619
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.217
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6457 0.717
h = 0.003 0.006
y[1] (numeric) = 0.195325045006 0.60087228549
y[1] (closed_form) = 0.195334866377 0.60091834293
absolute error = 4.709e-05
relative error = 0.007453 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9649
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.618
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=938.6MB, alloc=52.3MB, time=11.39
x[1] = 0.6487 0.723
h = 0.0001 0.005
y[1] (numeric) = 0.195616022482 0.607460450191
y[1] (closed_form) = 0.195627500302 0.607512279186
absolute error = 5.308e-05
relative error = 0.008317 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9714
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7242
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6488 0.728
h = 0.0001 0.003
y[1] (numeric) = 0.19369246901 0.612007377759
y[1] (closed_form) = 0.193703525974 0.612055345091
absolute error = 4.923e-05
relative error = 0.007668 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9752
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5853
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6489 0.731
h = 0.001 0.001
y[1] (numeric) = 0.192567346581 0.614752803913
y[1] (closed_form) = 0.192579766906 0.61480010317
absolute error = 4.890e-05
relative error = 0.007591 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9775
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4605
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6499 0.732
h = 0.0001 0.004
y[1] (numeric) = 0.193063449079 0.616060900769
y[1] (closed_form) = 0.193076423702 0.616107645871
absolute error = 4.851e-05
relative error = 0.007514 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9789
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.77
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.65 0.736
h = 0.003 0.006
y[1] (numeric) = 0.191530938879 0.619712541905
y[1] (closed_form) = 0.191540787798 0.619759779674
absolute error = 4.825e-05
relative error = 0.007439 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9819
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.646
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.653 0.742
h = 0.0001 0.005
y[1] (numeric) = 0.191792381229 0.626359924717
y[1] (closed_form) = 0.191803899745 0.62641287588
absolute error = 5.419e-05
relative error = 0.008272 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9884
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7369
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6531 0.747
h = 0.0001 0.003
y[1] (numeric) = 0.189830173468 0.63093717373
y[1] (closed_form) = 0.189841256517 0.630986298647
absolute error = 5.036e-05
relative error = 0.007643 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9922
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5956
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6532 0.75
h = 0.001 0.001
y[1] (numeric) = 0.188682161187 0.633701129845
y[1] (closed_form) = 0.188694592671 0.633749586076
absolute error = 5.003e-05
relative error = 0.007565 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9946
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4686
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6542 0.751
h = 0.001 0.003
y[1] (numeric) = 0.189176362484 0.635022959872
y[1] (closed_form) = 0.189189340887 0.635070864147
absolute error = 4.963e-05
relative error = 0.00749 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.996
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.227
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=984.0MB, alloc=52.3MB, time=11.93
x[1] = 0.6552 0.754
h = 0.0001 0.004
y[1] (numeric) = 0.188844498948 0.638162503309
y[1] (closed_form) = 0.188856317906 0.63821148561
absolute error = 5.039e-05
relative error = 0.007571 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.9989
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.264
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6553 0.758
h = 0.0001 0.004
y[1] (numeric) = 0.187274986435 0.641843863465
y[1] (closed_form) = 0.187285512417 0.64189247467
absolute error = 4.974e-05
relative error = 0.007438 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.002
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.002
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6554 0.762
h = 0.003 0.006
y[1] (numeric) = 0.185697083755 0.645528537999
y[1] (closed_form) = 0.185707609738 0.645577149204
absolute error = 4.974e-05
relative error = 0.007404 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.005
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.685
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6584 0.768
h = 0.0001 0.005
y[1] (numeric) = 0.185917709826 0.652255336786
y[1] (closed_form) = 0.185929922849 0.6523095845
absolute error = 5.561e-05
relative error = 0.008198 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.012
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7541
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6585 0.773
h = 0.0001 0.003
y[1] (numeric) = 0.183902847403 0.656872864875
y[1] (closed_form) = 0.183914605592 0.65692333316
absolute error = 5.182e-05
relative error = 0.007596 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.015
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6095
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6586 0.776
h = 0.001 0.001
y[1] (numeric) = 0.18272364382 0.659661446627
y[1] (closed_form) = 0.182736730709 0.659711245397
absolute error = 5.149e-05
relative error = 0.007522 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.018
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4795
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6596 0.777
h = 0.001 0.003
y[1] (numeric) = 0.183215052985 0.661001775941
y[1] (closed_form) = 0.183228677031 0.661051025652
absolute error = 5.110e-05
relative error = 0.007449 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.019
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.279
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6606 0.78
h = 0.0001 0.004
y[1] (numeric) = 0.182859098543 0.664175496653
y[1] (closed_form) = 0.182871583227 0.664225819324
absolute error = 5.185e-05
relative error = 0.007526 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.022
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.293
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1029.5MB, alloc=52.3MB, time=12.47
x[1] = 0.6607 0.784
h = 0.003 0.006
y[1] (numeric) = 0.181247896244 0.667889276651
y[1] (closed_form) = 0.18125910043 0.667939240552
absolute error = 5.120e-05
relative error = 0.007398 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.025
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.719
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6637 0.79
h = 0.0001 0.005
y[1] (numeric) = 0.181436639317 0.674684265241
y[1] (closed_form) = 0.181449541818 0.674739801588
absolute error = 5.702e-05
relative error = 0.00816 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.032
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7692
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6638 0.795
h = 0.0001 0.003
y[1] (numeric) = 0.17937868187 0.679337385788
y[1] (closed_form) = 0.179391115455 0.679389182072
absolute error = 5.327e-05
relative error = 0.007581 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.036
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6216
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6639 0.798
h = 0.001 0.001
y[1] (numeric) = 0.178173972619 0.682147695093
y[1] (closed_form) = 0.178187718602 0.68219882197
absolute error = 5.294e-05
relative error = 0.007509 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.038
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4891
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6649 0.799
h = 0.001 0.003
y[1] (numeric) = 0.178663610187 0.683503698284
y[1] (closed_form) = 0.178677885397 0.68355427888
absolute error = 5.256e-05
relative error = 0.007439 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.039
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.324
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6659 0.802
h = 0.0001 0.004
y[1] (numeric) = 0.178288431442 0.686706971406
y[1] (closed_form) = 0.178301583645 0.68675861998
absolute error = 5.330e-05
relative error = 0.007512 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.042
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.319
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.666 0.806
h = 0.003 0.006
y[1] (numeric) = 0.176643119729 0.690449375263
y[1] (closed_form) = 0.176655002212 0.690500674733
absolute error = 5.266e-05
relative error = 0.007388 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.046
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.753
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.669 0.812
h = 0.0001 0.005
y[1] (numeric) = 0.176800625169 0.697312039024
y[1] (closed_form) = 0.176814215995 0.697368848586
absolute error = 5.841e-05
relative error = 0.008119 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.052
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7843
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1074.8MB, alloc=52.3MB, time=13.02
x[1] = 0.6691 0.817
h = 0.0001 0.003
y[1] (numeric) = 0.174700164581 0.702000612748
y[1] (closed_form) = 0.174713273377 0.70205372067
absolute error = 5.470e-05
relative error = 0.007561 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.056
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6338
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6692 0.82
h = 0.001 0.001
y[1] (numeric) = 0.173470301942 0.704832559611
y[1] (closed_form) = 0.173484707309 0.70488499846
absolute error = 5.438e-05
relative error = 0.007491 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.058
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4987
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6702 0.821
h = 0.001 0.003
y[1] (numeric) = 0.173958259691 0.706204092504
y[1] (closed_form) = 0.173973186622 0.706255987879
absolute error = 5.400e-05
relative error = 0.007424 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.06
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.37
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6712 0.824
h = 0.0001 0.004
y[1] (numeric) = 0.17356418425 0.709436722247
y[1] (closed_form) = 0.173578003985 0.709489680537
absolute error = 5.473e-05
relative error = 0.007493 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.063
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.345
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6713 0.828
h = 0.003 0.006
y[1] (numeric) = 0.171885229168 0.713207633693
y[1] (closed_form) = 0.171897789785 0.713260252114
absolute error = 5.410e-05
relative error = 0.007373 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.066
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.787
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6743 0.834
h = 0.0001 0.005
y[1] (numeric) = 0.172012116365 0.720137463868
y[1] (closed_form) = 0.172026394208 0.720195531683
absolute error = 5.980e-05
relative error = 0.008076 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.072
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7995
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6744 0.839
h = 0.0001 0.003
y[1] (numeric) = 0.169869725518 0.724861347265
y[1] (closed_form) = 0.169883509114 0.724915750943
absolute error = 5.612e-05
relative error = 0.007538 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.076
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6461
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6745 0.842
h = 0.001 0.001
y[1] (numeric) = 0.168615050383 0.72771483943
y[1] (closed_form) = 0.168630115181 0.727768574572
absolute error = 5.581e-05
relative error = 0.00747 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.079
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5083
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6755 0.843
h = 0.001 0.003
y[1] (numeric) = 0.169101415468 0.729101760737
y[1] (closed_form) = 0.169116994425 0.729154955238
absolute error = 5.543e-05
relative error = 0.007405 %
Correct digits = 4
memory used=1120.3MB, alloc=52.3MB, time=13.56
Radius of convergence (given) for eq 1 = 1.08
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.416
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6765 0.846
h = 0.0001 0.004
y[1] (numeric) = 0.168688758832 0.73236355244
y[1] (closed_form) = 0.168703245885 0.732417804721
absolute error = 5.615e-05
relative error = 0.007471 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.083
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.371
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6766 0.85
h = 0.003 0.006
y[1] (numeric) = 0.166976611485 0.736162852175
y[1] (closed_form) = 0.166989849842 0.736216773419
absolute error = 5.552e-05
relative error = 0.007355 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.086
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.821
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6796 0.856
h = 0.0001 0.005
y[1] (numeric) = 0.167073475225 0.743159346185
y[1] (closed_form) = 0.167088438635 0.74321865773
absolute error = 6.117e-05
relative error = 0.00803 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.093
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8148
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6797 0.861
h = 0.0001 0.003
y[1] (numeric) = 0.164889708805 0.747918392152
y[1] (closed_form) = 0.164904166589 0.747974076165
absolute error = 5.753e-05
relative error = 0.007511 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.097
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6584
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6798 0.864
h = 0.001 0.001
y[1] (numeric) = 0.163610551168 0.750793335461
y[1] (closed_form) = 0.163626275224 0.750848351661
absolute error = 5.722e-05
relative error = 0.007446 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.099
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.518
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6808 0.865
h = 0.0001 0.004
y[1] (numeric) = 0.164095406407 0.75219550675
y[1] (closed_form) = 0.164111637462 0.752249985156
absolute error = 5.684e-05
relative error = 0.007383 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.101
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.114
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6809 0.869
h = 0.003 0.006
y[1] (numeric) = 0.162356395134 0.756017881236
y[1] (closed_form) = 0.162369693463 0.756072911129
absolute error = 5.661e-05
relative error = 0.007321 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.104
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.851
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6839 0.875
h = 0.0001 0.005
y[1] (numeric) = 0.162427088068 0.763071011272
y[1] (closed_form) = 0.162442118084 0.763131381922
absolute error = 6.221e-05
relative error = 0.007974 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.111
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8279
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1165.6MB, alloc=52.3MB, time=14.10
x[1] = 0.684 0.88
h = 0.0001 0.003
y[1] (numeric) = 0.160207721372 0.76785971968
y[1] (closed_form) = 0.16022223617 0.767916493483
absolute error = 5.860e-05
relative error = 0.00747 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.115
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.669
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6841 0.883
h = 0.001 0.001
y[1] (numeric) = 0.158907492314 0.770752764324
y[1] (closed_form) = 0.158923260862 0.770808870899
absolute error = 5.828e-05
relative error = 0.007405 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.117
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5263
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6851 0.884
h = 0.001 0.003
y[1] (numeric) = 0.159390931663 0.772167936867
y[1] (closed_form) = 0.1594072012 0.772223508027
absolute error = 5.790e-05
relative error = 0.007343 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.118
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.501
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6861 0.887
h = 0.0001 0.004
y[1] (numeric) = 0.158944158499 0.775483265793
y[1] (closed_form) = 0.158959363345 0.775539885215
absolute error = 5.863e-05
relative error = 0.007405 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.121
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.419
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6862 0.891
h = 0.003 0.006
y[1] (numeric) = 0.157171065467 0.779334680182
y[1] (closed_form) = 0.157185040443 0.779390984119
absolute error = 5.801e-05
relative error = 0.007296 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.125
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.885
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6892 0.897
h = 0.0001 0.005
y[1] (numeric) = 0.157212786386 0.786453562567
y[1] (closed_form) = 0.15722849911 0.786515151005
absolute error = 6.356e-05
relative error = 0.007925 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.131
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8433
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6893 0.902
h = 0.0001 0.003
y[1] (numeric) = 0.154953032275 0.791277158247
y[1] (closed_form) = 0.154968219819 0.791335184845
absolute error = 5.998e-05
relative error = 0.007438 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.135
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6814
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6894 0.905
h = 0.001 0.001
y[1] (numeric) = 0.153628908492 0.794191478482
y[1] (closed_form) = 0.153645335629 0.794248838876
absolute error = 5.967e-05
relative error = 0.007376 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.138
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.536
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1211.2MB, alloc=52.3MB, time=14.65
x[1] = 0.6904 0.906
h = 0.001 0.003
y[1] (numeric) = 0.154110983013 0.795621651747
y[1] (closed_form) = 0.154127904405 0.795678479593
absolute error = 5.929e-05
relative error = 0.007316 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.139
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.547
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6914 0.909
h = 0.0001 0.004
y[1] (numeric) = 0.153646471828 0.798965597063
y[1] (closed_form) = 0.153662342461 0.79902346791
absolute error = 6.001e-05
relative error = 0.007375 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.142
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.445
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6915 0.913
h = 0.003 0.006
y[1] (numeric) = 0.151841401591 0.80284505056
y[1] (closed_form) = 0.151856052272 0.802902613716
absolute error = 5.940e-05
relative error = 0.007269 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.145
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.92
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6945 0.919
h = 0.0001 0.005
y[1] (numeric) = 0.151854681684 0.810029201318
y[1] (closed_form) = 0.151871075338 0.810091994174
absolute error = 6.490e-05
relative error = 0.007874 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.152
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8588
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6946 0.924
h = 0.0001 0.003
y[1] (numeric) = 0.149555046959 0.814887529577
y[1] (closed_form) = 0.149570906153 0.814946794771
absolute error = 6.135e-05
relative error = 0.007404 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.156
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6938
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6947 0.927
h = 0.001 0.001
y[1] (numeric) = 0.148207329785 0.817823027346
y[1] (closed_form) = 0.14822441481 0.8178816275
absolute error = 6.104e-05
relative error = 0.007344 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.158
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5458
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6957 0.928
h = 0.001 0.003
y[1] (numeric) = 0.148688111242 0.819268070784
y[1] (closed_form) = 0.148705684004 0.819326141257
absolute error = 6.067e-05
relative error = 0.007286 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.16
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.593
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6967 0.931
h = 0.0001 0.004
y[1] (numeric) = 0.148206136087 0.82264044379
y[1] (closed_form) = 0.148222671582 0.822699551982
absolute error = 6.138e-05
relative error = 0.007342 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.163
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.471
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1256.7MB, alloc=52.3MB, time=15.19
x[1] = 0.6968 0.935
h = 0.003 0.006
y[1] (numeric) = 0.146369487799 0.826547809243
y[1] (closed_form) = 0.146384813085 0.826606617213
absolute error = 6.077e-05
relative error = 0.007239 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.166
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.955
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6998 0.941
h = 0.0001 0.005
y[1] (numeric) = 0.146354838222 0.833796751259
y[1] (closed_form) = 0.146371910937 0.833860735537
absolute error = 6.622e-05
relative error = 0.007822 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.173
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8742
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6999 0.946
h = 0.0001 0.003
y[1] (numeric) = 0.14401581428 0.83868965567
y[1] (closed_form) = 0.144032343891 0.838750145659
absolute error = 6.271e-05
relative error = 0.007368 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.177
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7063
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7 0.949
h = 0.001 0.001
y[1] (numeric) = 0.142644795839 0.841646232081
y[1] (closed_form) = 0.142662537899 0.841706058318
absolute error = 6.240e-05
relative error = 0.007309 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.179
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5556
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.701 0.95
h = 0.001 0.003
y[1] (numeric) = 0.143124352577 0.843106017817
y[1] (closed_form) = 0.143142576062 0.843165317238
absolute error = 6.204e-05
relative error = 0.007254 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.181
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.64
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.702 0.953
h = 0.0001 0.004
y[1] (numeric) = 0.142625178001 0.846506631718
y[1] (closed_form) = 0.142642377295 0.846566963565
absolute error = 6.274e-05
relative error = 0.007308 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.184
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.498
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7021 0.957
h = 0.003 0.006
y[1] (numeric) = 0.140757338713 0.850441780819
y[1] (closed_form) = 0.140773337364 0.850501819605
absolute error = 6.213e-05
relative error = 0.007207 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.187
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.99
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7051 0.963
h = 0.0001 0.005
y[1] (numeric) = 0.14071525161 0.857755043911
y[1] (closed_form) = 0.140733001436 0.857820206974
absolute error = 6.754e-05
relative error = 0.007769 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.194
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8898
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7052 0.968
h = 0.0001 0.003
y[1] (numeric) = 0.138337315089 0.862682366676
y[1] (closed_form) = 0.138354513763 0.862744068042
absolute error = 6.405e-05
relative error = 0.007331 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.198
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7188
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1302.2MB, alloc=52.3MB, time=15.74
x[1] = 0.7053 0.971
h = 0.001 0.001
y[1] (numeric) = 0.136943278686 0.865659922208
y[1] (closed_form) = 0.136961676791 0.865720961221
absolute error = 6.375e-05
relative error = 0.007274 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.2
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5654
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7063 0.972
h = 0.0001 0.004
y[1] (numeric) = 0.137421675832 0.86713432499
y[1] (closed_form) = 0.137440549247 0.867194840045
absolute error = 6.339e-05
relative error = 0.00722 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.202
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.399
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7064 0.976
h = 0.003 0.006
y[1] (numeric) = 0.135528564553 0.871092051845
y[1] (closed_form) = 0.13554464137 0.871153148448
absolute error = 6.318e-05
relative error = 0.007166 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.205
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.02
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7094 0.982
h = 0.0001 0.005
y[1] (numeric) = 0.135462481729 0.878459989999
y[1] (closed_form) = 0.135480313018 0.878526167182
absolute error = 6.854e-05
relative error = 0.00771 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.211
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9031
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7095 0.987
h = 0.0001 0.003
y[1] (numeric) = 0.133051014012 0.883416355712
y[1] (closed_form) = 0.133068287289 0.883479098554
absolute error = 6.508e-05
relative error = 0.007284 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.216
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7296
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7096 0.99
h = 0.001 0.001
y[1] (numeric) = 0.131637136634 0.88641161958
y[1] (closed_form) = 0.131655598402 0.886473701206
absolute error = 6.477e-05
relative error = 0.007227 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.218
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5739
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7106 0.991
h = 0.001 0.003
y[1] (numeric) = 0.132114413338 0.887898493075
y[1] (closed_form) = 0.132133345269 0.887960053126
absolute error = 6.441e-05
relative error = 0.007174 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.219
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.727
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7116 0.994
h = 0.0001 0.004
y[1] (numeric) = 0.13158357684 0.89135096857
y[1] (closed_form) = 0.131601507921 0.891413551339
absolute error = 6.510e-05
relative error = 0.007225 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.222
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.547
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1347.8MB, alloc=52.3MB, time=16.28
x[1] = 0.7117 0.998
h = 0.003 0.006
y[1] (numeric) = 0.129658361858 0.895337111008
y[1] (closed_form) = 0.129675109565 0.895399413391
absolute error = 6.451e-05
relative error = 0.007131 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.226
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.055
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7147 1.004
h = 0.0001 0.005
y[1] (numeric) = 0.129565715316 0.902768519292
y[1] (closed_form) = 0.12958422005 0.902835852626
absolute error = 6.983e-05
relative error = 0.007656 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.232
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9188
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7148 1.009
h = 0.0001 0.003
y[1] (numeric) = 0.127116186654 0.907759012472
y[1] (closed_form) = 0.127134126336 0.90782294267
absolute error = 6.640e-05
relative error = 0.007243 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.237
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7422
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7149 1.012
h = 0.001 0.001
y[1] (numeric) = 0.125679797457 0.910775072363
y[1] (closed_form) = 0.125698913256 0.910838342929
absolute error = 6.610e-05
relative error = 0.007188 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.239
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5838
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7159 1.013
h = 0.001 0.003
y[1] (numeric) = 0.126156029237 0.912276337313
y[1] (closed_form) = 0.126175609426 0.912339089143
absolute error = 6.574e-05
relative error = 0.007137 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.24
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.774
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7169 1.016
h = 0.0001 0.004
y[1] (numeric) = 0.125608703754 0.915756533407
y[1] (closed_form) = 0.125627295072 0.915820302665
absolute error = 6.642e-05
relative error = 0.007186 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.243
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.573
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.717 1.02
h = 0.003 0.006
y[1] (numeric) = 0.1236533442 0.919770092522
y[1] (closed_form) = 0.123670761226 0.919833587766
absolute error = 6.584e-05
relative error = 0.007094 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.247
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.09
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.72 1.026
h = 0.0001 0.005
y[1] (numeric) = 0.123534576713 0.927264520547
y[1] (closed_form) = 0.123553752756 0.927332998345
absolute error = 7.111e-05
relative error = 0.007601 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.253
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9344
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1393.1MB, alloc=52.3MB, time=16.82
x[1] = 0.7201 1.031
h = 0.0001 0.003
y[1] (numeric) = 0.121047424839 0.93228898101
y[1] (closed_form) = 0.121066029281 0.93235408616
absolute error = 6.771e-05
relative error = 0.007202 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.258
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7548
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7202 1.034
h = 0.001 0.001
y[1] (numeric) = 0.119588783889 0.935325736469
y[1] (closed_form) = 0.1196085524 0.935390183651
absolute error = 6.741e-05
relative error = 0.007149 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.26
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5937
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7212 1.035
h = 0.001 0.003
y[1] (numeric) = 0.120064027619 0.936841274772
y[1] (closed_form) = 0.120084254922 0.936905206044
absolute error = 6.705e-05
relative error = 0.007099 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.261
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.821
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7222 1.038
h = 0.0001 0.004
y[1] (numeric) = 0.119500445027 0.940349012648
y[1] (closed_form) = 0.119519695081 0.940413956075
absolute error = 6.774e-05
relative error = 0.007145 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.265
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.6
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7223 1.042
h = 0.003 0.006
y[1] (numeric) = 0.117515285789 0.944389857853
y[1] (closed_form) = 0.11753337047 0.944454533386
absolute error = 6.716e-05
relative error = 0.007056 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.268
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.126
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7253 1.048
h = 0.0001 0.005
y[1] (numeric) = 0.117370824513 0.951946862204
y[1] (closed_form) = 0.117390669683 0.952016473086
absolute error = 7.238e-05
relative error = 0.007546 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.275
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9502
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7254 1.053
h = 0.0001 0.003
y[1] (numeric) = 0.114846474627 0.957005129481
y[1] (closed_form) = 0.114865742103 0.957071397506
absolute error = 6.901e-05
relative error = 0.007159 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.279
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7675
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7255 1.056
h = 0.001 0.001
y[1] (numeric) = 0.113365834508 0.960062480034
y[1] (closed_form) = 0.11338625432 0.960128091832
absolute error = 6.872e-05
relative error = 0.007108 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.281
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6036
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7265 1.057
h = 0.001 0.003
y[1] (numeric) = 0.113840144499 0.961592175989
y[1] (closed_form) = 0.113861017669 0.961657274686
absolute error = 6.836e-05
relative error = 0.00706 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.283
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.868
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1438.5MB, alloc=52.3MB, time=17.36
x[1] = 0.7275 1.06
h = 0.0001 0.004
y[1] (numeric) = 0.113260529146 0.965127279048
y[1] (closed_form) = 0.113280436353 0.965193384644
absolute error = 6.904e-05
relative error = 0.007104 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.286
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.627
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7276 1.064
h = 0.003 0.006
y[1] (numeric) = 0.111245905267 0.969195279679
y[1] (closed_form) = 0.111264655857 0.969261123266
absolute error = 6.846e-05
relative error = 0.007017 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.289
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.161
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7306 1.07
h = 0.0001 0.005
y[1] (numeric) = 0.111076162503 0.976814423877
y[1] (closed_form) = 0.111096674573 0.976885156758
absolute error = 7.365e-05
relative error = 0.007491 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.296
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9659
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7307 1.075
h = 0.0001 0.003
y[1] (numeric) = 0.108515027782 0.981906337423
y[1] (closed_form) = 0.108534956491 0.981973756566
absolute error = 7.030e-05
relative error = 0.007116 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.3
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7802
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7308 1.078
h = 0.001 0.001
y[1] (numeric) = 0.107012633902 0.984984182702
y[1] (closed_form) = 0.107033703519 0.985050947422
absolute error = 7.001e-05
relative error = 0.007066 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.302
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6136
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7318 1.079
h = 0.0001 0.004
y[1] (numeric) = 0.107486062041 0.98652792295
y[1] (closed_form) = 0.107507579742 0.986594177359
absolute error = 6.966e-05
relative error = 0.007019 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.304
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.689
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7319 1.083
h = 0.003 0.006
y[1] (numeric) = 0.105447541863 0.990617989096
y[1] (closed_form) = 0.105466384119 0.990684845155
absolute error = 6.946e-05
relative error = 0.006972 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.307
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.191
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7349 1.089
h = 0.0001 0.005
y[1] (numeric) = 0.105255623719 0.998289982206
y[1] (closed_form) = 0.105276228483 0.99836168881
absolute error = 7.461e-05
relative error = 0.007432 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.314
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9794
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1484.0MB, alloc=52.3MB, time=17.90
x[1] = 0.735 1.094
h = 0.0001 0.003
y[1] (numeric) = 0.102662749682 1.00341029716
y[1] (closed_form) = 0.102682766194 1.00347871451
absolute error = 7.129e-05
relative error = 0.007067 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.318
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7911
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7351 1.097
h = 0.001 0.001
y[1] (numeric) = 0.101141579637 1.00650544812
y[1] (closed_form) = 0.10116272743 1.00657321252
absolute error = 7.099e-05
relative error = 0.007017 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.321
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6222
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7361 1.098
h = 0.001 0.003
y[1] (numeric) = 0.101614123005 1.0080611785
y[1] (closed_form) = 0.101635714432 1.0081284349
absolute error = 7.064e-05
relative error = 0.006971 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.322
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.956
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7371 1.101
h = 0.0001 0.004
y[1] (numeric) = 0.101004926076 1.01164655443
y[1] (closed_form) = 0.101025571749 1.01171480815
absolute error = 7.131e-05
relative error = 0.007013 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.325
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.676
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7372 1.105
h = 0.003 0.006
y[1] (numeric) = 0.0989360152285 1.01576439559
y[1] (closed_form) = 0.098955520089 1.01583239777
absolute error = 7.074e-05
relative error = 0.006931 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.328
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.227
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7402 1.111
h = 0.0001 0.005
y[1] (numeric) = 0.0987195506725 1.02349773915
y[1] (closed_form) = 0.0987408182238 1.02357054785
absolute error = 7.585e-05
relative error = 0.007376 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.335
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9952
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7403 1.116
h = 0.0001 0.003
y[1] (numeric) = 0.0960906321788 1.02865140667
y[1] (closed_form) = 0.0961113065422 1.02872095404
absolute error = 7.256e-05
relative error = 0.007022 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.339
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8038
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7404 1.119
h = 0.001 0.001
y[1] (numeric) = 0.0945481481064 1.03176686896
y[1] (closed_form) = 0.0945699428568 1.03183576528
absolute error = 7.226e-05
relative error = 0.006974 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.342
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6322
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1529.5MB, alloc=52.3MB, time=18.44
x[1] = 0.7414 1.12
h = 0.001 0.003
y[1] (numeric) = 0.0950199014646 1.03333643928
y[1] (closed_form) = 0.0950421348522 1.03340483037
absolute error = 7.191e-05
relative error = 0.00693 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.343
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.003
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7424 1.123
h = 0.0001 0.004
y[1] (numeric) = 0.0943952770472 1.03694869001
y[1] (closed_form) = 0.0944165750738 1.03701807323
absolute error = 7.258e-05
relative error = 0.00697 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.346
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.703
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7425 1.127
h = 0.003 0.006
y[1] (numeric) = 0.0922978107196 1.04109331734
y[1] (closed_form) = 0.0923179762443 1.0411624543
absolute error = 7.202e-05
relative error = 0.00689 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.35
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.263
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7455 1.133
h = 0.0001 0.005
y[1] (numeric) = 0.0920571732745 1.04888759422
y[1] (closed_form) = 0.092079101291 1.04896149471
absolute error = 7.709e-05
relative error = 0.007321 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.356
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.011
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7456 1.138
h = 0.0001 0.003
y[1] (numeric) = 0.0893925917066 1.05407445439
y[1] (closed_form) = 0.0894139219537 1.05414512086
absolute error = 7.382e-05
relative error = 0.006977 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.361
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8166
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7457 1.141
h = 0.001 0.001
y[1] (numeric) = 0.0878290200537 1.05721012838
y[1] (closed_form) = 0.0878514600658 1.05728014577
absolute error = 7.353e-05
relative error = 0.00693 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.363
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6422
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7467 1.142
h = 0.001 0.003
y[1] (numeric) = 0.0883000290412 1.05879343165
y[1] (closed_form) = 0.0883229028351 1.05886294653
absolute error = 7.318e-05
relative error = 0.006887 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.364
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.051
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7477 1.145
h = 0.0001 0.004
y[1] (numeric) = 0.0876601754686 1.06243238923
y[1] (closed_form) = 0.0876821240067 1.06250289111
absolute error = 7.384e-05
relative error = 0.006926 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.368
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.73
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7478 1.149
h = 0.003 0.006
y[1] (numeric) = 0.0855344542808 1.066603673
y[1] (closed_form) = 0.0855552784763 1.06667393369
absolute error = 7.328e-05
relative error = 0.006848 %
Correct digits = 4
memory used=1574.8MB, alloc=52.3MB, time=18.98
Radius of convergence (given) for eq 1 = 1.371
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.298
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7508 1.155
h = 0.0001 0.005
y[1] (numeric) = 0.0852700051499 1.07445847275
y[1] (closed_form) = 0.0852925912861 1.07453345499
absolute error = 7.831e-05
relative error = 0.007265 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.378
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.027
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7509 1.16
h = 0.0001 0.003
y[1] (numeric) = 0.0825701316194 1.0796783662
y[1] (closed_form) = 0.0825921157365 1.07975014112
absolute error = 7.507e-05
relative error = 0.006932 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.382
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8294
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.751 1.163
h = 0.001 0.001
y[1] (numeric) = 0.0809856927095 1.08283415274
y[1] (closed_form) = 0.0810087762323 1.08290528058
absolute error = 7.478e-05
relative error = 0.006886 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.384
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6523
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.752 1.164
h = 0.001 0.003
y[1] (numeric) = 0.0814560010144 1.08443108406
y[1] (closed_form) = 0.0814795135986 1.08450171212
absolute error = 7.444e-05
relative error = 0.006845 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.386
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.099
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.753 1.167
h = 0.0001 0.004
y[1] (numeric) = 0.0808011105976 1.08809658282
y[1] (closed_form) = 0.080823707755 1.08816819276
absolute error = 7.509e-05
relative error = 0.006882 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.389
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.757
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7531 1.171
h = 0.003 0.006
y[1] (numeric) = 0.0786474271 1.09229439384
y[1] (closed_form) = 0.0786689079268 1.09236576748
absolute error = 7.454e-05
relative error = 0.006806 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.392
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.334
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7561 1.177
h = 0.0001 0.005
y[1] (numeric) = 0.0783595157355 1.10020931258
y[1] (closed_form) = 0.0783827576268 1.10028536678
absolute error = 7.953e-05
relative error = 0.00721 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.399
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.043
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7562 1.182
h = 0.0001 0.003
y[1] (numeric) = 0.0756247114864 1.1054620806
y[1] (closed_form) = 0.0756473474195 1.10553495361
absolute error = 7.631e-05
relative error = 0.006886 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.403
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8422
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1620.2MB, alloc=52.3MB, time=19.52
x[1] = 0.7563 1.185
h = 0.001 0.001
y[1] (numeric) = 0.0740196197618 1.10863788104
y[1] (closed_form) = 0.0740433449947 1.108710109
absolute error = 7.602e-05
relative error = 0.006842 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.406
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6623
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7573 1.186
h = 0.0001 0.004
y[1] (numeric) = 0.0744892692235 1.11024833761
y[1] (closed_form) = 0.0745134189268 1.11032006847
absolute error = 7.569e-05
relative error = 0.006801 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.407
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.981
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7574 1.19
h = 0.003 0.006
y[1] (numeric) = 0.0723128886472 1.11446770415
y[1] (closed_form) = 0.0723344712289 1.11454004966
absolute error = 7.550e-05
relative error = 0.00676 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.411
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.365
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7604 1.196
h = 0.0001 0.005
y[1] (numeric) = 0.0720043433191 1.12243377884
y[1] (closed_form) = 0.0720276864432 1.12251077035
absolute error = 8.045e-05
relative error = 0.007152 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.417
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.057
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7605 1.201
h = 0.0001 0.003
y[1] (numeric) = 0.0692393648513 1.12771430727
y[1] (closed_form) = 0.0692620985589 1.12778813959
absolute error = 7.725e-05
relative error = 0.006837 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.422
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8532
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7606 1.204
h = 0.001 0.001
y[1] (numeric) = 0.0676164264542 1.1309070138
y[1] (closed_form) = 0.0676402409337 1.13098020274
absolute error = 7.697e-05
relative error = 0.006793 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.424
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.671
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7616 1.205
h = 0.001 0.003
y[1] (numeric) = 0.0680853814864 1.13252902447
y[1] (closed_form) = 0.0681096165527 1.13260171852
absolute error = 7.663e-05
relative error = 0.006753 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.426
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.188
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7626 1.208
h = 0.0001 0.004
y[1] (numeric) = 0.0674026917026 1.136243303
y[1] (closed_form) = 0.0674260289938 1.13631696966
absolute error = 7.727e-05
relative error = 0.006789 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.429
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.808
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1665.6MB, alloc=52.3MB, time=20.07
x[1] = 0.7627 1.212
h = 0.003 0.006
y[1] (numeric) = 0.065197416784 1.14048980817
y[1] (closed_form) = 0.0652196522179 1.14056324728
absolute error = 7.673e-05
relative error = 0.006717 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.432
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.401
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7657 1.218
h = 0.0001 0.005
y[1] (numeric) = 0.0648660346395 1.14851527139
y[1] (closed_form) = 0.0648900291891 1.14859331721
absolute error = 8.165e-05
relative error = 0.007097 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.439
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.073
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7658 1.223
h = 0.0001 0.003
y[1] (numeric) = 0.0620667745466 1.15382838523
y[1] (closed_form) = 0.0620901562757 1.15390329696
absolute error = 7.848e-05
relative error = 0.006791 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.443
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8661
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7659 1.226
h = 0.001 0.001
y[1] (numeric) = 0.0604235686461 1.15704092605
y[1] (closed_form) = 0.0604480214879 1.1571151965
absolute error = 7.819e-05
relative error = 0.006748 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.446
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6811
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7669 1.227
h = 0.001 0.003
y[1] (numeric) = 0.0608919392649 1.15867627642
y[1] (closed_form) = 0.0609168083301 1.15875005462
absolute error = 7.786e-05
relative error = 0.00671 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.447
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.235
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7679 1.23
h = 0.0001 0.004
y[1] (numeric) = 0.0601947337043 1.16241663673
y[1] (closed_form) = 0.0602187140922 1.16249138254
absolute error = 7.850e-05
relative error = 0.006744 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.45
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.835
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.768 1.234
h = 0.003 0.006
y[1] (numeric) = 0.0579622931117 1.16668930647
y[1] (closed_form) = 0.0579851792518 1.16676382915
absolute error = 7.796e-05
relative error = 0.006673 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.453
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.437
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.771 1.24
h = 0.0001 0.005
y[1] (numeric) = 0.0576083927702 1.17477377252
y[1] (closed_form) = 0.0576330363412 1.1748528635
absolute error = 8.284e-05
relative error = 0.007043 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.46
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.089
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1711.0MB, alloc=52.3MB, time=20.61
x[1] = 0.7711 1.245
h = 0.0001 0.003
y[1] (numeric) = 0.0547751861107 1.18011931539
y[1] (closed_form) = 0.0547992137164 1.18019529687
absolute error = 7.969e-05
relative error = 0.006745 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.464
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.879
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7712 1.248
h = 0.001 0.001
y[1] (numeric) = 0.0531119115478 1.18335159355
y[1] (closed_form) = 0.0531370008356 1.18342693587
absolute error = 7.941e-05
relative error = 0.006703 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.467
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6912
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7722 1.249
h = 0.001 0.003
y[1] (numeric) = 0.0535797347963 1.1850001864
y[1] (closed_form) = 0.0536052360593 1.18507503908
absolute error = 7.908e-05
relative error = 0.006666 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.468
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.284
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7732 1.252
h = 0.0001 0.004
y[1] (numeric) = 0.0528681848267 1.18876647145
y[1] (closed_form) = 0.0528928062735 1.18884228678
absolute error = 7.971e-05
relative error = 0.006698 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.472
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.862
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7733 1.256
h = 0.003 0.006
y[1] (numeric) = 0.0506088427818 1.1930651793
y[1] (closed_form) = 0.0506323774552 1.19314077576
absolute error = 7.918e-05
relative error = 0.00663 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.475
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.473
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7763 1.262
h = 0.0001 0.005
y[1] (numeric) = 0.0502327330234 1.20120826866
y[1] (closed_form) = 0.0502580232046 1.20128839588
absolute error = 8.402e-05
relative error = 0.006988 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.482
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.105
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7764 1.267
h = 0.0001 0.003
y[1] (numeric) = 0.0473659063699 1.20658608519
y[1] (closed_form) = 0.0473905776846 1.20666312697
absolute error = 8.090e-05
relative error = 0.006699 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.486
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8919
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7765 1.27
h = 0.001 0.001
y[1] (numeric) = 0.0456827569325 1.20983800445
y[1] (closed_form) = 0.0457084807188 1.2099144092
absolute error = 8.062e-05
relative error = 0.006658 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.489
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7013
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7775 1.271
h = 0.001 0.003
y[1] (numeric) = 0.0461500683478 1.21149974443
y[1] (closed_form) = 0.046176199972 1.21157566213
absolute error = 8.029e-05
relative error = 0.006622 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.49
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.332
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1756.4MB, alloc=52.3MB, time=21.15
x[1] = 0.7785 1.274
h = 0.0001 0.004
y[1] (numeric) = 0.0454243404628 1.21529179937
y[1] (closed_form) = 0.0454496009045 1.21536867482
absolute error = 8.092e-05
relative error = 0.006653 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.493
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.889
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7786 1.278
h = 0.003 0.006
y[1] (numeric) = 0.043138354519 1.21961641975
y[1] (closed_form) = 0.0431625355296 1.21969308045
absolute error = 8.038e-05
relative error = 0.006586 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.496
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.509
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7816 1.284
h = 0.0001 0.005
y[1] (numeric) = 0.0427403347143 1.227817759
y[1] (closed_form) = 0.0427662690899 1.22789891373
absolute error = 8.520e-05
relative error = 0.006934 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.503
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.121
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7817 1.289
h = 0.0001 0.003
y[1] (numeric) = 0.0398402064724 1.2332276949
y[1] (closed_form) = 0.0398655193089 1.23330578776
absolute error = 8.209e-05
relative error = 0.006653 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.508
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9048
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7818 1.292
h = 0.001 0.001
y[1] (numeric) = 0.038137371085 1.23649915974
y[1] (closed_form) = 0.0381637273954 1.23657661772
absolute error = 8.182e-05
relative error = 0.006613 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.51
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7115
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7828 1.293
h = 0.0001 0.004
y[1] (numeric) = 0.0386042047743 1.2381739533
y[1] (closed_form) = 0.0386309648918 1.23825092679
absolute error = 8.149e-05
relative error = 0.006578 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.511
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.276
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7829 1.297
h = 0.003 0.006
y[1] (numeric) = 0.0362965758515 1.24251963137
y[1] (closed_form) = 0.0363208661899 1.2425972274
absolute error = 8.131e-05
relative error = 0.006541 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.515
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.54
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7859 1.303
h = 0.0001 0.005
y[1] (numeric) = 0.0358792415238 1.25077055942
y[1] (closed_form) = 0.0359052836446 1.25085261849
absolute error = 8.609e-05
relative error = 0.00688 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.522
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.134
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1801.8MB, alloc=52.3MB, time=21.69
x[1] = 0.786 1.308
h = 0.0001 0.003
y[1] (numeric) = 0.0329503172175 1.25620762823
y[1] (closed_form) = 0.0329757353988 1.25628664529
absolute error = 8.300e-05
relative error = 0.006605 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.526
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9159
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7861 1.311
h = 0.001 0.001
y[1] (numeric) = 0.0312304532347 1.25949560982
y[1] (closed_form) = 0.0312569072836 1.25957399377
absolute error = 8.273e-05
relative error = 0.006566 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.529
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7202
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7871 1.312
h = 0.001 0.003
y[1] (numeric) = 0.0316967479755 1.26118156076
y[1] (closed_form) = 0.0317236024142 1.26125946234
absolute error = 8.240e-05
relative error = 0.006531 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.53
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.421
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7881 1.315
h = 0.0001 0.004
y[1] (numeric) = 0.0309447628446 1.26502099839
y[1] (closed_form) = 0.0309707616473 1.26509984882
absolute error = 8.303e-05
relative error = 0.006561 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.533
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.94
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7882 1.319
h = 0.003 0.006
y[1] (numeric) = 0.0286095573201 1.26939319447
y[1] (closed_form) = 0.0286344899672 1.26947183754
absolute error = 8.250e-05
relative error = 0.006497 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.537
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.576
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7912 1.325
h = 0.0001 0.005
y[1] (numeric) = 0.0281708506217 1.27770169671
y[1] (closed_form) = 0.0281975325351 1.27778476754
absolute error = 8.725e-05
relative error = 0.006827 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.543
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.151
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7913 1.33
h = 0.0001 0.003
y[1] (numeric) = 0.0252091983011 1.28317060438
y[1] (closed_form) = 0.0252352539981 1.28325065588
absolute error = 8.419e-05
relative error = 0.006559 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.548
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9289
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7914 1.333
h = 0.001 0.001
y[1] (numeric) = 0.0234699887006 1.28647795797
y[1] (closed_form) = 0.0234970716438 1.28655737855
absolute error = 8.391e-05
relative error = 0.006521 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.55
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7304
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1847.3MB, alloc=52.3MB, time=22.23
x[1] = 0.7924 1.334
h = 0.001 0.003
y[1] (numeric) = 0.0239358666811 1.28817679348
y[1] (closed_form) = 0.0239633461711 1.2882557342
absolute error = 8.359e-05
relative error = 0.006487 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.552
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.469
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7934 1.337
h = 0.0001 0.004
y[1] (numeric) = 0.0231701565318 1.29204157184
y[1] (closed_form) = 0.0231967884147 1.29212145663
absolute error = 8.421e-05
relative error = 0.006516 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.555
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.967
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7935 1.341
h = 0.003 0.006
y[1] (numeric) = 0.020809010727 1.29643932924
y[1] (closed_form) = 0.0208345834369 1.29651901041
absolute error = 8.368e-05
relative error = 0.006454 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.558
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.612
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7965 1.347
h = 0.0001 0.005
y[1] (numeric) = 0.020349206216 1.30480504894
y[1] (closed_form) = 0.0203765255023 1.30488912337
absolute error = 8.840e-05
relative error = 0.006774 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.565
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.167
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7966 1.352
h = 0.0001 0.003
y[1] (numeric) = 0.0173551225343 1.31030564444
y[1] (closed_form) = 0.0173818135192 1.31038672176
absolute error = 8.536e-05
relative error = 0.006513 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.569
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9419
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7967 1.355
h = 0.001 0.001
y[1] (numeric) = 0.0155967432919 1.31363227671
y[1] (closed_form) = 0.0156244530941 1.3137127253
absolute error = 8.509e-05
relative error = 0.006476 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.572
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7406
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7977 1.356
h = 0.001 0.003
y[1] (numeric) = 0.0160622348874 1.31534390816
y[1] (closed_form) = 0.0160903374889 1.31542387937
absolute error = 8.477e-05
relative error = 0.006443 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.573
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.518
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7987 1.359
h = 0.0001 0.004
y[1] (numeric) = 0.0152829491668 1.31923388065
y[1] (closed_form) = 0.0153102119939 1.3193147912
absolute error = 8.538e-05
relative error = 0.006471 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.576
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.995
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7988 1.363
h = 0.003 0.006
y[1] (numeric) = 0.0128960971186 1.3236570775
y[1] (closed_form) = 0.0129223076344 1.32373778805
absolute error = 8.486e-05
relative error = 0.00641 %
Correct digits = 4
memory used=1892.7MB, alloc=52.3MB, time=22.77
Radius of convergence (given) for eq 1 = 1.58
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.649
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8018 1.369
h = 0.0001 0.005
y[1] (numeric) = 0.0124154613999 1.3320796636
y[1] (closed_form) = 0.0124434156423 1.33216473362
absolute error = 8.955e-05
relative error = 0.006721 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.587
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.183
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8019 1.374
h = 0.0001 0.003
y[1] (numeric) = 0.00938923593791 1.33761179712
y[1] (closed_form) = 0.00941655997465 1.33769389181
absolute error = 8.652e-05
relative error = 0.006468 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.591
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9549
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.802 1.377
h = 0.001 0.001
y[1] (numeric) = 0.00761185882108 1.34095761557
y[1] (closed_form) = 0.00764019343228 1.34103908374
absolute error = 8.625e-05
relative error = 0.006432 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.594
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7508
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.803 1.378
h = 0.001 0.003
y[1] (numeric) = 0.00807699323031 1.34268195597
y[1] (closed_form) = 0.00810571698518 1.34276294921
absolute error = 8.594e-05
relative error = 0.0064 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.595
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.566
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.804 1.381
h = 0.0001 0.004
y[1] (numeric) = 0.0072842773971 1.34659697808
y[1] (closed_form) = 0.00731216902117 1.34667890598
absolute error = 8.655e-05
relative error = 0.006426 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.598
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.022
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8041 1.385
h = 0.003 0.006
y[1] (numeric) = 0.00487194758261 1.35104549354
y[1] (closed_form) = 0.00489879363938 1.35112722495
absolute error = 8.603e-05
relative error = 0.006367 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.601
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.685
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8071 1.391
h = 0.0001 0.005
y[1] (numeric) = 0.00437073963762 1.35952460053
y[1] (closed_form) = 0.00439932642401 1.35961065833
absolute error = 9.068e-05
relative error = 0.00667 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.608
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.199
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8072 1.396
h = 0.0001 0.003
y[1] (numeric) = 0.00131265515741 1.36508812355
y[1] (closed_form) = 0.00134061000389 1.36517122738
absolute error = 8.768e-05
relative error = 0.006423 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.613
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9679
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1938.1MB, alloc=52.3MB, time=23.32
x[1] = 0.8073 1.399
h = 0.001 0.001
y[1] (numeric) = -0.000483552123619 1.36845303652
y[1] (closed_form) = -0.000454594765675 1.36853551602
absolute error = 8.742e-05
relative error = 0.006387 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.615
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.761
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8083 1.4
h = 0.003 0.006
y[1] (numeric) = -1.87468225520e-05 1.37019000047
y[1] (closed_form) = 1.05961119227e-05 1.37027200746
absolute error = 8.710e-05
relative error = 0.006356 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.617
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.668
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8113 1.406
h = 0.0001 0.005
y[1] (numeric) = -0.000529377110251 1.37870565325
y[1] (closed_form) = -0.000501465322405 1.37879461162
absolute error = 9.323e-05
relative error = 0.006762 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.623
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.21
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8114 1.411
h = 0.0001 0.003
y[1] (numeric) = -0.00360843002829 1.38429147751
y[1] (closed_form) = -0.00358115075441 1.38437749638
absolute error = 9.024e-05
relative error = 0.006518 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.628
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9769
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8115 1.414
h = 0.001 0.001
y[1] (numeric) = -0.00541701677082 1.38766994205
y[1] (closed_form) = -0.00538874037501 1.38775533832
absolute error = 8.996e-05
relative error = 0.006482 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.63
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7681
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8125 1.415
h = 0.001 0.003
y[1] (numeric) = -0.00495210663214 1.38941554831
y[1] (closed_form) = -0.00492344700372 1.38950047381
absolute error = 8.963e-05
relative error = 0.006451 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.632
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.649
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8135 1.418
h = 0.0001 0.004
y[1] (numeric) = -0.0057665484378 1.39337285993
y[1] (closed_form) = -0.00573870856372 1.39345871212
absolute error = 9.025e-05
relative error = 0.006477 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.635
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.068
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8136 1.422
h = 0.003 0.006
y[1] (numeric) = -0.00822074725164 1.39786446893
y[1] (closed_form) = -0.00819394173875 1.39795013014
absolute error = 8.976e-05
relative error = 0.006421 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.638
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.747
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1983.6MB, alloc=52.3MB, time=23.86
x[1] = 0.8166 1.428
h = 0.0001 0.005
y[1] (numeric) = -0.00875470639182 1.40643871282
y[1] (closed_form) = -0.00872616630532 1.40652864621
absolute error = 9.435e-05
relative error = 0.006708 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.645
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.226
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8167 1.433
h = 0.0001 0.003
y[1] (numeric) = -0.0118651595255 1.4120556721
y[1] (closed_form) = -0.0118372534324 1.41214268664
absolute error = 9.138e-05
relative error = 0.006471 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.649
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.99
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8168 1.436
h = 0.001 0.001
y[1] (numeric) = -0.0136923044217 1.41545307436
y[1] (closed_form) = -0.0136634089794 1.41553946849
absolute error = 9.110e-05
relative error = 0.006435 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.652
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7783
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8178 1.437
h = 0.001 0.003
y[1] (numeric) = -0.0132276804604 1.41721116288
y[1] (closed_form) = -0.0131984052111 1.41729708861
absolute error = 9.078e-05
relative error = 0.006405 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.653
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.697
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8188 1.44
h = 0.0001 0.004
y[1] (numeric) = -0.0140551834628 1.4211931424
y[1] (closed_form) = -0.0140267207982 1.4212799903
absolute error = 9.139e-05
relative error = 0.00643 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.657
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.096
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8189 1.444
h = 0.003 0.006
y[1] (numeric) = -0.0165342749243 1.42570974523
y[1] (closed_form) = -0.0165068401822 1.42579640535
absolute error = 9.090e-05
relative error = 0.006375 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.66
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.783
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8219 1.45
h = 0.0001 0.005
y[1] (numeric) = -0.0170881538686 1.434339602
y[1] (closed_form) = -0.017058987873 1.43443050301
absolute error = 9.547e-05
relative error = 0.006655 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.667
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.243
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.822 1.455
h = 0.0001 0.003
y[1] (numeric) = -0.0202297415846 1.43998755148
y[1] (closed_form) = -0.0202012109166 1.44007555389
absolute error = 9.251e-05
relative error = 0.006423 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.671
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.003
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2029.1MB, alloc=52.3MB, time=24.41
x[1] = 0.8221 1.458
h = 0.001 0.001
y[1] (numeric) = -0.0220752871111 1.44340380218
y[1] (closed_form) = -0.0220457747022 1.4434911864
absolute error = 9.223e-05
relative error = 0.006389 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.674
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7886
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8231 1.459
h = 0.001 0.003
y[1] (numeric) = -0.021610923969 1.44517429164
y[1] (closed_form) = -0.0215810350986 1.44526120981
absolute error = 9.191e-05
relative error = 0.006359 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.675
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.746
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8241 1.462
h = 0.0001 0.004
y[1] (numeric) = -0.0224513560779 1.44918080208
y[1] (closed_form) = -0.0224222727879 1.44926863791
absolute error = 9.253e-05
relative error = 0.006384 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.678
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.124
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8242 1.466
h = 0.003 0.006
y[1] (numeric) = -0.0249551305377 1.45372228204
y[1] (closed_form) = -0.0249270688392 1.45380993322
absolute error = 9.203e-05
relative error = 0.00633 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.682
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.82
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8272 1.472
h = 0.0001 0.005
y[1] (numeric) = -0.0255286957113 1.46240742585
y[1] (closed_form) = -0.0254989061871 1.46249928725
absolute error = 9.657e-05
relative error = 0.006602 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.689
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.259
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8273 1.477
h = 0.0001 0.003
y[1] (numeric) = -0.0287011583568 1.46808622203
y[1] (closed_form) = -0.0286720053576 1.46817520472
absolute error = 9.364e-05
relative error = 0.006377 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.693
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.016
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8274 1.48
h = 0.001 0.001
y[1] (numeric) = -0.0305649505471 1.47152123279
y[1] (closed_form) = -0.0305348232561 1.47160959948
absolute error = 9.336e-05
relative error = 0.006343 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.696
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7989
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8284 1.481
h = 0.0001 0.004
y[1] (numeric) = -0.0301008238059 1.47330404334
y[1] (closed_form) = -0.0300703233215 1.4733919463
absolute error = 9.304e-05
relative error = 0.006314 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.697
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.801
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8285 1.485
h = 0.003 0.006
y[1] (numeric) = -0.0326246703855 1.47786574392
y[1] (closed_form) = -0.0325964905243 1.47795427437
absolute error = 9.291e-05
relative error = 0.006285 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.7
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.851
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2074.4MB, alloc=52.3MB, time=24.95
x[1] = 0.8315 1.491
h = 0.0001 0.005
y[1] (numeric) = -0.0332156519696 1.48659798906
y[1] (closed_form) = -0.0331857469574 1.48669070379
absolute error = 9.742e-05
relative error = 0.006551 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.707
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.273
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8316 1.496
h = 0.0001 0.003
y[1] (numeric) = -0.036414852363 1.49230285953
y[1] (closed_form) = -0.0363855850334 1.49239271233
absolute error = 9.450e-05
relative error = 0.00633 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.712
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.027
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8317 1.499
h = 0.001 0.001
y[1] (numeric) = -0.0382944520595 1.49575373328
y[1] (closed_form) = -0.0382642167528 1.49584297189
absolute error = 9.422e-05
relative error = 0.006297 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.714
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8077
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8327 1.5
h = 0.001 0.003
y[1] (numeric) = -0.0378306554368 1.49754708408
y[1] (closed_form) = -0.037800049717 1.4976358609
absolute error = 9.390e-05
relative error = 0.006268 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.716
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.836
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8337 1.503
h = 0.0001 0.004
y[1] (numeric) = -0.0386950937635 1.50159873231
y[1] (closed_form) = -0.0386652809592 1.50168841864
absolute error = 9.451e-05
relative error = 0.006292 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.719
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.175
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8338 1.507
h = 0.003 0.006
y[1] (numeric) = -0.0412445486317 1.50618590767
y[1] (closed_form) = -0.0412157459507 1.50627541498
absolute error = 9.403e-05
relative error = 0.00624 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.722
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.887
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8368 1.513
h = 0.0001 0.005
y[1] (numeric) = -0.041854794636 1.51497284947
y[1] (closed_form) = -0.041824270416 1.51506651151
absolute error = 9.851e-05
relative error = 0.0065 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.729
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.289
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8369 1.518
h = 0.0001 0.003
y[1] (numeric) = -0.0450844003603 1.52070830622
y[1] (closed_form) = -0.0450545147816 1.52079912551
absolute error = 9.561e-05
relative error = 0.006284 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.733
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.04
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2119.8MB, alloc=52.3MB, time=25.49
x[1] = 0.837 1.521
h = 0.001 0.001
y[1] (numeric) = -0.0469819682496 1.52417777958
y[1] (closed_form) = -0.0469511218603 1.52426798689
absolute error = 9.534e-05
relative error = 0.006252 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.736
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8179
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.838 1.522
h = 0.001 0.003
y[1] (numeric) = -0.0465183640349 1.52598330684
y[1] (closed_form) = -0.0464871503633 1.52607305462
absolute error = 9.502e-05
relative error = 0.006224 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.737
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.885
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.839 1.525
h = 0.0001 0.004
y[1] (numeric) = -0.0473953699517 1.53005910604
y[1] (closed_form) = -0.0473649426341 1.53014975898
absolute error = 9.562e-05
relative error = 0.006246 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.741
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.202
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8391 1.529
h = 0.003 0.006
y[1] (numeric) = -0.0499689321461 1.53467083316
y[1] (closed_form) = -0.0499395089136 1.53476130994
absolute error = 9.514e-05
relative error = 0.006196 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.744
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.924
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8421 1.535
h = 0.0001 0.005
y[1] (numeric) = -0.0505982264121 1.54351215983
y[1] (closed_form) = -0.0505670853362 1.54360676236
absolute error = 9.960e-05
relative error = 0.006449 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.751
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.305
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8422 1.54
h = 0.0001 0.003
y[1] (numeric) = -0.0538579938436 1.54927806321
y[1] (closed_form) = -0.0538274922519 1.54936984181
absolute error = 9.671e-05
relative error = 0.006238 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.755
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.054
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8423 1.543
h = 0.001 0.001
y[1] (numeric) = -0.0557733854904 1.55276605026
y[1] (closed_form) = -0.0557419301094 1.55285721907
absolute error = 9.644e-05
relative error = 0.006207 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.758
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8282
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8433 1.544
h = 0.001 0.003
y[1] (numeric) = -0.0553099517408 1.55458367801
y[1] (closed_form) = -0.0552781321385 1.55467438955
absolute error = 9.613e-05
relative error = 0.006179 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.759
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.934
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2165.2MB, alloc=52.3MB, time=26.04
x[1] = 0.8443 1.547
h = 0.0001 0.004
y[1] (numeric) = -0.0561994053374 1.55868349843
y[1] (closed_form) = -0.0561683656718 1.55877511082
absolute error = 9.673e-05
relative error = 0.006201 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.762
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.23
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8444 1.551
h = 0.003 0.006
y[1] (numeric) = -0.0587968825208 1.56331966488
y[1] (closed_form) = -0.0587668410003 1.56341110388
absolute error = 9.625e-05
relative error = 0.006152 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.766
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.961
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8474 1.557
h = 0.0001 0.005
y[1] (numeric) = -0.0594450145124 1.57221506938
y[1] (closed_form) = -0.0594132589201 1.57231060571
absolute error = 0.0001007
relative error = 0.006398 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.773
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.322
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8475 1.562
h = 0.0001 0.003
y[1] (numeric) = -0.0627347052679 1.5780112811
y[1] (closed_form) = -0.0627035898936 1.578104012
absolute error = 9.781e-05
relative error = 0.006193 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.777
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.067
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8476 1.565
h = 0.001 0.001
y[1] (numeric) = -0.0646677793524 1.58151769678
y[1] (closed_form) = -0.0646357170694 1.58160982007
absolute error = 9.754e-05
relative error = 0.006162 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.78
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8385
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8486 1.566
h = 0.001 0.003
y[1] (numeric) = -0.0642044949112 1.58334735037
y[1] (closed_form) = -0.0641720714001 1.58343901861
absolute error = 9.723e-05
relative error = 0.006136 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.781
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.983
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8496 1.569
h = 0.0001 0.004
y[1] (numeric) = -0.0651062791518 1.58747106406
y[1] (closed_form) = -0.0650746293 1.58756362889
absolute error = 9.783e-05
relative error = 0.006157 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.784
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.258
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8497 1.573
h = 0.003 0.006
y[1] (numeric) = -0.0677274831098 1.59213155854
y[1] (closed_form) = -0.067696825559 1.59222395268
absolute error = 9.735e-05
relative error = 0.006108 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.788
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.997
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8527 1.579
h = 0.0001 0.005
y[1] (numeric) = -0.0683942477008 1.60108073846
y[1] (closed_form) = -0.068361879919 1.60117720205
absolute error = 0.0001017
relative error = 0.006349 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.795
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.338
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2210.5MB, alloc=52.3MB, time=26.58
x[1] = 0.8528 1.584
h = 0.0001 0.003
y[1] (numeric) = -0.0717136284659 1.60690712162
y[1] (closed_form) = -0.0716819015327 1.60700079793
absolute error = 9.890e-05
relative error = 0.006148 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.799
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.08
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8529 1.587
h = 0.001 0.001
y[1] (numeric) = -0.0736642466808 1.61043188174
y[1] (closed_form) = -0.0736315795832 1.61052495263
absolute error = 9.864e-05
relative error = 0.006118 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.802
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8488
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8539 1.588
h = 0.0001 0.004
y[1] (numeric) = -0.073201091143 1.61227348779
y[1] (closed_form) = -0.0731680657453 1.61236610581
absolute error = 9.833e-05
relative error = 0.006092 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.803
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.101
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.854 1.592
h = 0.003 0.006
y[1] (numeric) = -0.0758415997866 1.61695375932
y[1] (closed_form) = -0.0758108206396 1.61704700477
absolute error = 9.819e-05
relative error = 0.006066 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.807
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.029
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.857 1.598
h = 0.0001 0.005
y[1] (numeric) = -0.076524878174 1.62594876991
y[1] (closed_form) = -0.0764923918288 1.62604606119
absolute error = 0.0001026
relative error = 0.006301 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.813
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.352
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8571 1.603
h = 0.0001 0.003
y[1] (numeric) = -0.0798699892341 1.63180066508
y[1] (closed_form) = -0.0798381444132 1.63189518444
absolute error = 9.974e-05
relative error = 0.006105 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.818
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.091
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8572 1.606
h = 0.001 0.001
y[1] (numeric) = -0.081835817497 1.63534094194
y[1] (closed_form) = -0.0818030382369 1.63543485766
absolute error = 9.947e-05
relative error = 0.006075 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.82
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8577
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8582 1.607
h = 0.001 0.003
y[1] (numeric) = -0.0813728983355 1.63719277723
y[1] (closed_form) = -0.0813397632707 1.63728624192
absolute error = 9.916e-05
relative error = 0.006049 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.822
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.074
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2256.0MB, alloc=52.3MB, time=27.12
x[1] = 0.8592 1.61
h = 0.0001 0.004
y[1] (numeric) = -0.0822976060545 1.64136047254
y[1] (closed_form) = -0.0822652332747 1.64145482609
absolute error = 9.975e-05
relative error = 0.006069 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.825
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.309
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8593 1.614
h = 0.003 0.006
y[1] (numeric) = -0.0849627593451 1.64606566591
y[1] (closed_form) = -0.0849313682688 1.64615985365
absolute error = 9.928e-05
relative error = 0.006023 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.828
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.066
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8623 1.62
h = 0.0001 0.005
y[1] (numeric) = -0.0856642988772 1.65511390352
y[1] (closed_form) = -0.0856312045616 1.65521211018
absolute error = 0.0001036
relative error = 0.006253 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.835
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.368
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8624 1.625
h = 0.0001 0.003
y[1] (numeric) = -0.089038677142 1.66099572168
y[1] (closed_form) = -0.0890062248008 1.66109117396
absolute error = 0.0001008
relative error = 0.006061 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.84
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.104
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8625 1.628
h = 0.001 0.001
y[1] (numeric) = -0.0910217988847 1.66455419021
y[1] (closed_form) = -0.090988418606 1.66464904104
absolute error = 0.0001006
relative error = 0.006031 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.842
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.868
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8635 1.629
h = 0.001 0.003
y[1] (numeric) = -0.0905589717069 1.6664178449
y[1] (closed_form) = -0.0905252384353 1.66651224683
absolute error = 0.0001002
relative error = 0.006007 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.844
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.123
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8645 1.632
h = 0.0001 0.004
y[1] (numeric) = -0.0914956887791 1.67060907845
y[1] (closed_form) = -0.0914627118901 1.67070436511
absolute error = 0.0001008
relative error = 0.006026 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.847
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.337
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8646 1.636
h = 0.003 0.006
y[1] (numeric) = -0.09418405071 1.67533828975
y[1] (closed_form) = -0.0941520499412 1.67543341309
absolute error = 0.0001004
relative error = 0.005981 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.85
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.102
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2301.5MB, alloc=52.3MB, time=27.66
x[1] = 0.8676 1.642
h = 0.0001 0.005
y[1] (numeric) = -0.0949036607047 1.68443946465
y[1] (closed_form) = -0.0948699607075 1.6845385805
absolute error = 0.0001047
relative error = 0.006205 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.857
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.384
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8677 1.647
h = 0.0001 0.003
y[1] (numeric) = -0.0983070864898 1.69035107275
y[1] (closed_form) = -0.0982740288297 1.69044745146
absolute error = 0.0001019
relative error = 0.006017 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.862
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.117
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8678 1.65
h = 0.001 0.001
y[1] (numeric) = -0.100307371506 1.69392765122
y[1] (closed_form) = -0.100273392285 1.69402343063
absolute error = 0.0001016
relative error = 0.005989 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.864
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8783
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8688 1.651
h = 0.001 0.003
y[1] (numeric) = -0.0998446178956 1.69580305537
y[1] (closed_form) = -0.0998102884343 1.69589838801
absolute error = 0.0001013
relative error = 0.005964 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.866
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.172
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8698 1.654
h = 0.0001 0.004
y[1] (numeric) = -0.100793237481 1.70001770588
y[1] (closed_form) = -0.100759658623 1.70011391917
absolute error = 0.0001019
relative error = 0.005983 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.869
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.365
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8699 1.658
h = 0.003 0.006
y[1] (numeric) = -0.103504634552 1.70477082808
y[1] (closed_form) = -0.103472026318 1.70486688046
absolute error = 0.0001014
relative error = 0.005939 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.872
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.139
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8729 1.664
h = 0.0001 0.005
y[1] (numeric) = -0.104242129007 1.71392465484
y[1] (closed_form) = -0.104207825603 1.71402467379
absolute error = 0.0001057
relative error = 0.006158 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.879
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.401
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.873 1.669
h = 0.0001 0.003
y[1] (numeric) = -0.107674387098 1.71986592118
y[1] (closed_form) = -0.107640726311 1.71996321994
absolute error = 0.000103
relative error = 0.005974 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.884
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.131
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8731 1.672
h = 0.001 0.001
y[1] (numeric) = -0.109691707837 1.72346052873
y[1] (closed_form) = -0.109657131744 1.72355723033
absolute error = 0.0001027
relative error = 0.005946 %
Correct digits = 4
memory used=2347.0MB, alloc=52.3MB, time=28.20
Radius of convergence (given) for eq 1 = 1.886
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8887
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8741 1.673
h = 0.001 0.003
y[1] (numeric) = -0.109229010012 1.72534761354
y[1] (closed_form) = -0.109194086373 1.72544387047
absolute error = 0.0001024
relative error = 0.005923 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.888
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.221
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8751 1.676
h = 0.0001 0.004
y[1] (numeric) = -0.110189427688 1.72958556138
y[1] (closed_form) = -0.110155248993 1.72968269493
absolute error = 0.000103
relative error = 0.005941 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.891
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.392
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8752 1.68
h = 0.003 0.006
y[1] (numeric) = -0.112923689917 1.73436248859
y[1] (closed_form) = -0.112890476435 1.73445946357
absolute error = 0.0001025
relative error = 0.005897 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.894
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.176
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8782 1.686
h = 0.0001 0.005
y[1] (numeric) = -0.113678887342 1.74356868592
y[1] (closed_form) = -0.113643982789 1.74366960201
absolute error = 0.0001068
relative error = 0.006111 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.901
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.417
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8783 1.691
h = 0.0001 0.003
y[1] (numeric) = -0.117139766853 1.7495394802
y[1] (closed_form) = -0.117105505119 1.74963769274
absolute error = 0.000104
relative error = 0.005932 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.905
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.144
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8784 1.694
h = 0.001 0.001
y[1] (numeric) = -0.119173998337 1.75315203679
y[1] (closed_form) = -0.119138827436 1.75324965432
absolute error = 0.0001038
relative error = 0.005905 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.908
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.899
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8794 1.695
h = 0.0001 0.004
y[1] (numeric) = -0.118711339121 1.7550507346
y[1] (closed_form) = -0.118675823314 1.75514790952
absolute error = 0.0001035
relative error = 0.005881 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.91
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.403
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8795 1.699
h = 0.003 0.006
y[1] (numeric) = -0.121464213728 1.75984701641
y[1] (closed_form) = -0.121430876115 1.75994481711
absolute error = 0.0001033
relative error = 0.005857 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.913
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.207
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2392.4MB, alloc=52.3MB, time=28.75
x[1] = 0.8825 1.705
h = 0.0001 0.005
y[1] (numeric) = -0.122235126628 1.76909786248
y[1] (closed_form) = -0.122200101205 1.76919958268
absolute error = 0.0001076
relative error = 0.006066 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.92
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.431
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8826 1.71
h = 0.0001 0.003
y[1] (numeric) = -0.125720826488 1.77509363247
y[1] (closed_form) = -0.125686444193 1.77519266323
absolute error = 0.0001048
relative error = 0.005891 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.924
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.155
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8827 1.713
h = 0.001 0.001
y[1] (numeric) = -0.12776972853 1.77872137612
y[1] (closed_form) = -0.127734442285 1.77881981363
absolute error = 0.0001046
relative error = 0.005864 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.927
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9079
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8837 1.714
h = 0.001 0.003
y[1] (numeric) = -0.127307226497 1.78063001646
y[1] (closed_form) = -0.127271597599 1.78072801309
absolute error = 0.0001043
relative error = 0.005841 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.928
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.312
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8847 1.717
h = 0.0001 0.004
y[1] (numeric) = -0.128289601912 1.78491086465
y[1] (closed_form) = -0.128254707681 1.78500973058
absolute error = 0.0001048
relative error = 0.005858 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.932
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.444
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8848 1.721
h = 0.003 0.006
y[1] (numeric) = -0.131066250682 1.78973154158
y[1] (closed_form) = -0.131032311843 1.7898302532
absolute error = 0.0001044
relative error = 0.005816 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.935
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.244
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8878 1.727
h = 0.0001 0.005
y[1] (numeric) = -0.131854537067 1.79903424772
y[1] (closed_form) = -0.131818914591 1.79913685422
absolute error = 0.0001086
relative error = 0.006021 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.942
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.448
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8879 1.732
h = 0.0001 0.003
y[1] (numeric) = -0.135368475494 1.8050593091
y[1] (closed_form) = -0.13533349621 1.80515924229
absolute error = 0.0001059
relative error = 0.005849 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.946
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.168
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2437.8MB, alloc=52.3MB, time=29.29
x[1] = 0.888 1.735
h = 0.001 0.001
y[1] (numeric) = -0.137434061372 1.80870485657
y[1] (closed_form) = -0.137398184066 1.80880419863
absolute error = 0.0001056
relative error = 0.005823 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.949
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9183
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.889 1.736
h = 0.001 0.003
y[1] (numeric) = -0.136971566743 1.81062498706
y[1] (closed_form) = -0.136935349325 1.81072389027
absolute error = 0.0001053
relative error = 0.0058 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.95
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.361
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.89 1.739
h = 0.0001 0.004
y[1] (numeric) = -0.137965452788 1.8149288004
y[1] (closed_form) = -0.137929964696 1.815028569
absolute error = 0.0001059
relative error = 0.005817 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.954
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.472
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8901 1.743
h = 0.003 0.006
y[1] (numeric) = -0.140764497681 1.81977298733
y[1] (closed_form) = -0.140729959804 1.81987260379
absolute error = 0.0001054
relative error = 0.005776 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.957
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.281
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8931 1.749
h = 0.0001 0.005
y[1] (numeric) = -0.141569988156 1.82912728373
y[1] (closed_form) = -0.141533770841 1.82923077087
absolute error = 0.0001096
relative error = 0.005976 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.964
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.464
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8932 1.754
h = 0.0001 0.003
y[1] (numeric) = -0.145111965944 1.83518150994
y[1] (closed_form) = -0.14507639182 1.83528233963
absolute error = 0.0001069
relative error = 0.005808 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.968
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.181
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8933 1.757
h = 0.001 0.001
y[1] (numeric) = -0.147194117617 1.8388447836
y[1] (closed_form) = -0.147157651291 1.83894502427
absolute error = 0.0001067
relative error = 0.005782 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.971
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9286
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8943 1.758
h = 0.001 0.003
y[1] (numeric) = -0.146731614832 1.84077633962
y[1] (closed_form) = -0.146694810883 1.84087614343
absolute error = 0.0001064
relative error = 0.00576 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.972
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.41
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2483.2MB, alloc=52.3MB, time=29.83
x[1] = 0.8953 1.761
h = 0.0001 0.004
y[1] (numeric) = -0.147736915697 1.84510300457
y[1] (closed_form) = -0.14770083584 1.84520366991
absolute error = 0.0001069
relative error = 0.005777 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.976
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.5
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8954 1.765
h = 0.003 0.006
y[1] (numeric) = -0.150558199334 1.84997059977
y[1] (closed_form) = -0.150523064591 1.85007111509
absolute error = 0.0001065
relative error = 0.005736 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.979
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.318
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8984 1.771
h = 0.0001 0.005
y[1] (numeric) = -0.151380728431 1.85937622045
y[1] (closed_form) = -0.151343918478 1.85948058268
absolute error = 0.0001107
relative error = 0.005932 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.986
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.48
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8985 1.776
h = 0.0001 0.003
y[1] (numeric) = -0.154950550216 1.86545948626
y[1] (closed_form) = -0.154914383389 1.86556120663
absolute error = 0.000108
relative error = 0.005767 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.99
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.195
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8986 1.779
h = 0.001 0.001
y[1] (numeric) = -0.157049151926 1.86914040931
y[1] (closed_form) = -0.157012098612 1.86924154275
absolute error = 0.0001077
relative error = 0.005742 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.993
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.939
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.8996 1.78
h = 0.001 0.003
y[1] (numeric) = -0.156586625939 1.87108332725
y[1] (closed_form) = -0.156549237443 1.87118402581
absolute error = 0.0001074
relative error = 0.005721 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.994
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.46
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9006 1.783
h = 0.0001 0.004
y[1] (numeric) = -0.157603247863 1.8754327318
y[1] (closed_form) = -0.157566578325 1.87553428807
absolute error = 0.000108
relative error = 0.005737 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.998
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.528
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9007 1.787
h = 0.003 0.006
y[1] (numeric) = -0.160446615889 1.88032363461
y[1] (closed_form) = -0.160410886442 1.88042504293
absolute error = 0.0001075
relative error = 0.005697 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.001
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.355
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9037 1.793
h = 0.0001 0.005
y[1] (numeric) = -0.16128602194 1.88978031738
y[1] (closed_form) = -0.161248621531 1.88988554922
absolute error = 0.0001117
relative error = 0.005888 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.008
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.497
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2528.6MB, alloc=52.3MB, time=30.37
x[1] = 0.9038 1.798
h = 0.0001 0.003
y[1] (numeric) = -0.164883496083 1.89589249887
y[1] (closed_form) = -0.164846738678 1.8959951042
absolute error = 0.000109
relative error = 0.005727 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.012
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.208
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9039 1.801
h = 0.001 0.001
y[1] (numeric) = -0.166998434285 1.89959099531
y[1] (closed_form) = -0.166960796005 1.89969301579
absolute error = 0.0001087
relative error = 0.005702 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.015
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9494
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9049 1.802
h = 0.0001 0.004
y[1] (numeric) = -0.166535870546 1.90154521255
y[1] (closed_form) = -0.166497899476 1.90164680011
absolute error = 0.0001085
relative error = 0.005681 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.016
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.705
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.905 1.806
h = 0.003 0.006
y[1] (numeric) = -0.16939722294 1.90645506828
y[1] (closed_form) = -0.169361367526 1.90655727878
absolute error = 0.0001083
relative error = 0.005659 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.02
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.387
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.908 1.812
h = 0.0001 0.005
y[1] (numeric) = -0.170251633523 1.91595529795
y[1] (closed_form) = -0.170214110547 1.91606131214
absolute error = 0.0001125
relative error = 0.005846 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.027
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.511
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9081 1.817
h = 0.0001 0.003
y[1] (numeric) = -0.173873101658 1.9220919445
y[1] (closed_form) = -0.173836221713 1.92219534517
absolute error = 0.0001098
relative error = 0.005688 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.031
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.219
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9082 1.82
h = 0.001 0.001
y[1] (numeric) = -0.176002220602 1.9258053145
y[1] (closed_form) = -0.175964464559 1.92590813204
absolute error = 0.0001095
relative error = 0.005664 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.034
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9583
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9092 1.821
h = 0.001 0.003
y[1] (numeric) = -0.175539746678 1.92776920909
y[1] (closed_form) = -0.175501659891 1.92787159535
absolute error = 0.0001092
relative error = 0.005643 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.035
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.551
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2574.1MB, alloc=52.3MB, time=30.92
x[1] = 0.9102 1.824
h = 0.0001 0.004
y[1] (numeric) = -0.176577459444 1.93216050134
y[1] (closed_form) = -0.176540082281 1.93226373837
absolute error = 0.0001098
relative error = 0.005659 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.038
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.579
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9103 1.828
h = 0.003 0.006
y[1] (numeric) = -0.179461795388 1.93709425107
y[1] (closed_form) = -0.179425349188 1.9371973439
absolute error = 0.0001093
relative error = 0.00562 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.042
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.424
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9133 1.834
h = 0.0001 0.005
y[1] (numeric) = -0.180332788744 1.94664506653
y[1] (closed_form) = -0.180294679271 1.94675194041
absolute error = 0.0001135
relative error = 0.005804 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.049
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.527
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9134 1.839
h = 0.0001 0.003
y[1] (numeric) = -0.183981560746 1.95281040379
y[1] (closed_form) = -0.183944094075 1.95291467903
absolute error = 0.0001108
relative error = 0.005649 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.053
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.232
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9135 1.842
h = 0.001 0.001
y[1] (numeric) = -0.186126809685 1.95654120924
y[1] (closed_form) = -0.186088472346 1.95664490341
absolute error = 0.0001106
relative error = 0.005625 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.056
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9687
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9145 1.843
h = 0.001 0.003
y[1] (numeric) = -0.185664271466 1.95851628935
y[1] (closed_form) = -0.185625605691 1.95861955414
absolute error = 0.0001103
relative error = 0.005605 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.057
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.601
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9155 1.846
h = 0.0001 0.004
y[1] (numeric) = -0.186713046527 1.96293000988
y[1] (closed_form) = -0.186675085519 1.96303412175
absolute error = 0.0001108
relative error = 0.00562 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.061
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.607
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9156 1.85
h = 0.003 0.006
y[1] (numeric) = -0.189619040039 1.96788678685
y[1] (closed_form) = -0.189582005179 1.96799075643
absolute error = 0.0001104
relative error = 0.005582 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.064
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.461
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2619.6MB, alloc=52.3MB, time=31.46
x[1] = 0.9186 1.856
h = 0.0001 0.005
y[1] (numeric) = -0.190506464714 1.97748793621
y[1] (closed_form) = -0.190467770881 1.97759566459
absolute error = 0.0001145
relative error = 0.005762 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.071
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.544
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9187 1.861
h = 0.0001 0.003
y[1] (numeric) = -0.194182359027 1.9836818439
y[1] (closed_form) = -0.194144307717 1.98378698827
absolute error = 0.0001118
relative error = 0.00561 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.075
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.246
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9188 1.864
h = 0.001 0.001
y[1] (numeric) = -0.196343630401 1.98743001108
y[1] (closed_form) = -0.19630471376 1.98753457643
absolute error = 0.0001116
relative error = 0.005586 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.078
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9791
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9198 1.865
h = 0.001 0.003
y[1] (numeric) = -0.195881014658 1.9894162168
y[1] (closed_form) = -0.195841771844 1.98952035467
absolute error = 0.0001113
relative error = 0.005567 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.079
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.65
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9208 1.868
h = 0.0001 0.004
y[1] (numeric) = -0.196940765588 1.99385225916
y[1] (closed_form) = -0.196902222776 1.99395724045
absolute error = 0.0001118
relative error = 0.005581 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.083
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.635
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9209 1.872
h = 0.003 0.006
y[1] (numeric) = -0.199868273188 1.99883196672
y[1] (closed_form) = -0.199830651777 1.99893680758
absolute error = 0.0001114
relative error = 0.005545 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.086
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.498
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9239 1.878
h = 0.0001 0.005
y[1] (numeric) = -0.200771981056 2.00848320158
y[1] (closed_form) = -0.200732704984 2.00859177936
absolute error = 0.0001155
relative error = 0.00572 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.093
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.56
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.924 1.883
h = 0.0001 0.003
y[1] (numeric) = -0.204474819445 2.01470556067
y[1] (closed_form) = -0.20443618557 2.01481156885
absolute error = 0.0001128
relative error = 0.005571 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.097
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.259
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9241 1.886
h = 0.001 0.001
y[1] (numeric) = -0.20665200767 2.01847101667
y[1] (closed_form) = -0.206612513709 2.01857644785
absolute error = 0.0001126
relative error = 0.005548 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.1
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9895
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2665.2MB, alloc=52.3MB, time=32.00
x[1] = 0.9251 1.887
h = 0.001 0.003
y[1] (numeric) = -0.206189301598 2.02046828899
y[1] (closed_form) = -0.206149483684 2.02057329457
absolute error = 0.0001123
relative error = 0.005529 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.102
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.699
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9261 1.89
h = 0.0001 0.004
y[1] (numeric) = -0.207259943723 2.02492654811
y[1] (closed_form) = -0.207220821133 2.02503239349
absolute error = 0.0001128
relative error = 0.005544 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.105
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.663
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9262 1.894
h = 0.003 0.006
y[1] (numeric) = -0.210208824547 2.02992909064
y[1] (closed_form) = -0.210170618681 2.03003479741
absolute error = 0.0001124
relative error = 0.005507 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.108
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.535
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9292 1.9
h = 0.0001 0.005
y[1] (numeric) = -0.211128670706 2.03963016601
y[1] (closed_form) = -0.2110888145 2.03973958817
absolute error = 0.0001165
relative error = 0.005679 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.115
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.577
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9293 1.905
h = 0.0001 0.003
y[1] (numeric) = -0.214858278167 2.04588085873
y[1] (closed_form) = -0.214819063786 2.04598772546
absolute error = 0.0001138
relative error = 0.005533 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.12
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.272
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9294 1.908
h = 0.001 0.001
y[1] (numeric) = -0.217051279575 2.04966353138
y[1] (closed_form) = -0.217011210262 2.04976982314
absolute error = 0.0001136
relative error = 0.005511 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.122
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9999
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9304 1.909
h = 0.0001 0.004
y[1] (numeric) = -0.216588470774 2.05167181219
y[1] (closed_form) = -0.21654807969 2.05177768019
absolute error = 0.0001133
relative error = 0.005492 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.124
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.008
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9305 1.913
h = 0.003 0.006
y[1] (numeric) = -0.219554763391 2.05669292587
y[1] (closed_form) = -0.219516430269 2.05679941311
absolute error = 0.0001132
relative error = 0.005471 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.127
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.566
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2710.5MB, alloc=52.3MB, time=32.54
x[1] = 0.9335 1.919
h = 0.0001 0.005
y[1] (numeric) = -0.220488976991 2.06643651872
y[1] (closed_form) = -0.220448997002 2.06654670305
absolute error = 0.0001172
relative error = 0.00564 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.134
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.591
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9336 1.924
h = 0.0001 0.003
y[1] (numeric) = -0.224241824259 2.0727111906
y[1] (closed_form) = -0.224202485906 2.07281883153
absolute error = 0.0001146
relative error = 0.005497 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.139
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.284
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9337 1.927
h = 0.001 0.001
y[1] (numeric) = -0.226448559465 2.07650843888
y[1] (closed_form) = -0.226408370573 2.07661550651
absolute error = 0.0001144
relative error = 0.005475 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.141
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.009
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9347 1.928
h = 0.001 0.003
y[1] (numeric) = -0.225985782818 2.07852615097
y[1] (closed_form) = -0.22594527402 2.07863279638
absolute error = 0.0001141
relative error = 0.005456 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.143
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.791
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9357 1.931
h = 0.0001 0.004
y[1] (numeric) = -0.227076733088 2.08302534782
y[1] (closed_form) = -0.227036911093 2.08313282646
absolute error = 0.0001146
relative error = 0.00547 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.146
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.715
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9358 1.935
h = 0.003 0.006
y[1] (numeric) = -0.23006528761 2.08806987909
y[1] (closed_form) = -0.230026373833 2.08817722245
absolute error = 0.0001142
relative error = 0.005435 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.149
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.604
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9388 1.941
h = 0.0001 0.005
y[1] (numeric) = -0.231015375268 2.09786286704
y[1] (closed_form) = -0.230974818958 2.09797388661
absolute error = 0.0001182
relative error = 0.0056 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.156
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.607
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9389 1.946
h = 0.0001 0.003
y[1] (numeric) = -0.23479467288 2.10416565865
y[1] (closed_form) = -0.234754757756 2.10427414859
absolute error = 0.0001156
relative error = 0.00546 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.161
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.297
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2756.0MB, alloc=52.3MB, time=33.08
x[1] = 0.939 1.949
h = 0.001 0.001
y[1] (numeric) = -0.237017032445 2.10797999258
y[1] (closed_form) = -0.236976271778 2.10808791121
absolute error = 0.0001154
relative error = 0.005438 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.163
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.019
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.94 1.95
h = 0.001 0.003
y[1] (numeric) = -0.236554130364 2.11000860742
y[1] (closed_form) = -0.236513051896 2.11011610564
absolute error = 0.0001151
relative error = 0.00542 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.165
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.841
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.941 1.953
h = 0.0001 0.004
y[1] (numeric) = -0.237655737604 2.11452972877
y[1] (closed_form) = -0.237615341501 2.11463805673
absolute error = 0.0001156
relative error = 0.005433 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.168
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.743
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9411 1.957
h = 0.003 0.006
y[1] (numeric) = -0.240665275079 2.11959682858
y[1] (closed_form) = -0.240625782702 2.11970502294
absolute error = 0.0001152
relative error = 0.005399 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.172
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.641
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9441 1.963
h = 0.0001 0.005
y[1] (numeric) = -0.241631100588 2.12943897598
y[1] (closed_form) = -0.241589970016 2.129550826
absolute error = 0.0001192
relative error = 0.00556 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.178
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.624
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9442 1.968
h = 0.0001 0.003
y[1] (numeric) = -0.245436682299 2.13576977299
y[1] (closed_form) = -0.245396192423 2.13587910694
absolute error = 0.0001166
relative error = 0.005423 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.183
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.31
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9443 1.971
h = 0.001 0.001
y[1] (numeric) = -0.247674567756 2.13960112256
y[1] (closed_form) = -0.24763323725 2.13970988719
absolute error = 0.0001164
relative error = 0.005402 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.186
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.03
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9453 1.972
h = 0.001 0.003
y[1] (numeric) = -0.247211528933 2.14164058445
y[1] (closed_form) = -0.247169882695 2.14174893045
absolute error = 0.0001161
relative error = 0.005384 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.187
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.89
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9463 1.975
h = 0.0001 0.004
y[1] (numeric) = -0.248323714764 2.14618353032
y[1] (closed_form) = -0.24828274653 2.14629270259
absolute error = 0.0001166
relative error = 0.005397 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.19
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.771
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2801.4MB, alloc=52.3MB, time=33.62
x[1] = 0.9464 1.979
h = 0.003 0.006
y[1] (numeric) = -0.251354103774 2.15127310684
y[1] (closed_form) = -0.251314034839 2.15138214717
absolute error = 0.0001162
relative error = 0.005363 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.194
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.678
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9494 1.985
h = 0.0001 0.005
y[1] (numeric) = -0.252335533771 2.16116418117
y[1] (closed_form) = -0.252293830979 2.16127685694
absolute error = 0.0001201
relative error = 0.005522 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.2
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.64
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9495 1.99
h = 0.0001 0.003
y[1] (numeric) = -0.256167236232 2.16752287046
y[1] (closed_form) = -0.256126173609 2.16763304351
absolute error = 0.0001176
relative error = 0.005387 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.205
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.323
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9496 1.993
h = 0.001 0.001
y[1] (numeric) = -0.258420550831 2.17137116643
y[1] (closed_form) = -0.25837865241 2.17148077212
absolute error = 0.0001173
relative error = 0.005366 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.208
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.04
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9506 1.994
h = 0.001 0.003
y[1] (numeric) = -0.257957364311 2.17342142046
y[1] (closed_form) = -0.257915152189 2.1735306093
absolute error = 0.0001171
relative error = 0.005348 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.209
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.939
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9516 1.997
h = 0.0001 0.004
y[1] (numeric) = -0.259080051861 2.1779860921
y[1] (closed_form) = -0.259038513461 2.17809610378
absolute error = 0.0001176
relative error = 0.005361 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.212
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.799
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9517 2.001
h = 0.003 0.006
y[1] (numeric) = -0.262131163271 2.18309805448
y[1] (closed_form) = -0.262090519802 2.18320793584
absolute error = 0.0001172
relative error = 0.005328 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.216
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.715
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9547 2.007
h = 0.0001 0.005
y[1] (numeric) = -0.26312806715 2.19303782631
y[1] (closed_form) = -0.263085794161 2.1931513232
absolute error = 0.0001211
relative error = 0.005483 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.222
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.657
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2846.8MB, alloc=52.3MB, time=34.16
x[1] = 0.9548 2.012
h = 0.0001 0.003
y[1] (numeric) = -0.266985729825 2.19942429592
y[1] (closed_form) = -0.266944096446 2.19953530324
absolute error = 0.0001186
relative error = 0.005351 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.227
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.337
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9549 2.015
h = 0.001 0.001
y[1] (numeric) = -0.269254378489 2.20328946977
y[1] (closed_form) = -0.269211914066 2.20339991169
absolute error = 0.0001183
relative error = 0.00533 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.23
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.051
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9559 2.016
h = 0.0001 0.004
y[1] (numeric) = -0.268791033652 2.20535046184
y[1] (closed_form) = -0.268748257524 2.20546048864
absolute error = 0.000118
relative error = 0.005313 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.231
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.313
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.956 2.02
h = 0.003 0.006
y[1] (numeric) = -0.271859032396 2.2104806326
y[1] (closed_form) = -0.271818260816 2.2105912743
absolute error = 0.0001179
relative error = 0.005294 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.235
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.747
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.959 2.026
h = 0.0001 0.005
y[1] (numeric) = -0.272869729551 2.22046195792
y[1] (closed_form) = -0.27282733195 2.22057619824
absolute error = 0.0001219
relative error = 0.005447 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.242
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.671
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9591 2.031
h = 0.0001 0.003
y[1] (numeric) = -0.276749940583 2.22687194446
y[1] (closed_form) = -0.276708182236 2.22698370637
absolute error = 0.0001193
relative error = 0.005317 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.246
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.348
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9592 2.034
h = 0.001 0.001
y[1] (numeric) = -0.279031913356 2.23075141078
y[1] (closed_form) = -0.278989328019 2.2308626089
absolute error = 0.0001191
relative error = 0.005296 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.249
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.06
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9602 2.035
h = 0.001 0.003
y[1] (numeric) = -0.27856855104 2.23282160509
y[1] (closed_form) = -0.278525655709 2.23293238956
absolute error = 0.0001188
relative error = 0.005279 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.25
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.032
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2892.2MB, alloc=52.3MB, time=34.70
x[1] = 0.9612 2.038
h = 0.0001 0.004
y[1] (numeric) = -0.279710836312 2.23742632174
y[1] (closed_form) = -0.27966860689 2.23753792283
absolute error = 0.0001193
relative error = 0.005292 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.253
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.851
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9613 2.042
h = 0.003 0.006
y[1] (numeric) = -0.282800435278 2.24257945714
y[1] (closed_form) = -0.282759092838 2.24269093086
absolute error = 0.0001189
relative error = 0.00526 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.257
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.784
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9643 2.048
h = 0.0001 0.005
y[1] (numeric) = -0.283826367681 2.25260906251
y[1] (closed_form) = -0.283783403555 2.25272411549
absolute error = 0.0001228
relative error = 0.005409 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.264
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.688
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9644 2.053
h = 0.0001 0.003
y[1] (numeric) = -0.287732246149 2.25904662598
y[1] (closed_form) = -0.287689920655 2.25915921335
absolute error = 0.0001203
relative error = 0.005281 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.268
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.361
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9645 2.056
h = 0.001 0.001
y[1] (numeric) = -0.290029379566 2.2629428457
y[1] (closed_form) = -0.289986231696 2.2630548712
absolute error = 0.00012
relative error = 0.005262 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.271
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.07
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9655 2.057
h = 0.001 0.003
y[1] (numeric) = -0.289565839409 2.2650236795
y[1] (closed_form) = -0.289522383475 2.26513529307
absolute error = 0.0001198
relative error = 0.005245 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.272
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.081
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9665 2.06
h = 0.0001 0.004
y[1] (numeric) = -0.290718413312 2.26964984708
y[1] (closed_form) = -0.290675619213 2.26976227394
absolute error = 0.0001203
relative error = 0.005257 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.275
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.879
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9666 2.064
h = 0.003 0.006
y[1] (numeric) = -0.293828376257 2.2748251151
y[1] (closed_form) = -0.293786464941 2.27493741611
absolute error = 0.0001199
relative error = 0.005226 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.279
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.821
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9696 2.07
h = 0.0001 0.005
y[1] (numeric) = -0.294869420762 2.28490277953
y[1] (closed_form) = -0.294825892088 2.28501864076
absolute error = 0.0001238
relative error = 0.005372 %
Correct digits = 4
memory used=2937.7MB, alloc=52.3MB, time=35.24
Radius of convergence (given) for eq 1 = 2.286
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.704
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9697 2.075
h = 0.0001 0.003
y[1] (numeric) = -0.29880081379 2.29136781124
y[1] (closed_form) = -0.298757923099 2.29148121946
absolute error = 0.0001212
relative error = 0.005247 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.29
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.375
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9698 2.078
h = 0.001 0.001
y[1] (numeric) = -0.30111301732 2.29528071787
y[1] (closed_form) = -0.301069308793 2.29539356614
absolute error = 0.000121
relative error = 0.005227 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.293
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.08
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9708 2.079
h = 0.001 0.003
y[1] (numeric) = -0.300649289611 2.29737213921
y[1] (closed_form) = -0.300605274918 2.29748457724
absolute error = 0.0001207
relative error = 0.005211 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.294
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.131
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9718 2.082
h = 0.0001 0.004
y[1] (numeric) = -0.301812080715 2.30201966361
y[1] (closed_form) = -0.301768723851 2.30213291164
absolute error = 0.0001213
relative error = 0.005223 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.298
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.907
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9719 2.086
h = 0.003 0.006
y[1] (numeric) = -0.304942286759 2.307216977
y[1] (closed_form) = -0.304899808536 2.30733010065
absolute error = 0.0001208
relative error = 0.005192 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.301
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.858
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9749 2.092
h = 0.0001 0.005
y[1] (numeric) = -0.305998322665 2.31734248234
y[1] (closed_form) = -0.305954231405 2.31745914747
absolute error = 0.0001247
relative error = 0.005335 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.308
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.721
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.975 2.097
h = 0.0001 0.003
y[1] (numeric) = -0.309955079916 2.32383487472
y[1] (closed_form) = -0.309911625961 2.32394909925
absolute error = 0.0001222
relative error = 0.005213 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.313
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.388
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9751 2.1
h = 0.001 0.001
y[1] (numeric) = -0.312282264531 2.32776440248
y[1] (closed_form) = -0.312237997211 2.32787806895
absolute error = 0.000122
relative error = 0.005194 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.315
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.091
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2983.1MB, alloc=52.3MB, time=35.78
x[1] = 0.9761 2.101
h = 0.001 0.003
y[1] (numeric) = -0.311818339852 2.32986636013
y[1] (closed_form) = -0.311773768231 2.32997961803
absolute error = 0.0001217
relative error = 0.005178 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.317
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.18
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9771 2.104
h = 0.0001 0.004
y[1] (numeric) = -0.312991278035 2.33453514839
y[1] (closed_form) = -0.312947360305 2.33464921305
absolute error = 0.0001222
relative error = 0.005189 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.32
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.935
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9772 2.108
h = 0.003 0.006
y[1] (numeric) = -0.316141608299 2.33975442079
y[1] (closed_form) = -0.316098565122 2.33986836251
absolute error = 0.0001218
relative error = 0.005159 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.323
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.895
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9802 2.114
h = 0.0001 0.005
y[1] (numeric) = -0.317212517277 2.34992755171
y[1] (closed_form) = -0.317167865378 2.35004501643
absolute error = 0.0001257
relative error = 0.005299 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.33
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.737
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9803 2.119
h = 0.0001 0.003
y[1] (numeric) = -0.321194490886 2.3564471983
y[1] (closed_form) = -0.321150475587 2.35656223467
absolute error = 0.0001232
relative error = 0.005179 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.335
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.401
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9804 2.122
h = 0.001 0.001
y[1] (numeric) = -0.323536569026 2.36039328208
y[1] (closed_form) = -0.323491744762 2.36050776227
absolute error = 0.0001229
relative error = 0.00516 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.338
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.101
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9814 2.123
h = 0.0001 0.004
y[1] (numeric) = -0.32307243824 2.36250572551
y[1] (closed_form) = -0.323027311511 2.36261979878
absolute error = 0.0001227
relative error = 0.005144 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.339
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.617
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9815 2.127
h = 0.003 0.006
y[1] (numeric) = -0.326239173413 2.3677428614
y[1] (closed_form) = -0.326196001613 2.36785754479
absolute error = 0.0001225
relative error = 0.005127 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.343
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.927
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3028.5MB, alloc=52.3MB, time=36.33
x[1] = 0.9845 2.133
h = 0.0001 0.005
y[1] (numeric) = -0.327323355517 2.37795664119
y[1] (closed_form) = -0.327278578485 2.37807483185
absolute error = 0.0001264
relative error = 0.005265 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.349
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.751
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9846 2.138
h = 0.0001 0.003
y[1] (numeric) = -0.331327240903 2.38449936486
y[1] (closed_form) = -0.33128309999 2.38461513757
absolute error = 0.0001239
relative error = 0.005146 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.354
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.413
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9847 2.141
h = 0.001 0.001
y[1] (numeric) = -0.333682266041 2.38845947187
y[1] (closed_form) = -0.333637319918 2.38857468997
absolute error = 0.0001237
relative error = 0.005128 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.357
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.11
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9857 2.142
h = 0.001 0.003
y[1] (numeric) = -0.333218074837 2.39058090378
y[1] (closed_form) = -0.333172827824 2.39069571634
absolute error = 0.0001234
relative error = 0.005113 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.358
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.272
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9867 2.145
h = 0.0001 0.004
y[1] (numeric) = -0.334409962801 2.39528889664
y[1] (closed_form) = -0.334365362484 2.39540451006
absolute error = 0.0001239
relative error = 0.005123 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.361
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.987
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9868 2.149
h = 0.003 0.006
y[1] (numeric) = -0.337597688963 2.40054856637
y[1] (closed_form) = -0.337553955753 2.40066405949
absolute error = 0.0001235
relative error = 0.005094 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.365
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.965
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9898 2.155
h = 0.0001 0.005
y[1] (numeric) = -0.338696527549 2.41080957962
y[1] (closed_form) = -0.338651193406 2.41092856205
absolute error = 0.0001273
relative error = 0.00523 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.371
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.768
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9899 2.16
h = 0.0001 0.003
y[1] (numeric) = -0.342725359269 2.41737936402
y[1] (closed_form) = -0.342680660494 2.41749594041
absolute error = 0.0001249
relative error = 0.005113 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.376
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.426
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3074.0MB, alloc=52.3MB, time=36.87
x[1] = 0.99 2.163
h = 0.001 0.001
y[1] (numeric) = -0.345095118018 2.4213559087
y[1] (closed_form) = -0.345049618309 2.42147193234
absolute error = 0.0001246
relative error = 0.005095 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.379
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.121
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.991 2.164
h = 0.001 0.003
y[1] (numeric) = -0.344630703842 2.4234877343
y[1] (closed_form) = -0.344584905021 2.42360335403
absolute error = 0.0001244
relative error = 0.00508 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.38
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.322
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.992 2.167
h = 0.0001 0.004
y[1] (numeric) = -0.345832544125 2.42821673207
y[1] (closed_form) = -0.345787388245 2.4283331495
absolute error = 0.0001249
relative error = 0.005091 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.383
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.016
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9921 2.171
h = 0.003 0.006
y[1] (numeric) = -0.349040064014 2.43349812
y[1] (closed_form) = -0.348995771304 2.43361441849
absolute error = 0.0001244
relative error = 0.005062 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.387
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.002
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9951 2.177
h = 0.0001 0.005
y[1] (numeric) = -0.350153447197 2.44380615904
y[1] (closed_form) = -0.350107557843 2.44392592914
absolute error = 0.0001283
relative error = 0.005195 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.394
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.784
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9952 2.182
h = 0.0001 0.003
y[1] (numeric) = -0.354207084121 2.45040290076
y[1] (closed_form) = -0.354161829363 2.45052027656
absolute error = 0.0001258
relative error = 0.005081 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.398
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.439
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9953 2.185
h = 0.001 0.001
y[1] (numeric) = -0.356591492917 2.45439581992
y[1] (closed_form) = -0.356545441437 2.45451264481
absolute error = 0.0001256
relative error = 0.005063 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.401
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.131
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9963 2.186
h = 0.001 0.003
y[1] (numeric) = -0.356126847394 2.45653799062
y[1] (closed_form) = -0.35608049855 2.4566544132
absolute error = 0.0001253
relative error = 0.005048 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.402
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.372
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.9973 2.189
h = 0.0001 0.004
y[1] (numeric) = -0.357338574608 2.46128790458
y[1] (closed_form) = -0.35729286501 2.46140512176
absolute error = 0.0001258
relative error = 0.005058 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.405
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.044
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3119.4MB, alloc=52.3MB, time=37.41
x[1] = 0.9974 2.193
h = 0.003 0.006
y[1] (numeric) = -0.360565776603 2.46659092772
y[1] (closed_form) = -0.360520926291 2.46670802727
absolute error = 0.0001254
relative error = 0.00503 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.409
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.039
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0004 2.199
h = 0.0001 0.005
y[1] (numeric) = -0.361693594617 2.47694578746
y[1] (closed_form) = -0.361647151936 2.47706634117
absolute error = 0.0001292
relative error = 0.005161 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.416
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.801
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0005 2.204
h = 0.0001 0.003
y[1] (numeric) = -0.36577189785 2.48356938416
y[1] (closed_form) = -0.365726088972 2.48368755516
absolute error = 0.0001267
relative error = 0.005048 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.42
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.453
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0006 2.207
h = 0.001 0.001
y[1] (numeric) = -0.368170874457 2.48757861524
y[1] (closed_form) = -0.368124273006 2.48769623716
absolute error = 0.0001265
relative error = 0.005031 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.423
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.142
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0016 2.208
h = 0.001 0.003
y[1] (numeric) = -0.367705989456 2.48973108311
y[1] (closed_form) = -0.367659092362 2.48984830431
absolute error = 0.0001263
relative error = 0.005016 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.425
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.421
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0026 2.211
h = 0.0001 0.004
y[1] (numeric) = -0.368927539355 2.49450182561
y[1] (closed_form) = -0.368881277871 2.49461983831
absolute error = 0.0001268
relative error = 0.005027 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.428
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.072
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0027 2.215
h = 0.003 0.006
y[1] (numeric) = -0.372174313599 2.4998264018
y[1] (closed_form) = -0.372128907566 2.49994429818
absolute error = 0.0001263
relative error = 0.004999 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.431
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.076
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0057 2.221
h = 0.0001 0.005
y[1] (numeric) = -0.373316458735 2.51022787969
y[1] (closed_form) = -0.373269464595 2.51034921303
absolute error = 0.0001301
relative error = 0.005127 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.438
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.818
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3164.7MB, alloc=52.3MB, time=37.95
x[1] = 1.0058 2.226
h = 0.0001 0.003
y[1] (numeric) = -0.377419291563 2.51687823007
y[1] (closed_form) = -0.377372930415 2.51699719213
absolute error = 0.0001277
relative error = 0.005017 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.443
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.466
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0059 2.229
h = 0.001 0.001
y[1] (numeric) = -0.379832755037 2.52090371117
y[1] (closed_form) = -0.379785605403 2.52102212595
absolute error = 0.0001275
relative error = 0.004999 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.445
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.152
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0069 2.23
h = 0.0001 0.004
y[1] (numeric) = -0.379367622666 2.5230664289
y[1] (closed_form) = -0.379320179081 2.52318444453
absolute error = 0.0001272
relative error = 0.004985 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.447
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.923
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.007 2.234
h = 0.003 0.006
y[1] (numeric) = -0.382630356328 2.52840854053
y[1] (closed_form) = -0.382584821435 2.52852716116
absolute error = 0.0001271
relative error = 0.004969 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.45
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.108
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.01 2.24
h = 0.0001 0.005
y[1] (numeric) = -0.383785301127 2.53884981652
y[1] (closed_form) = -0.383738181585 2.53897185946
absolute error = 0.0001308
relative error = 0.005095 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.457
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.832
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0101 2.245
h = 0.0001 0.003
y[1] (numeric) = -0.387909457427 2.54552282523
y[1] (closed_form) = -0.387862970297 2.54564250659
absolute error = 0.0001284
relative error = 0.004986 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.462
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.478
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0102 2.248
h = 0.001 0.001
y[1] (numeric) = -0.390335519438 2.54956207343
y[1] (closed_form) = -0.390288247313 2.54968120902
absolute error = 0.0001282
relative error = 0.004969 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.465
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.161
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0112 2.249
h = 0.001 0.003
y[1] (numeric) = -0.389870289334 2.55173357956
y[1] (closed_form) = -0.389822724713 2.55185231733
absolute error = 0.0001279
relative error = 0.004955 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.466
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.514
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3210.2MB, alloc=52.3MB, time=38.49
x[1] = 1.0122 2.252
h = 0.0001 0.004
y[1] (numeric) = -0.391110195438 2.55654273406
y[1] (closed_form) = -0.391063259779 2.55666225772
absolute error = 0.0001284
relative error = 0.004965 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.469
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.124
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0123 2.256
h = 0.003 0.006
y[1] (numeric) = -0.394393357007 2.56190696956
y[1] (closed_form) = -0.394347269807 2.56202637928
absolute error = 0.000128
relative error = 0.004938 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.473
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.146
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0153 2.262
h = 0.0001 0.005
y[1] (numeric) = -0.395562431442 2.57239449462
y[1] (closed_form) = -0.395514763832 2.5725173099
absolute error = 0.0001317
relative error = 0.005062 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.479
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.848
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0154 2.267
h = 0.0001 0.003
y[1] (numeric) = -0.399710867386 2.57909407281
y[1] (closed_form) = -0.39966383134 2.57921453765
absolute error = 0.0001293
relative error = 0.004955 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.484
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.491
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0155 2.27
h = 0.001 0.001
y[1] (numeric) = -0.402151268259 2.58314945843
y[1] (closed_form) = -0.402103451195 2.58326937929
absolute error = 0.0001291
relative error = 0.004938 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.487
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.172
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0165 2.271
h = 0.001 0.003
y[1] (numeric) = -0.401685776156 2.58533112814
y[1] (closed_form) = -0.401637668238 2.58545065271
absolute error = 0.0001288
relative error = 0.004924 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.488
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.564
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0175 2.274
h = 0.0001 0.004
y[1] (numeric) = -0.402935326183 2.59016086676
y[1] (closed_form) = -0.402887843753 2.59028117423
absolute error = 0.0001293
relative error = 0.004934 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.491
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.152
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0176 2.278
h = 0.003 0.006
y[1] (numeric) = -0.40623775413 2.59554642615
y[1] (closed_form) = -0.406191116461 2.5956666209
absolute error = 0.0001289
relative error = 0.004907 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.495
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.183
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3255.6MB, alloc=52.3MB, time=39.03
x[1] = 1.0206 2.284
h = 0.0001 0.005
y[1] (numeric) = -0.407420856092 2.6060800047
y[1] (closed_form) = -0.407372642239 2.60620358851
absolute error = 0.0001327
relative error = 0.005029 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.502
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.865
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0207 2.289
h = 0.0001 0.003
y[1] (numeric) = -0.411593440923 2.61280605394
y[1] (closed_form) = -0.41154585777 2.61292729828
absolute error = 0.0001302
relative error = 0.004924 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.506
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.504
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0208 2.292
h = 0.001 0.001
y[1] (numeric) = -0.414048103248 2.61687751685
y[1] (closed_form) = -0.413999742996 2.61699821899
absolute error = 0.00013
relative error = 0.004908 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.509
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.182
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0218 2.293
h = 0.001 0.003
y[1] (numeric) = -0.413582341894 2.61906930459
y[1] (closed_form) = -0.413533692406 2.61918961195
absolute error = 0.0001298
relative error = 0.004894 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.51
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.613
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0228 2.296
h = 0.0001 0.004
y[1] (numeric) = -0.414841475739 2.62391954354
y[1] (closed_form) = -0.414793448318 2.62404063085
absolute error = 0.0001303
relative error = 0.004903 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.514
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.18
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0229 2.3
h = 0.003 0.006
y[1] (numeric) = -0.418163066625 2.62932634783
y[1] (closed_form) = -0.418115880313 2.6294473236
absolute error = 0.0001299
relative error = 0.004877 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.517
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.22
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0259 2.306
h = 0.0001 0.005
y[1] (numeric) = -0.419360095852 2.63990578665
y[1] (closed_form) = -0.419311337565 2.64003013521
absolute error = 0.0001336
relative error = 0.004997 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.524
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.882
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.026 2.311
h = 0.0001 0.003
y[1] (numeric) = -0.423556700792 2.64665820949
y[1] (closed_form) = -0.423508572326 2.64678022942
absolute error = 0.0001312
relative error = 0.004894 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.529
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.518
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0261 2.314
h = 0.001 0.001
y[1] (numeric) = -0.426025548335 2.65074569016
y[1] (closed_form) = -0.425976646632 2.65086716965
absolute error = 0.000131
relative error = 0.004877 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.531
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.193
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3300.8MB, alloc=52.3MB, time=39.57
x[1] = 1.0271 2.315
h = 0.001 0.003
y[1] (numeric) = -0.425559510687 2.65294755096
y[1] (closed_form) = -0.425510321341 2.65306863718
absolute error = 0.0001307
relative error = 0.004864 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.533
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.663
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0281 2.318
h = 0.0001 0.004
y[1] (numeric) = -0.426828169248 2.65781820742
y[1] (closed_form) = -0.426779598601 2.65794007065
absolute error = 0.0001312
relative error = 0.004873 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.536
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.209
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0282 2.322
h = 0.003 0.006
y[1] (numeric) = -0.430168821196 2.66324617841
y[1] (closed_form) = -0.430121088051 2.66336793127
absolute error = 0.0001308
relative error = 0.004847 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.539
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.257
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0312 2.328
h = 0.0001 0.005
y[1] (numeric) = -0.431379679219 2.6738712866
y[1] (closed_form) = -0.431330378292 2.67399639619
absolute error = 0.0001345
relative error = 0.004965 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.546
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.898
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0313 2.333
h = 0.0001 0.003
y[1] (numeric) = -0.435600177427 2.68064998657
y[1] (closed_form) = -0.435551505428 2.68077277822
absolute error = 0.0001321
relative error = 0.004863 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.551
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.531
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0314 2.336
h = 0.001 0.001
y[1] (numeric) = -0.438083135098 2.68475342609
y[1] (closed_form) = -0.43803369367 2.68487567904
absolute error = 0.0001319
relative error = 0.004848 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.554
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.203
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0324 2.337
h = 0.0001 0.004
y[1] (numeric) = -0.437616814313 2.68696531554
y[1] (closed_form) = -0.43756708681 2.68708717672
absolute error = 0.0001316
relative error = 0.004834 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.555
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.229
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0325 2.341
h = 0.003 0.006
y[1] (numeric) = -0.440973012823 2.69241050967
y[1] (closed_form) = -0.440925150802 2.6925329705
absolute error = 0.0001315
relative error = 0.004819 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.559
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.29
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3346.3MB, alloc=52.3MB, time=40.11
x[1] = 1.0355 2.347
h = 0.0001 0.005
y[1] (numeric) = -0.442196237657 2.70307461422
y[1] (closed_form) = -0.442146811261 2.70320041808
absolute error = 0.0001352
relative error = 0.004935 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.565
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.912
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0356 2.352
h = 0.0001 0.003
y[1] (numeric) = -0.446437513729 2.70987557356
y[1] (closed_form) = -0.446388715607 2.70999906858
absolute error = 0.0001328
relative error = 0.004835 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.57
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.542
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0357 2.355
h = 0.001 0.001
y[1] (numeric) = -0.448932746813 2.7139925363
y[1] (closed_form) = -0.448883182517 2.71411549408
absolute error = 0.0001326
relative error = 0.004819 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.573
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.212
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0367 2.356
h = 0.001 0.003
y[1] (numeric) = -0.448466295733 2.71621302645
y[1] (closed_form) = -0.44841644671 2.71633559369
absolute error = 0.0001323
relative error = 0.004806 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.574
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.756
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0377 2.359
h = 0.0001 0.004
y[1] (numeric) = -0.449752764519 2.72112134609
y[1] (closed_form) = -0.449703528028 2.72124468502
absolute error = 0.0001328
relative error = 0.004815 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.577
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.261
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0378 2.363
h = 0.003 0.006
y[1] (numeric) = -0.453128868679 2.72658827365
y[1] (closed_form) = -0.45308046311 2.72671150436
absolute error = 0.0001324
relative error = 0.00479 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.581
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.327
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0408 2.369
h = 0.0001 0.005
y[1] (numeric) = -0.454365741484 2.73729769947
y[1] (closed_form) = -0.454315775704 2.73742425756
absolute error = 0.0001361
relative error = 0.004903 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.588
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.929
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0409 2.374
h = 0.0001 0.003
y[1] (numeric) = -0.458630678666 2.74412476043
y[1] (closed_form) = -0.45858134024 2.74424902012
absolute error = 0.0001337
relative error = 0.004805 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.592
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.556
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3391.7MB, alloc=52.3MB, time=40.65
x[1] = 1.041 2.377
h = 0.001 0.001
y[1] (numeric) = -0.46113988443 2.7482575748
y[1] (closed_form) = -0.461089783539 2.74838129896
absolute error = 0.0001335
relative error = 0.00479 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.595
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.223
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.042 2.378
h = 0.001 0.003
y[1] (numeric) = -0.460673137478 2.75048801256
y[1] (closed_form) = -0.460622753384 2.75061134765
absolute error = 0.0001332
relative error = 0.004777 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.596
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.805
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.043 2.381
h = 0.0001 0.004
y[1] (numeric) = -0.46196896626 2.75541651863
y[1] (closed_form) = -0.461919191474 2.75554062256
absolute error = 0.0001337
relative error = 0.004786 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.599
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.289
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0431 2.385
h = 0.003 0.006
y[1] (numeric) = -0.465363847436 2.76090439461
y[1] (closed_form) = -0.46531490009 2.76102839142
absolute error = 0.0001333
relative error = 0.004761 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.603
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.364
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0461 2.391
h = 0.0001 0.005
y[1] (numeric) = -0.466614274642 2.77165895714
y[1] (closed_form) = -0.466563771231 2.77178626589
absolute error = 0.000137
relative error = 0.004873 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.61
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.946
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0462 2.396
h = 0.0001 0.003
y[1] (numeric) = -0.470902751385 2.77851202594
y[1] (closed_form) = -0.470852874395 2.77863704658
absolute error = 0.0001346
relative error = 0.004776 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.614
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.569
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0463 2.399
h = 0.001 0.001
y[1] (numeric) = -0.47342585788 2.78266063468
y[1] (closed_form) = -0.473375222084 2.7827851215
absolute error = 0.0001344
relative error = 0.004761 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.617
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.233
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0473 2.4
h = 0.001 0.003
y[1] (numeric) = -0.472958808757 2.78490097723
y[1] (closed_form) = -0.472907891259 2.78502507643
absolute error = 0.0001341
relative error = 0.004748 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.619
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.855
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0483 2.403
h = 0.0001 0.004
y[1] (numeric) = -0.47426394208 2.78984959045
y[1] (closed_form) = -0.474213630712 2.78997445568
absolute error = 0.0001346
relative error = 0.004757 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.622
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.317
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3437.2MB, alloc=52.3MB, time=41.19
x[1] = 1.0484 2.407
h = 0.003 0.006
y[1] (numeric) = -0.477677504097 2.79535833961
y[1] (closed_form) = -0.477628016728 2.7954830988
absolute error = 0.0001342
relative error = 0.004733 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.625
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.402
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0514 2.413
h = 0.0001 0.005
y[1] (numeric) = -0.47894139375 2.80615785645
y[1] (closed_form) = -0.478890354444 2.80628591235
absolute error = 0.0001379
relative error = 0.004842 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.632
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.962
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0515 2.418
h = 0.0001 0.003
y[1] (numeric) = -0.483253290268 2.81303684023
y[1] (closed_form) = -0.483202876441 2.81316261818
absolute error = 0.0001355
relative error = 0.004747 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.637
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.583
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0516 2.421
h = 0.001 0.001
y[1] (numeric) = -0.485790226592 2.81720118663
y[1] (closed_form) = -0.485739057567 2.81732643246
absolute error = 0.0001353
relative error = 0.004732 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.64
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.244
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0526 2.422
h = 0.001 0.003
y[1] (numeric) = -0.485322869176 2.8194513917
y[1] (closed_form) = -0.485271419927 2.81957625133
absolute error = 0.000135
relative error = 0.00472 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.641
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.905
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0536 2.425
h = 0.0001 0.004
y[1] (numeric) = -0.486637252467 2.82442003369
y[1] (closed_form) = -0.486586406218 2.82454565656
absolute error = 0.0001355
relative error = 0.004728 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.644
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.345
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0537 2.429
h = 0.003 0.006
y[1] (numeric) = -0.490069400542 2.82994958151
y[1] (closed_form) = -0.490019374893 2.83007509939
absolute error = 0.0001351
relative error = 0.004704 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.648
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.439
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0567 2.435
h = 0.0001 0.005
y[1] (numeric) = -0.491346662262 2.84079387238
y[1] (closed_form) = -0.491295088786 2.84092267194
absolute error = 0.0001387
relative error = 0.004812 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.654
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.979
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3482.6MB, alloc=52.3MB, time=41.74
x[1] = 1.0568 2.44
h = 0.0001 0.003
y[1] (numeric) = -0.495681860494 2.84769867918
y[1] (closed_form) = -0.495630911543 2.84782521082
absolute error = 0.0001364
relative error = 0.004719 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.659
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.596
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0569 2.443
h = 0.001 0.001
y[1] (numeric) = -0.498232556766 2.85187870711
y[1] (closed_form) = -0.498180856174 2.85200470832
absolute error = 0.0001362
relative error = 0.004704 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.662
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.254
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0579 2.444
h = 0.0001 0.004
y[1] (numeric) = -0.497764885105 2.85413873292
y[1] (closed_form) = -0.497712905747 2.85426434935
absolute error = 0.0001359
relative error = 0.004692 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.663
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.535
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.058 2.448
h = 0.003 0.006
y[1] (numeric) = -0.501212195865 2.85968520633
y[1] (closed_form) = -0.501162041499 2.85981141691
absolute error = 0.0001358
relative error = 0.004678 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.667
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.471
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.061 2.454
h = 0.0001 0.005
y[1] (numeric) = -0.502501427077 2.87056773655
y[1] (closed_form) = -0.50244972823 2.87069721598
absolute error = 0.0001394
relative error = 0.004784 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.674
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.993
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0611 2.459
h = 0.0001 0.003
y[1] (numeric) = -0.506856895522 2.87749442232
y[1] (closed_form) = -0.506805820489 2.87762164237
absolute error = 0.0001371
relative error = 0.004692 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.678
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.607
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0612 2.462
h = 0.001 0.001
y[1] (numeric) = -0.5094195666 2.88168774106
y[1] (closed_form) = -0.509367742971 2.88181443207
absolute error = 0.0001369
relative error = 0.004677 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.681
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.263
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0622 2.463
h = 0.001 0.003
y[1] (numeric) = -0.508951736125 2.88395619102
y[1] (closed_form) = -0.508899634983 2.88408249845
absolute error = 0.0001366
relative error = 0.004665 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.682
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.998
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3528.1MB, alloc=52.3MB, time=42.28
x[1] = 1.0632 2.466
h = 0.0001 0.004
y[1] (numeric) = -0.510283425561 2.88896178755
y[1] (closed_form) = -0.510231921681 2.88908885313
absolute error = 0.0001371
relative error = 0.004673 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.685
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.398
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0633 2.47
h = 0.003 0.006
y[1] (numeric) = -0.51375015601 2.8945296222
y[1] (closed_form) = -0.513699466524 2.89465658475
absolute error = 0.0001367
relative error = 0.00465 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.689
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.508
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0663 2.476
h = 0.0001 0.005
y[1] (numeric) = -0.515052593076 2.9054565975
y[1] (closed_form) = -0.515000363185 2.90558681423
absolute error = 0.0001403
relative error = 0.004755 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.696
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.01
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0664 2.481
h = 0.0001 0.003
y[1] (numeric) = -0.51943114693 2.91240893892
y[1] (closed_form) = -0.51937953988 2.91253690607
absolute error = 0.000138
relative error = 0.004664 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.7
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.621
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0665 2.484
h = 0.001 0.001
y[1] (numeric) = -0.52200744991 2.916617837
y[1] (closed_form) = -0.521955097734 2.91674527677
absolute error = 0.0001378
relative error = 0.00465 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.703
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.274
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0675 2.485
h = 0.001 0.003
y[1] (numeric) = -0.521539294067 2.91889603141
y[1] (closed_form) = -0.521486665797 2.91902308898
absolute error = 0.0001375
relative error = 0.004638 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.705
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.048
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0685 2.488
h = 0.0001 0.004
y[1] (numeric) = -0.522880081147 2.92392143785
y[1] (closed_form) = -0.522828047135 2.92404925086
absolute error = 0.000138
relative error = 0.004646 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.708
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.426
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0686 2.492
h = 0.003 0.006
y[1] (numeric) = -0.526365133046 2.92950986306
y[1] (closed_form) = -0.526313910143 2.92963757405
absolute error = 0.0001376
relative error = 0.004623 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.711
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.546
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0716 2.498
h = 0.0001 0.005
y[1] (numeric) = -0.527680689893 2.94048110897
y[1] (closed_form) = -0.527627930642 2.94061205966
memory used=3573.5MB, alloc=52.3MB, time=42.83
absolute error = 0.0001412
relative error = 0.004726 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.718
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.026
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0717 2.503
h = 0.0001 0.003
y[1] (numeric) = -0.53208221582 2.9474590166
y[1] (closed_form) = -0.532030078429 2.94758772738
absolute error = 0.0001389
relative error = 0.004636 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.723
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.634
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0718 2.506
h = 0.001 0.001
y[1] (numeric) = -0.534672083624 2.95168343943
y[1] (closed_form) = -0.534619204529 2.95181162447
absolute error = 0.0001387
relative error = 0.004622 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.726
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.284
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0728 2.507
h = 0.001 0.003
y[1] (numeric) = -0.534203596927 2.95397133796
y[1] (closed_form) = -0.534150443135 2.95409914217
absolute error = 0.0001384
relative error = 0.004611 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.727
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.098
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0738 2.51
h = 0.0001 0.004
y[1] (numeric) = -0.535553430303 2.95901647918
y[1] (closed_form) = -0.53550086781 2.95914503617
absolute error = 0.0001389
relative error = 0.004618 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.73
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.454
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0739 2.514
h = 0.003 0.006
y[1] (numeric) = -0.539056713959 2.9646254232
y[1] (closed_form) = -0.539004959327 2.96475387914
absolute error = 0.0001385
relative error = 0.004596 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.734
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.583
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0769 2.52
h = 0.0001 0.005
y[1] (numeric) = -0.540385305938 2.97564076722
y[1] (closed_form) = -0.540332018995 2.97577244856
absolute error = 0.0001421
relative error = 0.004697 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.74
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.043
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.077 2.525
h = 0.0001 0.003
y[1] (numeric) = -0.544809692181 2.98264415247
y[1] (closed_form) = -0.544757026109 2.98277360346
absolute error = 0.0001398
relative error = 0.004609 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.745
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.648
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0771 2.528
h = 0.001 0.001
y[1] (numeric) = -0.547413058665 2.98688404599
y[1] (closed_form) = -0.547359654268 2.98701297287
absolute error = 0.0001395
relative error = 0.004595 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.748
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.295
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3618.8MB, alloc=52.3MB, time=43.36
x[1] = 1.0781 2.529
h = 0.001 0.003
y[1] (numeric) = -0.546944235777 2.98918160878
y[1] (closed_form) = -0.546890558061 2.9893101562
absolute error = 0.0001393
relative error = 0.004584 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.749
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.147
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0791 2.532
h = 0.0001 0.004
y[1] (numeric) = -0.54830306489 2.9942464105
y[1] (closed_form) = -0.548249975552 2.99437570803
absolute error = 0.0001398
relative error = 0.004592 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.752
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.483
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0792 2.536
h = 0.003 0.006
y[1] (numeric) = -0.551824491855 2.99987580225
y[1] (closed_form) = -0.551772207169 3.00000499969
absolute error = 0.0001394
relative error = 0.004569 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.756
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.621
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0822 2.542
h = 0.0001 0.005
y[1] (numeric) = -0.553166035705 3.01093507379
y[1] (closed_form) = -0.553112222725 3.01106748253
absolute error = 0.0001429
relative error = 0.004669 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.763
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.06
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0823 2.547
h = 0.0001 0.003
y[1] (numeric) = -0.557613172048 3.01796384894
y[1] (closed_form) = -0.557559978942 3.01809403676
absolute error = 0.0001406
relative error = 0.004582 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.767
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.661
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0824 2.55
h = 0.001 0.001
y[1] (numeric) = -0.560229971984 3.02221915961
y[1] (closed_form) = -0.560176043887 3.02234882494
absolute error = 0.0001404
relative error = 0.004569 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.77
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.305
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0834 2.551
h = 0.0001 0.004
y[1] (numeric) = -0.559760807714 3.02452634729
y[1] (closed_form) = -0.559706607656 3.0246556345
absolute error = 0.0001402
relative error = 0.004557 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.772
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.842
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0835 2.555
h = 0.003 0.006
y[1] (numeric) = -0.563297039346 3.03017238084
y[1] (closed_form) = -0.563244626243 3.03030225664
absolute error = 0.0001401
relative error = 0.004544 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.775
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.653
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3664.2MB, alloc=52.3MB, time=43.91
x[1] = 1.0865 2.561
h = 0.0001 0.005
y[1] (numeric) = -0.56465018663 3.04126917563
y[1] (closed_form) = -0.56459624851 3.04140225068
absolute error = 0.0001436
relative error = 0.004642 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.782
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.074
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0866 2.566
h = 0.0001 0.003
y[1] (numeric) = -0.569117119433 3.0483194667
y[1] (closed_form) = -0.569063800434 3.04845032887
absolute error = 0.0001413
relative error = 0.004557 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.787
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.673
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0867 2.569
h = 0.001 0.001
y[1] (numeric) = -0.571745613678 3.05258784649
y[1] (closed_form) = -0.571691562542 3.05271818751
absolute error = 0.0001411
relative error = 0.004543 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.789
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.314
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0877 2.57
h = 0.001 0.003
y[1] (numeric) = -0.571276265531 3.05490329192
y[1] (closed_form) = -0.571221943604 3.05503325596
absolute error = 0.0001409
relative error = 0.004532 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.791
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.24
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0887 2.573
h = 0.0001 0.004
y[1] (numeric) = -0.572651933789 3.06000437641
y[1] (closed_form) = -0.572598194886 3.06013508573
absolute error = 0.0001413
relative error = 0.004539 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.794
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.535
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0888 2.577
h = 0.003 0.006
y[1] (numeric) = -0.576207131567 3.06567141611
y[1] (closed_form) = -0.576154191451 3.06580202711
absolute error = 0.0001409
relative error = 0.004518 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.798
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.69
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0918 2.583
h = 0.0001 0.005
y[1] (numeric) = -0.577573077392 3.07681182701
y[1] (closed_form) = -0.57751861624 3.07694562348
absolute error = 0.0001445
relative error = 0.004614 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.804
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.091
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0919 2.588
h = 0.0001 0.003
y[1] (numeric) = -0.582062558178 3.08388734821
y[1] (closed_form) = -0.582008715137 3.08401894103
absolute error = 0.0001422
relative error = 0.00453 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.809
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.686
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3709.7MB, alloc=52.3MB, time=44.45
x[1] = 1.092 2.591
h = 0.001 0.001
y[1] (numeric) = -0.584704366241 3.08817104764
y[1] (closed_form) = -0.584649794317 3.08830212091
absolute error = 0.000142
relative error = 0.004517 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.812
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.325
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.093 2.592
h = 0.001 0.003
y[1] (numeric) = -0.584234666972 3.09049604598
y[1] (closed_form) = -0.58417982558 3.09062674359
absolute error = 0.0001417
relative error = 0.004506 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.813
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.29
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.094 2.595
h = 0.0001 0.004
y[1] (numeric) = -0.585619189634 3.09561658334
y[1] (closed_form) = -0.585564928462 3.09574802364
absolute error = 0.0001422
relative error = 0.004513 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.816
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.563
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0941 2.599
h = 0.003 0.006
y[1] (numeric) = -0.589192283505 3.10130387219
y[1] (closed_form) = -0.589138818013 3.10143521509
absolute error = 0.0001418
relative error = 0.004492 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.82
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.728
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0971 2.605
h = 0.0001 0.005
y[1] (numeric) = -0.590570948415 3.11248773396
y[1] (closed_form) = -0.590515965848 3.11262224872
absolute error = 0.0001453
relative error = 0.004587 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.827
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.107
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0972 2.61
h = 0.0001 0.003
y[1] (numeric) = -0.595082871207 3.1195883999
y[1] (closed_form) = -0.595028505735 3.11972072011
absolute error = 0.0001431
relative error = 0.004504 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.831
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.699
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0973 2.613
h = 0.001 0.001
y[1] (numeric) = -0.597737930374 3.12388736689
y[1] (closed_form) = -0.597682839231 3.12401916913
absolute error = 0.0001429
relative error = 0.004491 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.834
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.335
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0983 2.614
h = 0.001 0.003
y[1] (numeric) = -0.597267875189 3.12622188006
y[1] (closed_form) = -0.597212515883 3.12635330795
absolute error = 0.0001426
relative error = 0.004481 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.835
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.34
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.0993 2.617
h = 0.0001 0.004
y[1] (numeric) = -0.598661204562 3.13136179899
y[1] (closed_form) = -0.598606422709 3.13149396702
absolute error = 0.0001431
relative error = 0.004488 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.839
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.592
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3755.2MB, alloc=52.3MB, time=44.99
x[1] = 1.0994 2.621
h = 0.003 0.006
y[1] (numeric) = -0.602252110641 3.13706926849
y[1] (closed_form) = -0.602198121397 3.13720134002
absolute error = 0.0001427
relative error = 0.004466 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.842
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.765
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1024 2.627
h = 0.0001 0.005
y[1] (numeric) = -0.603643416442 3.14829641768
y[1] (closed_form) = -0.603587914064 3.14843164763
absolute error = 0.0001462
relative error = 0.00456 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.849
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.124
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1025 2.632
h = 0.0001 0.003
y[1] (numeric) = -0.608177676681 3.15542214378
y[1] (closed_form) = -0.608122790375 3.15555518818
absolute error = 0.0001439
relative error = 0.004478 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.854
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.713
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1026 2.635
h = 0.001 0.001
y[1] (numeric) = -0.610845925076 3.15973632673
y[1] (closed_form) = -0.610790316271 3.15986885473
absolute error = 0.0001437
relative error = 0.004466 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.856
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.346
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1036 2.636
h = 0.001 0.003
y[1] (numeric) = -0.610375509312 3.1620803171
y[1] (closed_form) = -0.610319633631 3.16221247205
absolute error = 0.0001435
relative error = 0.004455 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.858
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.39
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1046 2.639
h = 0.0001 0.004
y[1] (numeric) = -0.611777598401 3.16723954705
y[1] (closed_form) = -0.611722297444 3.16737243961
absolute error = 0.0001439
relative error = 0.004462 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.861
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.62
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1047 2.643
h = 0.003 0.006
y[1] (numeric) = -0.615386233923 3.17296712935
y[1] (closed_form) = -0.615331722538 3.17309992628
absolute error = 0.0001435
relative error = 0.004441 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.865
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.803
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1077 2.649
h = 0.0001 0.005
y[1] (numeric) = -0.616790103651 3.18423740429
y[1] (closed_form) = -0.616734083051 3.18437334636
absolute error = 0.000147
relative error = 0.004533 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.871
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.141
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3800.6MB, alloc=52.3MB, time=45.53
x[1] = 1.1078 2.654
h = 0.0001 0.003
y[1] (numeric) = -0.621346598163 3.19138810676
y[1] (closed_form) = -0.621291192609 3.19152187218
absolute error = 0.0001448
relative error = 0.004453 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.876
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.726
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1079 2.657
h = 0.001 0.001
y[1] (numeric) = -0.624027974732 3.19571745455
y[1] (closed_form) = -0.623971849811 3.19585070513
absolute error = 0.0001446
relative error = 0.00444 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.879
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.356
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1089 2.658
h = 0.0001 0.004
y[1] (numeric) = -0.623557193852 3.19807088492
y[1] (closed_form) = -0.623500803324 3.19820376373
absolute error = 0.0001443
relative error = 0.00443 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.88
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.149
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.109 2.662
h = 0.003 0.006
y[1] (numeric) = -0.627180299197 3.2038148381
y[1] (closed_form) = -0.627125659809 3.20394829988
absolute error = 0.0001442
relative error = 0.004417 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.884
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.835
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.112 2.668
h = 0.0001 0.005
y[1] (numeric) = -0.628595433944 3.2151219577
y[1] (closed_form) = -0.628539288544 3.21525855327
absolute error = 0.0001477
relative error = 0.004508 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.89
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.155
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1121 2.673
h = 0.0001 0.003
y[1] (numeric) = -0.63317128157 3.22229382929
y[1] (closed_form) = -0.633115750432 3.22242825579
absolute error = 0.0001454
relative error = 0.004429 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.895
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.738
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1122 2.676
h = 0.001 0.001
y[1] (numeric) = -0.635864089983 3.2266360345
y[1] (closed_form) = -0.63580784216 3.22676994746
absolute error = 0.0001452
relative error = 0.004416 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.898
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.365
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1132 2.677
h = 0.001 0.003
y[1] (numeric) = -0.635393103136 3.22899756546
y[1] (closed_form) = -0.635336590801 3.22913110773
absolute error = 0.000145
relative error = 0.004406 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.899
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.483
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3845.9MB, alloc=52.3MB, time=46.07
x[1] = 1.1142 2.68
h = 0.0001 0.004
y[1] (numeric) = -0.636811597344 3.2341924404
y[1] (closed_form) = -0.636755654722 3.23432671567
absolute error = 0.0001455
relative error = 0.004413 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.902
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.672
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1143 2.684
h = 0.003 0.006
y[1] (numeric) = -0.640453244376 3.23995706058
y[1] (closed_form) = -0.640398085773 3.24009124184
absolute error = 0.0001451
relative error = 0.004393 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.906
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.872
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1173 2.69
h = 0.0001 0.005
y[1] (numeric) = -0.641880801133 3.2513070106
y[1] (closed_form) = -0.641824140401 3.25144431268
absolute error = 0.0001485
relative error = 0.004482 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.913
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.172
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1174 2.695
h = 0.0001 0.003
y[1] (numeric) = -0.646478693666 3.25850370591
y[1] (closed_form) = -0.646422646159 3.25863884762
absolute error = 0.0001463
relative error = 0.004404 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.917
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.751
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1175 2.698
h = 0.001 0.001
y[1] (numeric) = -0.649184518179 3.26286098284
y[1] (closed_form) = -0.649127757047 3.26299561254
absolute error = 0.0001461
relative error = 0.004392 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.92
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.376
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1185 2.699
h = 0.001 0.003
y[1] (numeric) = -0.648713157663 3.26523188575
y[1] (closed_form) = -0.648656133256 3.26536614602
absolute error = 0.0001459
relative error = 0.004382 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.922
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.533
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1195 2.702
h = 0.0001 0.004
y[1] (numeric) = -0.650140280053 3.27044587445
y[1] (closed_form) = -0.650083822733 3.27058086526
absolute error = 0.0001463
relative error = 0.004388 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.925
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.701
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1196 2.706
h = 0.003 0.006
y[1] (numeric) = -0.653799424938 3.27623041773
y[1] (closed_form) = -0.653743748694 3.27636531537
absolute error = 0.0001459
relative error = 0.004368 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.928
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.91
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3891.3MB, alloc=52.3MB, time=46.61
x[1] = 1.1226 2.712
h = 0.0001 0.005
y[1] (numeric) = -0.655239330121 3.2876230414
y[1] (closed_form) = -0.655182155609 3.28776104703
absolute error = 0.0001494
relative error = 0.004456 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.935
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.188
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1227 2.717
h = 0.0001 0.003
y[1] (numeric) = -0.659859168203 3.29484447883
y[1] (closed_form) = -0.659802605876 3.2949803327
absolute error = 0.0001472
relative error = 0.004379 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.94
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.765
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1228 2.72
h = 0.001 0.001
y[1] (numeric) = -0.662577950025 3.29921677772
y[1] (closed_form) = -0.662520677095 3.2993521211
absolute error = 0.000147
relative error = 0.004367 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.943
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.386
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1238 2.721
h = 0.001 0.003
y[1] (numeric) = -0.662106211645 3.30159701657
y[1] (closed_form) = -0.662048676662 3.30173199176
absolute error = 0.0001467
relative error = 0.004357 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.944
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.583
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1248 2.724
h = 0.0001 0.004
y[1] (numeric) = -0.663541917784 3.30683005125
y[1] (closed_form) = -0.663484947296 3.30696575454
absolute error = 0.0001472
relative error = 0.004364 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.947
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.729
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1249 2.728
h = 0.003 0.006
y[1] (numeric) = -0.667218481865 3.31263445218
y[1] (closed_form) = -0.667162289543 3.31277006311
absolute error = 0.0001468
relative error = 0.004344 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.951
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.947
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1279 2.734
h = 0.0001 0.005
y[1] (numeric) = -0.668670663009 3.32406959438
y[1] (closed_form) = -0.668612976259 3.32420830064
absolute error = 0.0001502
relative error = 0.00443 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.958
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.205
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.128 2.739
h = 0.0001 0.003
y[1] (numeric) = -0.673312348562 3.33131569309
y[1] (closed_form) = -0.673255272953 3.33145225608
absolute error = 0.000148
relative error = 0.004355 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.962
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.778
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1281 2.742
h = 0.001 0.001
y[1] (numeric) = -0.67604402966 3.33570296463
y[1] (closed_form) = -0.675986246433 3.33583901865
absolute error = 0.0001478
relative error = 0.004343 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.965
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.397
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3936.7MB, alloc=52.3MB, time=47.15
x[1] = 1.1291 2.743
h = 0.001 0.003
y[1] (numeric) = -0.675571909332 3.33809250381
y[1] (closed_form) = -0.675513865258 3.33822819088
absolute error = 0.0001476
relative error = 0.004333 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.966
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.633
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1301 2.746
h = 0.0001 0.004
y[1] (numeric) = -0.677016155412 3.34334451738
y[1] (closed_form) = -0.676958673275 3.34348093013
absolute error = 0.000148
relative error = 0.004339 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.969
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.757
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1302 2.75
h = 0.003 0.006
y[1] (numeric) = -0.680710061042 3.3491687111
y[1] (closed_form) = -0.680653354191 3.3493050323
absolute error = 0.0001476
relative error = 0.00432 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.973
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.985
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1332 2.756
h = 0.0001 0.005
y[1] (numeric) = -0.682174446777 3.36064621836
y[1] (closed_form) = -0.682116249317 3.36078562236
absolute error = 0.0001511
relative error = 0.004405 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.98
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.222
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1333 2.761
h = 0.0001 0.003
y[1] (numeric) = -0.686837882973 3.36791689823
y[1] (closed_form) = -0.686780295608 3.36805416738
absolute error = 0.0001489
relative error = 0.004331 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.985
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.791
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1334 2.764
h = 0.001 0.001
y[1] (numeric) = -0.689582406055 3.37231909358
y[1] (closed_form) = -0.68952411402 3.37245585525
absolute error = 0.0001487
relative error = 0.004319 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.987
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.407
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1344 2.765
h = 0.0001 0.004
y[1] (numeric) = -0.689109899805 3.37471789787
y[1] (closed_form) = -0.689051348114 3.37485429382
absolute error = 0.0001484
relative error = 0.004309 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.989
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.456
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1345 2.769
h = 0.003 0.006
y[1] (numeric) = -0.692817961267 3.38055820357
y[1] (closed_form) = -0.692761126919 3.38069517687
absolute error = 0.0001483
relative error = 0.004297 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.992
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.017
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=3982.3MB, alloc=52.3MB, time=47.70
x[1] = 1.1375 2.775
h = 0.0001 0.005
y[1] (numeric) = -0.694293298168 3.39207191132
y[1] (closed_form) = -0.694234976336 3.39221195672
absolute error = 0.0001517
relative error = 0.004381 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.999
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.236
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1376 2.78
h = 0.0001 0.003
y[1] (numeric) = -0.698975671518 3.39936342871
y[1] (closed_form) = -0.698917958976 3.39950134642
absolute error = 0.0001495
relative error = 0.004308 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.004
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.803
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1377 2.783
h = 0.001 0.001
y[1] (numeric) = -0.701731380217 3.40377827915
y[1] (closed_form) = -0.701672965532 3.40391569063
absolute error = 0.0001493
relative error = 0.004296 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.007
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.417
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1387 2.784
h = 0.001 0.003
y[1] (numeric) = -0.701258648479 3.4061850353
y[1] (closed_form) = -0.701199975163 3.40632208209
absolute error = 0.0001491
relative error = 0.004287 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.008
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.726
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1397 2.787
h = 0.0001 0.004
y[1] (numeric) = -0.702718895105 3.41147208742
y[1] (closed_form) = -0.702660779025 3.41160985548
absolute error = 0.0001495
relative error = 0.004293 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.011
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.81
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1398 2.791
h = 0.003 0.006
y[1] (numeric) = -0.706445099991 3.41733273589
y[1] (closed_form) = -0.706387753931 3.41747041389
absolute error = 0.0001491
relative error = 0.004274 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.015
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.054
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1428 2.797
h = 0.0001 0.005
y[1] (numeric) = -0.707932509727 3.42888852816
y[1] (closed_form) = -0.707873679964 3.42902926601
absolute error = 0.0001525
relative error = 0.004357 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.021
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.253
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1429 2.802
h = 0.0001 0.003
y[1] (numeric) = -0.712636455857 3.43620448072
y[1] (closed_form) = -0.712578234331 3.43634309911
absolute error = 0.0001503
relative error = 0.004284 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.026
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.816
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4027.8MB, alloc=52.3MB, time=48.24
x[1] = 1.143 2.805
h = 0.001 0.001
y[1] (numeric) = -0.715404901285 3.44063416593
y[1] (closed_form) = -0.715345980499 3.44077227956
absolute error = 0.0001502
relative error = 0.004273 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.029
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.427
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.144 2.806
h = 0.001 0.003
y[1] (numeric) = -0.714931776098 3.44305012274
y[1] (closed_form) = -0.714872597843 3.44318787289
absolute error = 0.0001499
relative error = 0.004263 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.03
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.776
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.145 2.809
h = 0.0001 0.004
y[1] (numeric) = -0.716400439902 3.44835596605
y[1] (closed_form) = -0.716341816416 3.44849443512
absolute error = 0.0001504
relative error = 0.004269 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.033
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.838
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1451 2.813
h = 0.003 0.006
y[1] (numeric) = -0.720143768842 3.45423622593
y[1] (closed_form) = -0.720085912584 3.45437460571
absolute error = 0.00015
relative error = 0.004251 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.037
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.092
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1481 2.819
h = 0.0001 0.005
y[1] (numeric) = -0.721643183059 3.46583395374
y[1] (closed_form) = -0.721583846858 3.46597538125
absolute error = 0.0001534
relative error = 0.004332 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.044
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.269
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1482 2.824
h = 0.0001 0.003
y[1] (numeric) = -0.72636860859 3.47317426342
y[1] (closed_form) = -0.726309879572 3.4733135796
absolute error = 0.0001512
relative error = 0.004261 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.048
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.83
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1483 2.827
h = 0.001 0.001
y[1] (numeric) = -0.7291497355 3.47761873581
y[1] (closed_form) = -0.72909031007 3.47775754871
absolute error = 0.000151
relative error = 0.004249 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.051
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.438
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1493 2.828
h = 0.001 0.003
y[1] (numeric) = -0.728676213187 3.48004385916
y[1] (closed_form) = -0.728616531434 3.48018230976
absolute error = 0.0001508
relative error = 0.00424 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.053
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.826
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1503 2.831
h = 0.0001 0.004
y[1] (numeric) = -0.730153252656 3.48536842914
y[1] (closed_form) = -0.730094123239 3.48550759633
absolute error = 0.0001512
relative error = 0.004246 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.056
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.866
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4073.2MB, alloc=52.3MB, time=48.78
x[1] = 1.1504 2.835
h = 0.003 0.006
y[1] (numeric) = -0.733913631716 3.49126823781
y[1] (closed_form) = -0.733855266764 3.49140731646
absolute error = 0.0001508
relative error = 0.004228 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.06
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.129
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1534 2.841
h = 0.0001 0.005
y[1] (numeric) = -0.735424983058 3.5029077537
y[1] (closed_form) = -0.735365141902 3.50304986812
absolute error = 0.0001542
relative error = 0.004308 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.066
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.286
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1535 2.846
h = 0.0001 0.003
y[1] (numeric) = -0.740171795771 3.51027234314
y[1] (closed_form) = -0.74011256074 3.51041235428
absolute error = 0.000152
relative error = 0.004238 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.071
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.843
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1536 2.849
h = 0.001 0.001
y[1] (numeric) = -0.7429655496 3.51473155556
y[1] (closed_form) = -0.742905620973 3.51487106487
absolute error = 0.0001518
relative error = 0.004226 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.074
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.448
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1546 2.85
h = 0.001 0.003
y[1] (numeric) = -0.742491626579 3.51716581169
y[1] (closed_form) = -0.742431442762 3.51730495988
absolute error = 0.0001516
relative error = 0.004217 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.075
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.876
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1556 2.853
h = 0.0001 0.004
y[1] (numeric) = -0.743977000766 3.52250904445
y[1] (closed_form) = -0.74391736688 3.52264890692
absolute error = 0.000152
relative error = 0.004223 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.078
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.895
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1557 2.857
h = 0.003 0.006
y[1] (numeric) = -0.747754356923 3.52842833987
y[1] (closed_form) = -0.747695484768 3.52856811454
absolute error = 0.0001517
relative error = 0.004205 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.082
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.167
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1587 2.863
h = 0.0001 0.005
y[1] (numeric) = -0.749277579017 3.54010949789
y[1] (closed_form) = -0.749217234375 3.5402522965
absolute error = 0.000155
relative error = 0.004284 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.089
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.303
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=4118.5MB, alloc=52.3MB, time=49.32
x[1] = 1.1588 2.868
h = 0.0001 0.003
y[1] (numeric) = -0.754045687822 3.54749829045
y[1] (closed_form) = -0.753985948247 3.54763899372
absolute error = 0.0001529
relative error = 0.004215 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.093
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.857
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1589 2.871
h = 0.001 0.001
y[1] (numeric) = -0.75685201468 3.55197219616
y[1] (closed_form) = -0.756791584292 3.55211239905
absolute error = 0.0001527
relative error = 0.004204 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.096
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.459
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 1.1599 2.872
h = 0.001 0.003
y[1] (numeric) = -0.756377687465 3.55441555168
y[1] (closed_form) = -0.756317003004 3.55455539463
absolute error = 0.0001524
relative error = 0.004195 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.097
Order of pole (given) = 1.5 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.926
Order of pole (three term test) = 1.5 0
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff ( y , x , 1 ) = sqrt ( x ) ;
Iterations = 754
Total Elapsed Time = 49 Seconds
Expected Time Remaining = 0 Seconds
Optimized Time Remaining = 0 Seconds
Expected Total Time = 49 Seconds
> quit
memory used=4138.9MB, alloc=52.3MB, time=49.55