|\^/| 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. | Type ? for help. #BEGIN OUTFILE1 # before write maple top matter # before write_ats library and user def block #BEGIN ATS LIBRARY BLOCK # Begin Function number 2 > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s\n",str); > fi;# end if 1; > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc # End Function number 2 # Begin Function number 3 > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s",str); > fi;# end if 1; > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc # End Function number 3 # Begin Function number 4 > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > print(label,str); > fi;# end if 1; > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc # End Function number 4 # Begin Function number 5 > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc # End Function number 5 # Begin Function number 6 > omniout_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)/(c(1.0) - c(2.0)*c(x))); > end; exact_soln_y := proc(x) return c(2.0)/(c(1.0) - c(2.0)*c(x)) 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 + 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0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 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 mult FULL FULL $eq_no = 1 i = 1 > array_tmp1[1] := (array_y[1] * (array_y[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 mult FULL FULL $eq_no = 1 i = 2 > array_tmp1[2] := ats(2,array_y,array_y,1); > #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 mult FULL FULL $eq_no = 1 i = 3 > array_tmp1[3] := ats(3,array_y,array_y,1); > #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 mult FULL FULL $eq_no = 1 i = 4 > array_tmp1[4] := ats(4,array_y,array_y,1); > #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 mult FULL FULL $eq_no = 1 i = 5 > array_tmp1[5] := ats(5,array_y,array_y,1); > #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 mult FULL FULL $eq_no = 1 > array_tmp1[kkk] := ats(kkk,array_y,array_y,1); > #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] := array_y[1]*array_y[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] := ats(2, array_y, array_y, 1); 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] := ats(3, array_y, array_y, 1); 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] := ats(4, array_y, array_y, 1); 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] := ats(5, array_y, array_y, 1); 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] := ats(kkk, array_y, array_y, 1); 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 := 20; > # before first input block > #BEGIN FIRST INPUT BLOCK > #BEGIN BLOCK 1 > #BEGIN FIRST INPUT BLOCK > Digits:=32; > max_terms:=20; > #END BLOCK 1 > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > # before generate arrays > array_y_init:= Array(0..(20),[]); > array_norms:= Array(0..(20),[]); > array_fact_1:= Array(0..(20),[]); > array_1st_rel_error:= Array(0..(2),[]); > array_last_rel_error:= Array(0..(2),[]); > array_est_rel_error:= Array(0..(2),[]); > array_max_est_error:= Array(0..(2),[]); > array_type_pole:= Array(0..(2),[]); > array_type_real_pole:= Array(0..(2),[]); > array_type_complex_pole:= Array(0..(2),[]); > array_est_digits:= Array(0..(2),[]); > array_y:= Array(0..(20),[]); > array_x:= Array(0..(20),[]); > array_tmp0:= Array(0..(20),[]); > array_tmp1:= Array(0..(20),[]); > array_tmp2:= Array(0..(20),[]); > array_m1:= Array(0..(20),[]); > array_y_higher := Array(0..(2) ,(0..20+ 1),[]); > array_y_higher_work := Array(0..(2) ,(0..20+ 1),[]); > array_y_higher_work2 := Array(0..(2) ,(0..20+ 1),[]); > array_y_set_initial := Array(0..(2) ,(0..20+ 1),[]); > array_given_rad_poles := Array(0..(2) ,(0..3+ 1),[]); > array_given_ord_poles := Array(0..(2) ,(0..3+ 1),[]); > array_rad_test_poles := Array(0..(2) ,(0..4+ 1),[]); > array_ord_test_poles := Array(0..(2) ,(0..4+ 1),[]); > array_fact_2 := Array(0..(20) ,(0..20+ 1),[]); > # before generate constants > # before generate globals definition > #Top Generate Globals Definition > #Bottom Generate Globals Deninition > # before generate const definition > # before arrays initialized > term := 1; > while (term <= 20) do # do number 1 > array_y_init[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_norms[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_fact_1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_1st_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_last_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_est_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_max_est_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_real_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_complex_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_est_digits[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_y[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_x[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_tmp0[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_tmp1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_tmp2[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_m1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 20) do # do number 2 > array_y_higher[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 20) do # do number 2 > array_y_higher_work[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 20) do # do number 2 > array_y_higher_work2[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 20) do # do number 2 > array_y_set_initial[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_rad_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_ord_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 4) do # do number 2 > array_rad_test_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 4) do # do number 2 > array_ord_test_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=20) do # do number 1 > term := 1; > while (term <= 20) do # do number 2 > array_fact_2[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > # before symbols initialized > #BEGIN SYMBOLS INITIALIZATED > zero_ats_ar(array_y); > zero_ats_ar(array_x); > zero_ats_ar(array_tmp0); > zero_ats_ar(array_tmp1); > zero_ats_ar(array_tmp2); > zero_ats_ar(array_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; > # before generate init omniout const > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > ATS_MAX_TERMS := 20; > glob_iolevel := INFO; > # set default block > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > glob_display_flag := true; > glob_no_eqs := 1; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 10000; > glob_max_hours := (0.0); > glob_max_minutes := (15.0); > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/nonlinear2postcpx.cpx#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = y * y ; "); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=20;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"x_start := 0.1 + 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,""); > 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(0.5);"); > 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(0.0);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_ord_poles[1,2] := c(0.0);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > 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)/(c(1.0) - c(2.0)*c(x)));"); > 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 := 0.1 + 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_type_given_pole := 1; > array_given_rad_poles[1,1] := c(0.5); > array_given_rad_poles[1,2] := c(0.0); > array_given_ord_poles[1,1] := c(0.0); > array_given_ord_poles[1,2] := c(0.0); > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=8; > glob_max_minutes:=(3.0); > glob_subiter_method:=3; > glob_max_iter:=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 ) = y * y ; "); > 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,"2017-11-26T16:21:47-06:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"nonlinear2") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = y * y ; ") > ; > 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,"nonlinear2 diffeq.mxt") > ; > logitem_str(html_log_file,"nonlinear2 maple results") > ; > logitem_str(html_log_file,"OK - a little surprising") > ; > 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 := 20; Digits := 32; max_terms := 20; glob_html_log := true; array_y_init := Array(0 .. 20, []); array_norms := Array(0 .. 20, []); array_fact_1 := Array(0 .. 20, []); array_1st_rel_error := Array(0 .. 2, []); array_last_rel_error := Array(0 .. 2, []); array_est_rel_error := Array(0 .. 2, []); array_max_est_error := Array(0 .. 2, []); array_type_pole := Array(0 .. 2, []); array_type_real_pole := Array(0 .. 2, []); array_type_complex_pole := Array(0 .. 2, []); array_est_digits := Array(0 .. 2, []); array_y := Array(0 .. 20, []); array_x := Array(0 .. 20, []); array_tmp0 := Array(0 .. 20, []); array_tmp1 := Array(0 .. 20, []); array_tmp2 := Array(0 .. 20, []); array_m1 := Array(0 .. 20, []); array_y_higher := Array(0 .. 2, 0 .. 21, []); array_y_higher_work := Array(0 .. 2, 0 .. 21, []); array_y_higher_work2 := Array(0 .. 2, 0 .. 21, []); array_y_set_initial := Array(0 .. 2, 0 .. 21, []); array_given_rad_poles := Array(0 .. 2, 0 .. 4, []); array_given_ord_poles := Array(0 .. 2, 0 .. 4, []); array_rad_test_poles := Array(0 .. 2, 0 .. 5, []); array_ord_test_poles := Array(0 .. 2, 0 .. 5, []); array_fact_2 := Array(0 .. 20, 0 .. 21, []); term := 1; while term <= 20 do array_y_init[term] := c(0.); term := term + 1 end do; term := 1; while term <= 20 do array_norms[term] := c(0.); term := term + 1 end do ; term := 1; while term <= 20 do array_fact_1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_1st_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_last_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_est_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_max_est_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_type_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_type_real_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_type_complex_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_est_digits[term] := 0; term := term + 1 end do ; term := 1; while term <= 20 do array_y[term] := c(0.); term := term + 1 end do; term := 1; while term <= 20 do array_x[term] := c(0.); term := term + 1 end do; term := 1; while term <= 20 do array_tmp0[term] := c(0.); term := term + 1 end do; term := 1; while term <= 20 do array_tmp1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 20 do array_tmp2[term] := c(0.); term := term + 1 end do; term := 1; while term <= 20 do array_m1[term] := c(0.); term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 20 do array_y_higher[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 20 do array_y_higher_work[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 20 do array_y_higher_work2[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 20 do array_y_set_initial[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_rad_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_ord_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 4 do array_rad_test_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 4 do array_ord_test_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 20 do term := 1; while term <= 20 do array_fact_2[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; zero_ats_ar(array_y); zero_ats_ar(array_x); zero_ats_ar(array_tmp0); zero_ats_ar(array_tmp1); zero_ats_ar(array_tmp2); zero_ats_ar(array_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; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; ATS_MAX_TERMS := 20; glob_iolevel := INFO; glob_orig_start_sec := elapsed_time_seconds(); glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 10000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/nonlinear2postcpx.cpx#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = y * y ; "); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=20;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "x_start := 0.1 + 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, ""); 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(0.5);"); 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(0.0);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_ord_poles[1,2] := c(0.0);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); 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)/(c(1.0) - c(2.0)*c(x)));"); 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 + 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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(0.10*10^101); glob_larger_float := c(0.11*10^101); glob_almost_1 := c(0.99); x_start := 0.1 + 0.1*I; x_end := 99.0 + 99.0*I; array_y_init[1] := exact_soln_y(x_start); glob_look_poles := true; glob_type_given_pole := 1; array_given_rad_poles[1, 1] := c(0.5); array_given_rad_poles[1, 2] := c(0.); array_given_ord_poles[1, 1] := c(0.); array_given_ord_poles[1, 2] := c(0.); glob_desired_digits_correct := 8; glob_max_minutes := 3.0; glob_subiter_method := 3; glob_max_iter := 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 ) = y * y ; "); 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, "2017-11-26T16:21:47-06:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "nonlinear2"); logitem_str(html_log_file, "diff ( y , x , 1 ) = y * y ; "); 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, "nonlinear2 diffeq.mxt"); logitem_str(html_log_file, "nonlinear2 maple results"); logitem_str(html_log_file, "OK - a little surprising"); 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/nonlinear2postcpx.cpx################# diff ( y , x , 1 ) = y * y ; ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=20; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.1 + 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_type_given_pole := 1; array_given_rad_poles[1,1] := c(0.5); array_given_rad_poles[1,2] := c(0.0); array_given_ord_poles[1,1] := c(0.0); array_given_ord_poles[1,2] := c(0.0); #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=8; glob_max_minutes:=(3.0); glob_subiter_method:=3; glob_max_iter:=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)/(c(1.0) - c(2.0)*c(x))); 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] = 0.1 0.1 h = 0.0001 0.005 y[1] (numeric) = 2.35294117647 0.588235294118 y[1] (closed_form) = 2.35294117647 0.588235294118 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 0.4123 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4123 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4123 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1001 0.105 h = 0.0001 0.003 y[1] (numeric) = 2.33934877655 0.614232611996 y[1] (closed_form) = 2.33934877655 0.614232611996 absolute error = 1e-32 relative error = 4.135e-31 % Correct digits = 32 Radius of convergence (given) for eq 1 = 0.4135 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4135 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4135 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1002 0.108 h = 0.001 0.001 y[1] (numeric) = 2.33114042095 0.629722775044 y[1] (closed_form) = 2.33114042095 0.629722775044 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 0.4141 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4141 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4141 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1012 0.109 h = 0.001 0.003 y[1] (numeric) = 2.33322201579 0.637716147745 y[1] (closed_form) = 2.33322201579 0.637716147745 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 0.4134 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4134 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4134 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1022 0.112 h = 0.0001 0.004 y[1] (numeric) = 2.32919200107 0.655780553343 y[1] (closed_form) = 2.32919200107 0.655780553343 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 0.4133 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4133 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4133 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1023 0.116 h = 0.003 0.006 y[1] (numeric) = 2.31731156432 0.675906817855 y[1] (closed_form) = 2.31731156432 0.675906817855 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 0.4143 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4143 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4143 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1053 0.122 h = 0.0001 0.005 y[1] (numeric) = 2.31262182352 0.714821034886 y[1] (closed_form) = 2.31262182352 0.714821034886 absolute error = 1e-31 relative error = 4.131e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.4131 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4131 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4131 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1054 0.127 h = 0.0001 0.003 y[1] (numeric) = 2.29634674859 0.739067503982 y[1] (closed_form) = 2.29634674859 0.739067503982 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 0.4145 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4145 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4145 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1055 0.13 h = 0.001 0.001 y[1] (numeric) = 2.28655554606 0.753491054467 y[1] (closed_form) = 2.28655554606 0.753491054467 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 0.4154 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4154 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4154 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1065 0.131 h = 0.001 0.003 y[1] (numeric) = 2.28774746989 0.761613516024 y[1] (closed_form) = 2.28774746989 0.761613516024 absolute error = 1e-31 relative error = 4.147e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.4147 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4147 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4147 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=30.3MB, alloc=40.3MB, time=0.38 x[1] = 0.1075 0.134 h = 0.0001 0.004 y[1] (numeric) = 2.28181423125 0.77901428532 y[1] (closed_form) = 2.28181423125 0.77901428532 absolute error = 1e-31 relative error = 4.147e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.4147 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4147 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4147 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1076 0.138 h = 0.003 0.006 y[1] (numeric) = 2.26792283237 0.797587540434 y[1] (closed_form) = 2.26792283237 0.797587540434 absolute error = 1e-31 relative error = 4.160e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.416 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.416 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.416 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1106 0.144 h = 0.0001 0.005 y[1] (numeric) = 2.25911530399 0.835420143233 y[1] (closed_form) = 2.25911530399 0.835420143233 absolute error = 1.005e-31 relative error = 4.172e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.4152 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4152 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4152 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1107 0.149 h = 0.0001 0.003 y[1] (numeric) = 2.24050474607 0.857526861453 y[1] (closed_form) = 2.24050474607 0.857526861453 absolute error = 1e-32 relative error = 4.168e-31 % Correct digits = 32 Radius of convergence (given) for eq 1 = 0.4168 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4168 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4168 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1108 0.152 h = 0.001 0.001 y[1] (numeric) = 2.22934226842 0.870657823227 y[1] (closed_form) = 2.22934226842 0.870657823227 absolute error = 1.005e-31 relative error = 4.199e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.4178 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4178 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4178 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1118 0.153 h = 0.001 0.003 y[1] (numeric) = 2.22964748825 0.878763693206 y[1] (closed_form) = 2.22964748825 0.878763693206 absolute error = 1e-32 relative error = 4.173e-31 % Correct digits = 32 Radius of convergence (given) for eq 1 = 0.4173 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4173 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4173 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1128 0.156 h = 0.0001 0.004 y[1] (numeric) = 2.22196921563 0.895214869932 y[1] (closed_form) = 2.22196921563 0.895214869932 absolute error = 2e-32 relative error = 8.349e-31 % Correct digits = 32 Radius of convergence (given) for eq 1 = 0.4174 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4174 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4174 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1129 0.16 h = 0.003 0.006 y[1] (numeric) = 2.20637173482 0.911959384065 y[1] (closed_form) = 2.20637173482 0.911959384065 absolute error = 1.020e-31 relative error = 4.272e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.4189 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4189 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4189 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1159 0.166 h = 0.0001 0.005 y[1] (numeric) = 2.19374384919 0.948090286295 y[1] (closed_form) = 2.19374384919 0.948090286295 absolute error = 2e-32 relative error = 8.369e-31 % Correct digits = 32 Radius of convergence (given) for eq 1 = 0.4184 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4184 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4184 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.116 0.171 h = 0.0001 0.003 y[1] (numeric) = 2.1732117693 0.967758366016 y[1] (closed_form) = 2.1732117693 0.967758366016 absolute error = 2e-32 relative error = 8.407e-31 % Correct digits = 32 Radius of convergence (given) for eq 1 = 0.4204 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4204 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4204 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1161 0.174 h = 0.001 0.001 y[1] (numeric) = 2.16092733785 0.979425258623 y[1] (closed_form) = 2.16092733785 0.979425258623 absolute error = 2e-32 relative error = 8.430e-31 % Correct digits = 32 Radius of convergence (given) for eq 1 = 0.4215 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4215 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4215 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1171 0.175 h = 0.001 0.003 y[1] (numeric) = 2.16037912086 0.987376197835 y[1] (closed_form) = 2.16037912086 0.987376197835 absolute error = 2e-32 relative error = 8.420e-31 % Correct digits = 32 Radius of convergence (given) for eq 1 = 0.421 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.421 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.421 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1181 0.178 h = 0.0001 0.004 y[1] (numeric) = 2.1511662064 1.00263834705 y[1] (closed_form) = 2.1511662064 1.00263834705 absolute error = 1e-31 relative error = 4.213e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.4213 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4213 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4213 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1182 0.182 h = 0.003 0.006 y[1] (numeric) = 2.1342099432 1.01735518508 y[1] (closed_form) = 2.1342099432 1.01735518508 absolute error = 1e-31 relative error = 4.230e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.423 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.423 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.423 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1212 0.188 h = 0.0001 0.005 y[1] (numeric) = 2.11817208236 1.05125752767 y[1] (closed_form) = 2.11817208236 1.05125752767 absolute error = 1e-31 relative error = 4.229e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.4229 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4229 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4229 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1213 0.193 h = 0.0001 0.003 y[1] (numeric) = 2.09617160023 1.06828919685 y[1] (closed_form) = 2.09617160023 1.06828919685 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 0.425 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.425 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.425 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1214 0.196 h = 0.001 0.001 y[1] (numeric) = 2.08303576989 1.0783809057 y[1] (closed_form) = 2.08303576989 1.0783809057 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 0.4263 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4263 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4263 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1224 0.197 h = 0.0001 0.004 y[1] (numeric) = 2.08169368715 1.08605311538 y[1] (closed_form) = 2.08169368715 1.08605311538 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 0.4259 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4259 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4259 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1225 0.201 h = 0.003 0.006 y[1] (numeric) = 2.06388757143 1.09891762082 y[1] (closed_form) = 2.06388757143 1.09891762082 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 0.4277 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4277 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4277 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1255 0.207 h = 0.0001 0.005 y[1] (numeric) = 2.04533879849 1.13053439596 y[1] (closed_form) = 2.04533879849 1.13053439596 absolute error = 1e-31 relative error = 4.279e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.4279 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4279 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4279 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1256 0.212 h = 0.0001 0.003 y[1] (numeric) = 2.02247890226 1.14520707072 y[1] (closed_form) = 2.02247890226 1.14520707072 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 0.4303 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4303 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4303 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=75.5MB, alloc=52.3MB, time=0.93 x[1] = 0.1257 0.215 h = 0.001 0.001 y[1] (numeric) = 2.00885021153 1.15389472476 y[1] (closed_form) = 2.00885021153 1.15389472476 absolute error = 1e-31 relative error = 4.317e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.4317 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4317 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4317 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1267 0.216 h = 0.001 0.003 y[1] (numeric) = 2.00689332644 1.16123482055 y[1] (closed_form) = 2.00689332644 1.16123482055 absolute error = 1e-31 relative error = 4.313e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.4313 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4313 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4313 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1277 0.219 h = 0.0001 0.004 y[1] (numeric) = 1.99551595826 1.17383291662 y[1] (closed_form) = 1.99551595826 1.17383291662 absolute error = 1e-31 relative error = 4.319e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.4319 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4319 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4319 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1278 0.223 h = 0.003 0.006 y[1] (numeric) = 1.97703368882 1.184520453 y[1] (closed_form) = 1.97703368882 1.184520453 absolute error = 1e-31 relative error = 4.339e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.4339 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4339 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4339 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1308 0.229 h = 0.0001 0.005 y[1] (numeric) = 1.95603022077 1.21324734712 y[1] (closed_form) = 1.95603022077 1.21324734712 absolute error = 1e-31 relative error = 4.345e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.4345 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4345 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4345 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1309 0.234 h = 0.0001 0.003 y[1] (numeric) = 1.93255371816 1.22518984029 y[1] (closed_form) = 1.93255371816 1.22518984029 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 0.437 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.437 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.437 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.131 0.237 h = 0.001 0.001 y[1] (numeric) = 1.91857744502 1.23225705818 y[1] (closed_form) = 1.91857744502 1.23225705818 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 0.4386 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4386 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4386 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.132 0.238 h = 0.001 0.003 y[1] (numeric) = 1.91598808755 1.23914446967 y[1] (closed_form) = 1.91598808755 1.23914446967 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 0.4383 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4383 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4383 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.133 0.241 h = 0.0001 0.004 y[1] (numeric) = 1.90382320901 1.25019453234 y[1] (closed_form) = 1.90382320901 1.25019453234 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 0.4391 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4391 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4391 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1331 0.245 h = 0.003 0.006 y[1] (numeric) = 1.88501258807 1.25873012831 y[1] (closed_form) = 1.88501258807 1.25873012831 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 0.4412 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4412 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4412 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1361 0.251 h = 0.0001 0.005 y[1] (numeric) = 1.86210296053 1.2843853891 y[1] (closed_form) = 1.86210296053 1.2843853891 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 0.4421 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4421 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4421 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1362 0.256 h = 0.0001 0.003 y[1] (numeric) = 1.83842814091 1.29367125913 y[1] (closed_form) = 1.83842814091 1.29367125913 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 0.4448 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4448 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4448 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1363 0.259 h = 0.001 0.001 y[1] (numeric) = 1.82434986907 1.29916584022 y[1] (closed_form) = 1.82434986907 1.29916584022 absolute error = 1e-31 relative error = 4.465e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.4465 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4465 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4465 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1373 0.26 h = 0.001 0.003 y[1] (numeric) = 1.82122847409 1.3055401248 y[1] (closed_form) = 1.82122847409 1.3055401248 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 0.4463 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4463 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4463 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1383 0.263 h = 0.0001 0.004 y[1] (numeric) = 1.80853716544 1.31502702381 y[1] (closed_form) = 1.80853716544 1.31502702381 absolute error = 1.414e-31 relative error = 6.324e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.4472 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4472 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4472 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1384 0.267 h = 0.003 0.006 y[1] (numeric) = 1.7897130698 1.32149720585 y[1] (closed_form) = 1.7897130698 1.32149720585 absolute error = 1e-31 relative error = 4.495e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.4495 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4495 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4495 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1414 0.273 h = 0.0001 0.005 y[1] (numeric) = 1.765433115 1.34401349803 y[1] (closed_form) = 1.765433115 1.34401349803 absolute error = 1e-31 relative error = 4.507e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.4507 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4507 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4507 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1415 0.278 h = 0.0001 0.003 y[1] (numeric) = 1.74192960612 1.35078502232 y[1] (closed_form) = 1.74192960612 1.35078502232 absolute error = 1e-31 relative error = 4.537e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.4537 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4537 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4537 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1416 0.281 h = 0.001 0.001 y[1] (numeric) = 1.72796540366 1.35479430365 y[1] (closed_form) = 1.72796540366 1.35479430365 absolute error = 1e-31 relative error = 4.554e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.4554 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4554 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4554 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1426 0.282 h = 0.001 0.003 y[1] (numeric) = 1.72441444695 1.36061800235 y[1] (closed_form) = 1.72441444695 1.36061800235 absolute error = 1e-31 relative error = 4.553e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.4553 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4553 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4553 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1436 0.285 h = 0.0001 0.004 y[1] (numeric) = 1.71143776331 1.36857396897 y[1] (closed_form) = 1.71143776331 1.36857396897 absolute error = 1e-31 relative error = 4.563e-30 % Correct digits = 31 memory used=120.9MB, alloc=52.3MB, time=1.46 Radius of convergence (given) for eq 1 = 0.4563 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4563 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4563 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1437 0.289 h = 0.003 0.006 y[1] (numeric) = 1.69287229495 1.3731128073 y[1] (closed_form) = 1.69287229495 1.3731128073 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 0.4588 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4588 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4588 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1467 0.295 h = 0.0001 0.005 y[1] (numeric) = 1.66772175755 1.39252170528 y[1] (closed_form) = 1.66772175755 1.39252170528 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 0.4603 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4603 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4603 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1468 0.3 h = 0.0001 0.003 y[1] (numeric) = 1.64470130511 1.39697166345 y[1] (closed_form) = 1.64470130511 1.39697166345 absolute error = 1e-31 relative error = 4.634e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.4634 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4634 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4634 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1469 0.303 h = 0.001 0.001 y[1] (numeric) = 1.63103269036 1.39961173939 y[1] (closed_form) = 1.63103269036 1.39961173939 absolute error = 1.414e-31 relative error = 6.580e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.4653 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4653 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4653 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1479 0.304 h = 0.0001 0.004 y[1] (numeric) = 1.62715159142 1.40486817322 y[1] (closed_form) = 1.62715159142 1.40486817322 absolute error = 1e-31 relative error = 4.652e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.4652 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4652 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4652 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.148 0.308 h = 0.003 0.006 y[1] (numeric) = 1.60901045857 1.40788415125 y[1] (closed_form) = 1.60901045857 1.40788415125 absolute error = 1.414e-31 relative error = 6.615e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.4677 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4677 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4677 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.151 0.314 h = 0.0001 0.005 y[1] (numeric) = 1.58350612758 1.42470178814 y[1] (closed_form) = 1.58350612758 1.42470178814 absolute error = 1.414e-31 relative error = 6.639e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.4695 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4695 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4695 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1511 0.319 h = 0.0001 0.003 y[1] (numeric) = 1.56112823798 1.42734281432 y[1] (closed_form) = 1.56112823798 1.42734281432 absolute error = 1e-31 relative error = 4.727e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.4727 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4727 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4727 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1512 0.322 h = 0.001 0.001 y[1] (numeric) = 1.54784583172 1.42891731024 y[1] (closed_form) = 1.54784583172 1.42891731024 absolute error = 1e-31 relative error = 4.747e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.4747 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4747 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4747 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1522 0.323 h = 0.001 0.003 y[1] (numeric) = 1.54376169362 1.43368322898 y[1] (closed_form) = 1.54376169362 1.43368322898 absolute error = 1e-31 relative error = 4.747e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.4747 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4747 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4747 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1532 0.326 h = 0.0001 0.004 y[1] (numeric) = 1.53081331211 1.43899982626 y[1] (closed_form) = 1.53081331211 1.43899982626 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 0.476 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.476 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.476 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1533 0.33 h = 0.003 0.006 y[1] (numeric) = 1.51330708493 1.44041343532 y[1] (closed_form) = 1.51330708493 1.44041343532 absolute error = 1e-31 relative error = 4.786e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.4786 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4786 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4786 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1563 0.336 h = 0.0001 0.005 y[1] (numeric) = 1.48771333612 1.45438370945 y[1] (closed_form) = 1.48771333612 1.45438370945 absolute error = 1e-31 relative error = 4.807e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.4807 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4807 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4807 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1564 0.341 h = 0.0001 0.003 y[1] (numeric) = 1.46623336256 1.45513846517 y[1] (closed_form) = 1.46623336256 1.45513846517 absolute error = 1.414e-31 relative error = 6.846e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.4841 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4841 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4841 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1565 0.344 h = 0.001 0.001 y[1] (numeric) = 1.45348683452 1.45560253588 y[1] (closed_form) = 1.45348683452 1.45560253588 absolute error = 1.414e-31 relative error = 6.875e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.4861 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4861 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4861 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1575 0.345 h = 0.001 0.003 y[1] (numeric) = 1.44923703488 1.4598154074 y[1] (closed_form) = 1.44923703488 1.4598154074 absolute error = 1e-31 relative error = 4.861e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.4861 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4861 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4861 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1585 0.348 h = 0.0001 0.004 y[1] (numeric) = 1.43652625657 1.46386863041 y[1] (closed_form) = 1.43652625657 1.46386863041 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 0.4876 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4876 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4876 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1586 0.352 h = 0.003 0.006 y[1] (numeric) = 1.41979080252 1.46387335233 y[1] (closed_form) = 1.41979080252 1.46387335233 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 0.4904 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4904 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4904 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1616 0.358 h = 0.0001 0.005 y[1] (numeric) = 1.39443715176 1.47520242414 y[1] (closed_form) = 1.39443715176 1.47520242414 absolute error = 1.414e-31 relative error = 6.967e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.4926 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4926 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4926 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1617 0.363 h = 0.0001 0.003 y[1] (numeric) = 1.37399742965 1.47431589407 y[1] (closed_form) = 1.37399742965 1.47431589407 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 0.4962 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4962 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4962 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=166.1MB, alloc=52.3MB, time=1.98 x[1] = 0.1618 0.366 h = 0.001 0.001 y[1] (numeric) = 1.3618687384 1.47381418763 y[1] (closed_form) = 1.3618687384 1.47381418763 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 0.4983 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4983 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4983 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1628 0.367 h = 0.001 0.003 y[1] (numeric) = 1.35752705271 1.4774983047 y[1] (closed_form) = 1.35752705271 1.4774983047 absolute error = 1e-31 relative error = 4.984e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.4984 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4984 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4984 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1638 0.37 h = 0.0001 0.004 y[1] (numeric) = 1.34517428129 1.48041190981 y[1] (closed_form) = 1.34517428129 1.48041190981 absolute error = 1e-31 relative error = 4.999e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.4999 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.4999 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.4999 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1639 0.374 h = 0.003 0.006 y[1] (numeric) = 1.32930331494 1.47920095147 y[1] (closed_form) = 1.32930331494 1.47920095147 absolute error = 1e-31 relative error = 5.028e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.5028 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.5028 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.5028 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1669 0.38 h = 0.0001 0.005 y[1] (numeric) = 1.30445538283 1.488120821 y[1] (closed_form) = 1.30445538283 1.488120821 absolute error = 2e-31 relative error = 1.011e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.5053 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.5053 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.5053 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.167 0.385 h = 0.0001 0.003 y[1] (numeric) = 1.28514862184 1.48583249072 y[1] (closed_form) = 1.28514862184 1.48583249072 absolute error = 2e-31 relative error = 1.018e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.509 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.509 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.509 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1671 0.388 h = 0.001 0.001 y[1] (numeric) = 1.2736908312 1.48450598529 y[1] (closed_form) = 1.2736908312 1.48450598529 absolute error = 2e-31 relative error = 1.022e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.5112 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.5112 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.5112 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1681 0.389 h = 0.001 0.003 y[1] (numeric) = 1.26931988815 1.48769339106 y[1] (closed_form) = 1.26931988815 1.48769339106 absolute error = 2e-31 relative error = 1.023e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.5113 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.5113 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.5113 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1691 0.392 h = 0.0001 0.004 y[1] (numeric) = 1.25741562671 1.48959481919 y[1] (closed_form) = 1.25741562671 1.48959481919 absolute error = 2e-31 relative error = 1.026e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.513 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.513 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.513 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1692 0.396 h = 0.003 0.006 y[1] (numeric) = 1.24246632721 1.48735388626 y[1] (closed_form) = 1.24246632721 1.48735388626 absolute error = 3e-31 relative error = 1.548e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.516 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.516 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.516 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1722 0.402 h = 0.0001 0.005 y[1] (numeric) = 1.21832992612 1.49410808512 y[1] (closed_form) = 1.21832992612 1.49410808512 absolute error = 3e-31 relative error = 1.556e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.5187 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.5187 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.5187 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1723 0.407 h = 0.0001 0.003 y[1] (numeric) = 1.2002067564 1.49064433889 y[1] (closed_form) = 1.2002067564 1.49064433889 absolute error = 3.162e-31 relative error = 1.652e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.5225 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.5225 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.5225 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1724 0.41 h = 0.001 0.001 y[1] (numeric) = 1.18944850254 1.48862602577 y[1] (closed_form) = 1.18944850254 1.48862602577 absolute error = 3.162e-31 relative error = 1.660e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.5248 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.5248 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.5248 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1734 0.411 h = 0.0001 0.004 y[1] (numeric) = 1.18509999109 1.49135363239 y[1] (closed_form) = 1.18509999109 1.49135363239 absolute error = 3.162e-31 relative error = 1.660e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.525 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.525 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.525 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1735 0.415 h = 0.003 0.006 y[1] (numeric) = 1.17097593582 1.48837676375 y[1] (closed_form) = 1.17097593582 1.48837676375 absolute error = 3e-31 relative error = 1.584e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.528 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.528 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.528 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1765 0.421 h = 0.0001 0.005 y[1] (numeric) = 1.14759753914 1.49347314985 y[1] (closed_form) = 1.14759753914 1.49347314985 absolute error = 3e-31 relative error = 1.593e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.5309 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.5309 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.5309 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1766 0.426 h = 0.0001 0.003 y[1] (numeric) = 1.13051798698 1.48917953758 y[1] (closed_form) = 1.13051798698 1.48917953758 absolute error = 3e-31 relative error = 1.605e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.5348 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.5348 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.5348 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1767 0.429 h = 0.001 0.001 y[1] (numeric) = 1.12037580308 1.48667250085 y[1] (closed_form) = 1.12037580308 1.48667250085 absolute error = 3e-31 relative error = 1.612e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.5372 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.5372 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.5372 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1777 0.43 h = 0.001 0.003 y[1] (numeric) = 1.11608499408 1.48903675909 y[1] (closed_form) = 1.11608499408 1.48903675909 absolute error = 3e-31 relative error = 1.612e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.5374 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.5374 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.5374 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1787 0.433 h = 0.0001 0.004 y[1] (numeric) = 1.10517689555 1.48939183247 y[1] (closed_form) = 1.10517689555 1.48939183247 absolute error = 3.162e-31 relative error = 1.705e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.5392 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.5392 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.5392 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1788 0.437 h = 0.003 0.006 y[1] (numeric) = 1.09200279977 1.48569496731 y[1] (closed_form) = 1.09200279977 1.48569496731 absolute error = 3.162e-31 relative error = 1.715e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.5423 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.5423 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.5423 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=211.3MB, alloc=52.3MB, time=2.51 x[1] = 0.1818 0.443 h = 0.0001 0.005 y[1] (numeric) = 1.06957896908 1.48907442898 y[1] (closed_form) = 1.06957896908 1.48907442898 absolute error = 3.162e-31 relative error = 1.725e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.5454 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.5454 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.5454 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1819 0.448 h = 0.0001 0.003 y[1] (numeric) = 1.05368943509 1.48397631852 y[1] (closed_form) = 1.05368943509 1.48397631852 absolute error = 3.162e-31 relative error = 1.738e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.5494 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.5494 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.5494 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.182 0.451 h = 0.001 0.001 y[1] (numeric) = 1.04424924062 1.4809949922 y[1] (closed_form) = 1.04424924062 1.4809949922 absolute error = 2.236e-31 relative error = 1.234e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.5518 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.5518 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.5518 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.183 0.452 h = 0.001 0.003 y[1] (numeric) = 1.04005013238 1.48297369034 y[1] (closed_form) = 1.04005013238 1.48297369034 absolute error = 2.236e-31 relative error = 1.234e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.5521 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.5521 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.5521 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.184 0.455 h = 0.0001 0.004 y[1] (numeric) = 1.02971510129 1.48265940218 y[1] (closed_form) = 1.02971510129 1.48265940218 absolute error = 2.236e-31 relative error = 1.239e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.554 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.554 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.554 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1841 0.459 h = 0.003 0.006 y[1] (numeric) = 1.01747712633 1.47838556817 y[1] (closed_form) = 1.01747712633 1.47838556817 absolute error = 1.414e-31 relative error = 7.880e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.5572 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.5572 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.5572 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1871 0.465 h = 0.0001 0.005 y[1] (numeric) = 0.996079952654 1.48027222111 y[1] (closed_form) = 0.996079952654 1.48027222111 absolute error = 1.640e-31 relative error = 9.192e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.5605 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.5605 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.5605 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1872 0.47 h = 0.0001 0.003 y[1] (numeric) = 0.981352298448 1.4745383001 y[1] (closed_form) = 0.981352298448 1.4745383001 absolute error = 1.640e-31 relative error = 9.260e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.5646 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.5646 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.5646 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1873 0.473 h = 0.001 0.001 y[1] (numeric) = 0.972597175661 1.4711815289 y[1] (closed_form) = 0.972597175661 1.4711815289 absolute error = 1.3e-31 relative error = 7.371e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.567 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.567 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.567 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1883 0.474 h = 0.001 0.003 y[1] (numeric) = 0.968515057613 1.47281404334 y[1] (closed_form) = 0.968515057613 1.47281404334 absolute error = 1.720e-31 relative error = 9.760e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.5673 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.5673 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.5673 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1893 0.477 h = 0.0001 0.004 y[1] (numeric) = 0.958762741215 1.4719337868 y[1] (closed_form) = 0.958762741215 1.4719337868 absolute error = 1.720e-31 relative error = 9.794e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.5693 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.5693 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.5693 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1894 0.481 h = 0.003 0.006 y[1] (numeric) = 0.94743256147 1.46720882829 y[1] (closed_form) = 0.94743256147 1.46720882829 absolute error = 1.720e-31 relative error = 9.851e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.5726 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.5726 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.5726 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1924 0.487 h = 0.0001 0.005 y[1] (numeric) = 0.927101491331 1.46781022847 y[1] (closed_form) = 0.927101491331 1.46781022847 absolute error = 1.720e-31 relative error = 9.910e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.576 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.576 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.576 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1925 0.492 h = 0.0001 0.003 y[1] (numeric) = 0.91349228099 1.46158764958 y[1] (closed_form) = 0.91349228099 1.46158764958 absolute error = 1.720e-31 relative error = 9.982e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.5802 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.5802 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.5802 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1926 0.495 h = 0.001 0.001 y[1] (numeric) = 0.905396492976 1.45794165264 y[1] (closed_form) = 0.905396492976 1.45794165264 absolute error = 1.720e-31 relative error = 1.002e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.5827 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.5827 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.5827 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1936 0.496 h = 0.001 0.003 y[1] (numeric) = 0.901449662863 1.45926577278 y[1] (closed_form) = 0.901449662863 1.45926577278 absolute error = 1.720e-31 relative error = 1.003e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.583 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.583 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.583 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1946 0.499 h = 0.0001 0.004 y[1] (numeric) = 0.892277609009 1.45791266174 y[1] (closed_form) = 0.892277609009 1.45791266174 absolute error = 1.4e-31 relative error = 8.191e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.585 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.585 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.585 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1947 0.503 h = 0.003 0.006 y[1] (numeric) = 0.881816665954 1.45284566975 y[1] (closed_form) = 0.881816665954 1.45284566975 absolute error = 1.720e-31 relative error = 1.012e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.5884 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.5884 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.5884 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1977 0.509 h = 0.0001 0.005 y[1] (numeric) = 0.862565127162 1.45235080955 y[1] (closed_form) = 0.862565127162 1.45235080955 absolute error = 1.720e-31 relative error = 1.019e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.592 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.592 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.592 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1978 0.514 h = 0.0001 0.003 y[1] (numeric) = 0.850020493876 1.44576616099 y[1] (closed_form) = 0.850020493876 1.44576616099 absolute error = 1.5e-31 relative error = 8.944e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.5963 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.5963 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.5963 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1979 0.517 h = 0.001 0.001 y[1] (numeric) = 0.842552299252 1.44190512649 y[1] (closed_form) = 0.842552299252 1.44190512649 absolute error = 1.5e-31 relative error = 8.982e-30 % Correct digits = 31 memory used=256.6MB, alloc=52.3MB, time=3.04 Radius of convergence (given) for eq 1 = 0.5988 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.5988 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.5988 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1989 0.518 h = 0.0001 0.004 y[1] (numeric) = 0.838753217716 1.44295638252 y[1] (closed_form) = 0.838753217716 1.44295638252 absolute error = 1.5e-31 relative error = 8.987e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.5992 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.5992 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.5992 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.199 0.522 h = 0.003 0.006 y[1] (numeric) = 0.829006981836 1.43767988212 y[1] (closed_form) = 0.829006981836 1.43767988212 absolute error = 1.4e-31 relative error = 8.436e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.6026 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.6026 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.6026 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.202 0.528 h = 0.0001 0.005 y[1] (numeric) = 0.810690229278 1.43639074181 y[1] (closed_form) = 0.810690229278 1.43639074181 absolute error = 1.4e-31 relative error = 8.488e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.6063 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.6063 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.6063 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2021 0.533 h = 0.0001 0.003 y[1] (numeric) = 0.799016375705 1.42959291121 y[1] (closed_form) = 0.799016375705 1.42959291121 absolute error = 1.4e-31 relative error = 8.548e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.6106 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.6106 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.6106 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2022 0.536 h = 0.001 0.001 y[1] (numeric) = 0.792061638035 1.42560456006 y[1] (closed_form) = 0.792061638035 1.42560456006 absolute error = 1.4e-31 relative error = 8.584e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.6132 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.6132 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.6132 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2032 0.537 h = 0.001 0.003 y[1] (numeric) = 0.788398765295 1.42644924853 y[1] (closed_form) = 0.788398765295 1.42644924853 absolute error = 1.4e-31 relative error = 8.590e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.6136 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.6136 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.6136 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2042 0.54 h = 0.0001 0.004 y[1] (numeric) = 0.780273915712 1.42443514025 y[1] (closed_form) = 0.780273915712 1.42443514025 absolute error = 1.4e-31 relative error = 8.620e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.6157 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.6157 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.6157 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2043 0.544 h = 0.003 0.006 y[1] (numeric) = 0.771308492644 1.41897808589 y[1] (closed_form) = 0.771308492644 1.41897808589 absolute error = 1.4e-31 relative error = 8.668e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.6192 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.6192 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.6192 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2073 0.55 h = 0.0001 0.005 y[1] (numeric) = 0.75404466907 1.41689295521 y[1] (closed_form) = 0.75404466907 1.41689295521 absolute error = 1.4e-31 relative error = 8.722e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.623 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.623 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.623 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2074 0.555 h = 0.0001 0.003 y[1] (numeric) = 0.743319221615 1.40991855091 y[1] (closed_form) = 0.743319221615 1.40991855091 absolute error = 1.720e-31 relative error = 1.079e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.6274 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.6274 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.6274 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2075 0.558 h = 0.001 0.001 y[1] (numeric) = 0.736923853091 1.4058239659 y[1] (closed_form) = 0.736923853091 1.4058239659 absolute error = 1.5e-31 relative error = 9.450e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.63 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.63 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.63 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2085 0.559 h = 0.001 0.003 y[1] (numeric) = 0.733419590858 1.4064547214 y[1] (closed_form) = 0.733419590858 1.4064547214 absolute error = 1.5e-31 relative error = 9.457e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.6304 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.6304 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.6304 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2095 0.562 h = 0.0001 0.004 y[1] (numeric) = 0.72582493877 1.40417767845 y[1] (closed_form) = 0.72582493877 1.40417767845 absolute error = 1.720e-31 relative error = 1.088e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.6326 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.6326 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.6326 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2096 0.566 h = 0.003 0.006 y[1] (numeric) = 0.717589563283 1.39860775764 y[1] (closed_form) = 0.717589563283 1.39860775764 absolute error = 1.803e-31 relative error = 1.147e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.6362 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.6362 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.6362 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2126 0.572 h = 0.0001 0.005 y[1] (numeric) = 0.701347221147 1.39586155357 y[1] (closed_form) = 0.701347221147 1.39586155357 absolute error = 1.4e-31 relative error = 8.962e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.6401 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.6401 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.6401 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2127 0.577 h = 0.0001 0.003 y[1] (numeric) = 0.691505522573 1.38878763148 y[1] (closed_form) = 0.691505522573 1.38878763148 absolute error = 1.4e-31 relative error = 9.024e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.6446 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.6446 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.6446 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2128 0.58 h = 0.001 0.001 y[1] (numeric) = 0.685631606127 1.38463207366 y[1] (closed_form) = 0.685631606127 1.38463207366 absolute error = 1.720e-31 relative error = 1.114e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.6472 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.6472 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.6472 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2138 0.581 h = 0.001 0.003 y[1] (numeric) = 0.682287213642 1.38507641903 y[1] (closed_form) = 0.682287213642 1.38507641903 absolute error = 1.720e-31 relative error = 1.114e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.6477 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.6477 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.6477 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2148 0.584 h = 0.0001 0.004 y[1] (numeric) = 0.675197322393 1.38259199256 y[1] (closed_form) = 0.675197322393 1.38259199256 absolute error = 1.720e-31 relative error = 1.118e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.6499 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.6499 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.6499 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2149 0.588 h = 0.003 0.006 y[1] (numeric) = 0.66764083059 1.37696530476 y[1] (closed_form) = 0.66764083059 1.37696530476 absolute error = 1.640e-31 relative error = 1.072e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.6535 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.6535 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.6535 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=301.9MB, alloc=52.3MB, time=3.58 x[1] = 0.2179 0.594 h = 0.0001 0.005 y[1] (numeric) = 0.652380421918 1.37367589727 y[1] (closed_form) = 0.652380421918 1.37367589727 absolute error = 1.640e-31 relative error = 1.079e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.6576 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.6576 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.6576 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.218 0.599 h = 0.0001 0.003 y[1] (numeric) = 0.64335823875 1.36656590429 y[1] (closed_form) = 0.64335823875 1.36656590429 absolute error = 1.640e-31 relative error = 1.086e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.6621 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.6621 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.6621 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2181 0.602 h = 0.001 0.001 y[1] (numeric) = 0.637968119291 1.36238668965 y[1] (closed_form) = 0.637968119291 1.36238668965 absolute error = 1.640e-31 relative error = 1.090e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.6647 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.6647 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.6647 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2191 0.603 h = 0.001 0.003 y[1] (numeric) = 0.634782448936 1.36266933681 y[1] (closed_form) = 0.634782448936 1.36266933681 absolute error = 1.3e-31 relative error = 8.648e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.6652 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.6652 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.6652 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2201 0.606 h = 0.0001 0.004 y[1] (numeric) = 0.628170011487 1.36002510526 y[1] (closed_form) = 0.628170011487 1.36002510526 absolute error = 1.3e-31 relative error = 8.678e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.6675 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.6675 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.6675 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2202 0.61 h = 0.003 0.006 y[1] (numeric) = 0.621242073835 1.35438765203 y[1] (closed_form) = 0.621242073835 1.35438765203 absolute error = 1.562e-31 relative error = 1.048e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.6711 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.6711 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.6711 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2232 0.616 h = 0.0001 0.005 y[1] (numeric) = 0.606918733231 1.3506572965 y[1] (closed_form) = 0.606918733231 1.3506572965 absolute error = 1.2e-31 relative error = 8.104e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.6753 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.6753 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.6753 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2233 0.621 h = 0.0001 0.003 y[1] (numeric) = 0.598653550925 1.34356290251 y[1] (closed_form) = 0.598653550925 1.34356290251 absolute error = 1.487e-31 relative error = 1.011e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.6799 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.6799 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.6799 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2234 0.624 h = 0.001 0.001 y[1] (numeric) = 0.593710582962 1.33939046915 y[1] (closed_form) = 0.593710582962 1.33939046915 absolute error = 1.1e-31 relative error = 7.508e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.6826 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.6826 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.6826 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2244 0.625 h = 0.0001 0.004 y[1] (numeric) = 0.590680670742 1.33953345143 y[1] (closed_form) = 0.590680670742 1.33953345143 absolute error = 1.1e-31 relative error = 7.514e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.6831 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.6831 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.6831 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2245 0.629 h = 0.003 0.006 y[1] (numeric) = 0.584254293765 1.33392359629 y[1] (closed_form) = 0.584254293765 1.33392359629 absolute error = 1.1e-31 relative error = 7.554e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.6867 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.6867 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.6867 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2275 0.635 h = 0.0001 0.005 y[1] (numeric) = 0.570703038077 1.32989515295 y[1] (closed_form) = 0.570703038077 1.32989515295 absolute error = 1.414e-31 relative error = 9.772e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.691 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.691 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.691 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2276 0.64 h = 0.0001 0.003 y[1] (numeric) = 0.563040531312 1.32285587386 y[1] (closed_form) = 0.563040531312 1.32285587386 absolute error = 1.414e-31 relative error = 9.837e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.6956 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.6956 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.6956 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2277 0.643 h = 0.001 0.001 y[1] (numeric) = 0.558453797915 1.31871388931 y[1] (closed_form) = 0.558453797915 1.31871388931 absolute error = 2.236e-31 relative error = 1.561e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.6983 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.6983 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.6983 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2287 0.644 h = 0.001 0.003 y[1] (numeric) = 0.555555908224 1.31875416475 y[1] (closed_form) = 0.555555908224 1.31875416475 absolute error = 1.345e-31 relative error = 9.402e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.6988 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.6988 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.6988 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2297 0.647 h = 0.0001 0.004 y[1] (numeric) = 0.549757765908 1.31592036457 y[1] (closed_form) = 0.549757765908 1.31592036457 absolute error = 1.345e-31 relative error = 9.434e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.7012 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.7012 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.7012 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2298 0.651 h = 0.003 0.006 y[1] (numeric) = 0.543870940835 1.31036262947 y[1] (closed_form) = 0.543870940835 1.31036262947 absolute error = 1.414e-31 relative error = 9.968e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.7048 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.7048 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.7048 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2328 0.657 h = 0.0001 0.005 y[1] (numeric) = 0.531165372852 1.30604659418 y[1] (closed_form) = 0.531165372852 1.30604659418 absolute error = 2.236e-31 relative error = 1.586e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.7093 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.7093 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.7093 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2329 0.662 h = 0.0001 0.003 y[1] (numeric) = 0.524150555742 1.29909272894 y[1] (closed_form) = 0.524150555742 1.29909272894 absolute error = 1.414e-31 relative error = 1.010e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.7139 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.7139 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.7139 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.233 0.665 h = 0.001 0.001 y[1] (numeric) = 0.51994687584 1.29499877316 y[1] (closed_form) = 0.51994687584 1.29499877316 absolute error = 1.414e-31 relative error = 1.013e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.7166 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.7166 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.7166 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.234 0.666 h = 0.001 0.003 y[1] (numeric) = 0.517195787771 1.29493381449 y[1] (closed_form) = 0.517195787771 1.29493381449 absolute error = 1.414e-31 relative error = 1.014e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.7172 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.7172 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.7172 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=347.1MB, alloc=52.3MB, time=4.11 x[1] = 0.235 0.669 h = 0.0001 0.004 y[1] (numeric) = 0.511794447899 1.29203956847 y[1] (closed_form) = 0.511794447899 1.29203956847 absolute error = 1.487e-31 relative error = 1.070e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.7196 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.7196 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.7196 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2351 0.673 h = 0.003 0.006 y[1] (numeric) = 0.506403151468 1.28655840294 y[1] (closed_form) = 0.506403151468 1.28655840294 absolute error = 1.414e-31 relative error = 1.023e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.7233 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.7233 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.7233 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2381 0.679 h = 0.0001 0.005 y[1] (numeric) = 0.494493720845 1.28202075775 y[1] (closed_form) = 0.494493720845 1.28202075775 absolute error = 1.0e-31 relative error = 7.278e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.7278 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.7278 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.7278 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2382 0.684 h = 0.0001 0.003 y[1] (numeric) = 0.488072936665 1.27517910114 y[1] (closed_form) = 0.488072936665 1.27517910114 absolute error = 1.414e-31 relative error = 1.036e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.7324 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.7324 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.7324 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2383 0.687 h = 0.001 0.001 y[1] (numeric) = 0.484220830677 1.27114906639 y[1] (closed_form) = 0.484220830677 1.27114906639 absolute error = 1.345e-31 relative error = 9.891e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.7352 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.7352 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.7352 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2393 0.688 h = 0.001 0.003 y[1] (numeric) = 0.481610772445 1.27099429015 y[1] (closed_form) = 0.481610772445 1.27099429015 absolute error = 1.345e-31 relative error = 9.898e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.7357 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.7357 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.7357 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2403 0.691 h = 0.0001 0.004 y[1] (numeric) = 0.47657926707 1.2680642031 y[1] (closed_form) = 0.47657926707 1.2680642031 absolute error = 2.236e-31 relative error = 1.651e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.7382 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.7382 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.7382 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2404 0.695 h = 0.003 0.006 y[1] (numeric) = 0.4716422722 1.26267865631 y[1] (closed_form) = 0.4716422722 1.26267865631 absolute error = 2.236e-31 relative error = 1.659e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.7419 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.7419 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.7419 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2434 0.701 h = 0.0001 0.005 y[1] (numeric) = 0.460480044884 1.25797549284 y[1] (closed_form) = 0.460480044884 1.25797549284 absolute error = 2.193e-31 relative error = 1.637e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.7465 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.7465 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.7465 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2435 0.706 h = 0.0001 0.003 y[1] (numeric) = 0.454603256749 1.2512666638 y[1] (closed_form) = 0.454603256749 1.2512666638 absolute error = 2.193e-31 relative error = 1.647e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.7512 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.7512 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.7512 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2436 0.709 h = 0.001 0.001 y[1] (numeric) = 0.451073354027 1.24731282373 y[1] (closed_form) = 0.451073354027 1.24731282373 absolute error = 2.193e-31 relative error = 1.654e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.7539 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.7539 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.7539 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2446 0.71 h = 0.001 0.003 y[1] (numeric) = 0.448598136094 1.2470817409 y[1] (closed_form) = 0.448598136094 1.2470817409 absolute error = 3.132e-31 relative error = 2.363e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.7545 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.7545 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.7545 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2456 0.713 h = 0.0001 0.004 y[1] (numeric) = 0.443910603942 1.24413624454 y[1] (closed_form) = 0.443910603942 1.24413624454 absolute error = 2.154e-31 relative error = 1.631e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.757 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.757 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.757 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2457 0.717 h = 0.003 0.006 y[1] (numeric) = 0.439389561939 1.2388608569 y[1] (closed_form) = 0.439389561939 1.2388608569 absolute error = 3.105e-31 relative error = 2.362e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.7608 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.7608 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.7608 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2487 0.723 h = 0.0001 0.005 y[1] (numeric) = 0.428926920257 1.23403964722 y[1] (closed_form) = 0.428926920257 1.23403964722 absolute error = 3.081e-31 relative error = 2.358e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.7654 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.7654 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.7654 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2488 0.728 h = 0.0001 0.003 y[1] (numeric) = 0.423547743812 1.22747913016 y[1] (closed_form) = 0.423547743812 1.22747913016 absolute error = 2.119e-31 relative error = 1.632e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.7701 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.7701 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.7701 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2489 0.731 h = 0.001 0.001 y[1] (numeric) = 0.42031280211 1.22361074609 y[1] (closed_form) = 0.42031280211 1.22361074609 absolute error = 2.119e-31 relative error = 1.638e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.7729 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.7729 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.7729 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2499 0.732 h = 0.0001 0.004 y[1] (numeric) = 0.417966014266 1.22331516371 y[1] (closed_form) = 0.417966014266 1.22331516371 absolute error = 2.119e-31 relative error = 1.639e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.7735 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.7735 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.7735 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.25 0.736 h = 0.003 0.006 y[1] (numeric) = 0.413773014055 1.21814775338 y[1] (closed_form) = 0.413773014055 1.21814775338 absolute error = 2.088e-31 relative error = 1.623e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.7773 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.7773 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.7773 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.253 0.742 h = 0.0001 0.005 y[1] (numeric) = 0.403876560934 1.21326481058 y[1] (closed_form) = 0.403876560934 1.21326481058 absolute error = 2.119e-31 relative error = 1.657e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.782 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.782 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.782 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2531 0.747 h = 0.0001 0.003 y[1] (numeric) = 0.398889371789 1.20684633749 y[1] (closed_form) = 0.398889371789 1.20684633749 absolute error = 2.088e-31 relative error = 1.643e-29 % Correct digits = 31 memory used=392.3MB, alloc=52.3MB, time=4.64 Radius of convergence (given) for eq 1 = 0.7867 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.7867 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.7867 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2532 0.75 h = 0.001 0.001 y[1] (numeric) = 0.395886984468 1.20306012298 y[1] (closed_form) = 0.395886984468 1.20306012298 absolute error = 1.166e-31 relative error = 9.208e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.7896 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.7896 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.7896 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2542 0.751 h = 0.001 0.003 y[1] (numeric) = 0.393646160211 1.20271874011 y[1] (closed_form) = 0.393646160211 1.20271874011 absolute error = 2.088e-31 relative error = 1.650e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.7902 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.7902 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.7902 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2552 0.754 h = 0.0001 0.004 y[1] (numeric) = 0.389534109567 1.19979051721 y[1] (closed_form) = 0.389534109567 1.19979051721 absolute error = 2.088e-31 relative error = 1.655e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.7927 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.7927 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.7927 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2553 0.758 h = 0.0001 0.004 y[1] (numeric) = 0.385693200147 1.1947504933 y[1] (closed_form) = 0.385693200147 1.1947504933 absolute error = 2.062e-31 relative error = 1.642e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.7965 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.7965 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.7965 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2554 0.762 h = 0.003 0.006 y[1] (numeric) = 0.381905152747 1.18974540635 y[1] (closed_form) = 0.381905152747 1.18974540635 absolute error = 2.062e-31 relative error = 1.650e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.8003 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.8003 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.8003 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2584 0.768 h = 0.0001 0.005 y[1] (numeric) = 0.372727595863 1.1848294438 y[1] (closed_form) = 0.372727595863 1.1848294438 absolute error = 1.118e-31 relative error = 9.001e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.8051 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.8051 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.8051 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2585 0.773 h = 0.0001 0.003 y[1] (numeric) = 0.368223739758 1.17862091442 y[1] (closed_form) = 0.368223739758 1.17862091442 absolute error = 1.118e-31 relative error = 9.054e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.8098 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.8098 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.8098 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2586 0.776 h = 0.001 0.001 y[1] (numeric) = 0.365508387645 1.17495654024 y[1] (closed_form) = 0.365508387645 1.17495654024 absolute error = 1.118e-31 relative error = 9.086e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.8127 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.8127 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.8127 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2596 0.777 h = 0.001 0.003 y[1] (numeric) = 0.363404853142 1.17456560271 y[1] (closed_form) = 0.363404853142 1.17456560271 absolute error = 1.118e-31 relative error = 9.093e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.8133 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.8133 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.8133 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2606 0.78 h = 0.0001 0.004 y[1] (numeric) = 0.359614774165 1.17167720906 y[1] (closed_form) = 0.359614774165 1.17167720906 absolute error = 1.118e-31 relative error = 9.122e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.8159 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.8159 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.8159 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2607 0.784 h = 0.003 0.006 y[1] (numeric) = 0.356143328804 1.1668047212 y[1] (closed_form) = 0.356143328804 1.1668047212 absolute error = 1.077e-31 relative error = 8.829e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.8197 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.8197 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.8197 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2637 0.79 h = 0.0001 0.005 y[1] (numeric) = 0.347531845161 1.16187117087 y[1] (closed_form) = 0.347531845161 1.16187117087 absolute error = 1.077e-31 relative error = 8.881e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.8246 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.8246 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.8246 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2638 0.795 h = 0.0001 0.003 y[1] (numeric) = 0.343406074164 1.15583331482 y[1] (closed_form) = 0.343406074164 1.15583331482 absolute error = 1.118e-31 relative error = 9.272e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.8293 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.8293 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.8293 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2639 0.798 h = 0.001 0.001 y[1] (numeric) = 0.340915386837 1.1522680165 y[1] (closed_form) = 0.340915386837 1.1522680165 absolute error = 4e-32 relative error = 3.329e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.8322 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.8322 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.8322 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2649 0.799 h = 0.001 0.003 y[1] (numeric) = 0.338920495119 1.15183953892 y[1] (closed_form) = 0.338920495119 1.15183953892 absolute error = 1.077e-31 relative error = 8.970e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.8329 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.8329 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.8329 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2659 0.802 h = 0.0001 0.004 y[1] (numeric) = 0.335383547332 1.14898592465 y[1] (closed_form) = 0.335383547332 1.14898592465 absolute error = 1.077e-31 relative error = 8.998e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.8355 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.8355 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.8355 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.266 0.806 h = 0.003 0.006 y[1] (numeric) = 0.332201387864 1.14424922486 y[1] (closed_form) = 0.332201387864 1.14424922486 absolute error = 1.077e-31 relative error = 9.039e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.8393 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.8393 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.8393 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.269 0.812 h = 0.0001 0.005 y[1] (numeric) = 0.324117271522 1.13932131808 y[1] (closed_form) = 0.324117271522 1.13932131808 absolute error = 1.077e-31 relative error = 9.093e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.8442 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.8442 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.8442 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2691 0.817 h = 0.0001 0.003 y[1] (numeric) = 0.320336819529 1.13345682787 y[1] (closed_form) = 0.320336819529 1.13345682787 absolute error = 1.077e-31 relative error = 9.144e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.849 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.849 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.849 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2692 0.82 h = 0.001 0.001 y[1] (numeric) = 0.318051500751 1.12999233369 y[1] (closed_form) = 0.318051500751 1.12999233369 absolute error = 1.077e-31 relative error = 9.175e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.8519 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.8519 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.8519 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=437.3MB, alloc=52.3MB, time=5.16 x[1] = 0.2702 0.821 h = 0.001 0.003 y[1] (numeric) = 0.316159184856 1.12953303206 y[1] (closed_form) = 0.316159184856 1.12953303206 absolute error = 1.118e-31 relative error = 9.532e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.8526 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.8526 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.8526 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2712 0.824 h = 0.0001 0.004 y[1] (numeric) = 0.312856612782 1.12672136771 y[1] (closed_form) = 0.312856612782 1.12672136771 absolute error = 1.077e-31 relative error = 9.211e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.8552 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.8552 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.8552 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2713 0.828 h = 0.003 0.006 y[1] (numeric) = 0.309938765885 1.1221219858 y[1] (closed_form) = 0.309938765885 1.1221219858 absolute error = 2.062e-31 relative error = 1.771e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.859 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.859 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.859 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2743 0.834 h = 0.0001 0.005 y[1] (numeric) = 0.302345694887 1.11721891686 y[1] (closed_form) = 0.302345694887 1.11721891686 absolute error = 2.062e-31 relative error = 1.781e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.864 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.864 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.864 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2744 0.839 h = 0.0001 0.003 y[1] (numeric) = 0.298880644293 1.11152863724 y[1] (closed_form) = 0.298880644293 1.11152863724 absolute error = 2.040e-31 relative error = 1.772e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.8688 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.8688 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.8688 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2745 0.842 h = 0.001 0.001 y[1] (numeric) = 0.296783062439 1.10816558126 y[1] (closed_form) = 0.296783062439 1.10816558126 absolute error = 2.062e-31 relative error = 1.797e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.8717 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.8717 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.8717 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2755 0.843 h = 0.001 0.003 y[1] (numeric) = 0.294987479457 1.1076812703 y[1] (closed_form) = 0.294987479457 1.1076812703 absolute error = 2.062e-31 relative error = 1.798e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.8724 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.8724 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.8724 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2765 0.846 h = 0.0001 0.004 y[1] (numeric) = 0.291901877869 1.10491717529 y[1] (closed_form) = 0.291901877869 1.10491717529 absolute error = 2.062e-31 relative error = 1.804e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.875 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.875 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.875 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2766 0.85 h = 0.003 0.006 y[1] (numeric) = 0.289225548233 1.10045530885 y[1] (closed_form) = 0.289225548233 1.10045530885 absolute error = 2.062e-31 relative error = 1.812e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.8789 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.8789 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.8789 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2796 0.856 h = 0.0001 0.005 y[1] (numeric) = 0.282089555601 1.09559282938 y[1] (closed_form) = 0.282089555601 1.09559282938 absolute error = 2.062e-31 relative error = 1.822e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.8839 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.8839 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.8839 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2797 0.861 h = 0.0001 0.003 y[1] (numeric) = 0.278912626651 1.09007613049 y[1] (closed_form) = 0.278912626651 1.09007613049 absolute error = 2.062e-31 relative error = 1.832e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.8887 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.8887 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.8887 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2798 0.864 h = 0.001 0.001 y[1] (numeric) = 0.276986692714 1.08681427114 y[1] (closed_form) = 0.276986692714 1.08681427114 absolute error = 1.118e-31 relative error = 9.969e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.8916 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.8916 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.8916 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2808 0.865 h = 0.0001 0.004 y[1] (numeric) = 0.275282250961 1.08630997756 y[1] (closed_form) = 0.275282250961 1.08630997756 absolute error = 2.062e-31 relative error = 1.840e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.8923 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.8923 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.8923 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2809 0.869 h = 0.003 0.006 y[1] (numeric) = 0.27279547669 1.08196836715 y[1] (closed_form) = 0.27279547669 1.08196836715 absolute error = 1.118e-31 relative error = 1.002e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.8962 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.8962 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.8962 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2839 0.875 h = 0.0001 0.005 y[1] (numeric) = 0.266026787506 1.07715612711 y[1] (closed_form) = 0.266026787506 1.07715612711 absolute error = 2.040e-31 relative error = 1.838e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.9013 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.9013 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.9013 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.284 0.88 h = 0.0001 0.003 y[1] (numeric) = 0.263075843791 1.07179047471 y[1] (closed_form) = 0.263075843791 1.07179047471 absolute error = 1.077e-31 relative error = 9.759e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.9061 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.9061 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.9061 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2841 0.883 h = 0.001 0.001 y[1] (numeric) = 0.261284675148 1.0686168048 y[1] (closed_form) = 0.261284675148 1.0686168048 absolute error = 1.077e-31 relative error = 9.790e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.909 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.909 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.909 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2851 0.884 h = 0.001 0.003 y[1] (numeric) = 0.259654580147 1.06809980851 y[1] (closed_form) = 0.259654580147 1.06809980851 absolute error = 2.040e-31 relative error = 1.856e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.9097 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.9097 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.9097 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2861 0.887 h = 0.0001 0.004 y[1] (numeric) = 0.256930082382 1.06543704101 y[1] (closed_form) = 0.256930082382 1.06543704101 absolute error = 1.077e-31 relative error = 9.827e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.9124 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.9124 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.9124 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2862 0.891 h = 0.003 0.006 y[1] (numeric) = 0.254647665298 1.06123044799 y[1] (closed_form) = 0.254647665298 1.06123044799 absolute error = 2.040e-31 relative error = 1.869e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.9163 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.9163 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.9163 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2892 0.897 h = 0.0001 0.005 y[1] (numeric) = 0.248278761552 1.05648030888 y[1] (closed_form) = 0.248278761552 1.05648030888 absolute error = 1.077e-31 relative error = 9.924e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.9214 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.9214 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.9214 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=482.4MB, alloc=52.3MB, time=5.68 x[1] = 0.2893 0.902 h = 0.0001 0.003 y[1] (numeric) = 0.245571527754 1.05128390144 y[1] (closed_form) = 0.245571527754 1.05128390144 absolute error = 1.077e-31 relative error = 9.976e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.9263 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.9263 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.9263 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2894 0.905 h = 0.001 0.001 y[1] (numeric) = 0.243925784665 1.04820909365 y[1] (closed_form) = 0.243925784665 1.04820909365 absolute error = 1.077e-31 relative error = 1.001e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.9292 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.9292 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.9292 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2904 0.906 h = 0.001 0.003 y[1] (numeric) = 0.242377101396 1.0476796463 y[1] (closed_form) = 0.242377101396 1.0476796463 absolute error = 1.077e-31 relative error = 1.002e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.9299 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.9299 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.9299 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2914 0.909 h = 0.0001 0.004 y[1] (numeric) = 0.239826636843 1.0450738873 y[1] (closed_form) = 0.239826636843 1.0450738873 absolute error = 1.077e-31 relative error = 1.004e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.9326 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.9326 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.9326 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2915 0.913 h = 0.003 0.006 y[1] (numeric) = 0.237731121541 1.04100006699 y[1] (closed_form) = 0.237731121541 1.04100006699 absolute error = 1.077e-31 relative error = 1.009e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.9365 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.9365 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.9365 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2945 0.919 h = 0.0001 0.005 y[1] (numeric) = 0.231734356874 1.03632055458 y[1] (closed_form) = 0.231734356874 1.03632055458 absolute error = 1.077e-31 relative error = 1.014e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.9417 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.9417 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.9417 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2946 0.924 h = 0.0001 0.003 y[1] (numeric) = 0.229249985569 1.03129010061 y[1] (closed_form) = 0.229249985569 1.03129010061 absolute error = 1.044e-31 relative error = 9.882e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.9466 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.9466 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.9466 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2947 0.927 h = 0.001 0.001 y[1] (numeric) = 0.227737346048 1.02831232239 y[1] (closed_form) = 0.227737346048 1.02831232239 absolute error = 1.044e-31 relative error = 9.913e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.9495 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.9495 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.9495 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2957 0.928 h = 0.001 0.003 y[1] (numeric) = 0.226265268905 1.02777371289 y[1] (closed_form) = 0.226265268905 1.02777371289 absolute error = 4e-32 relative error = 3.801e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.9502 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.9502 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.9502 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2967 0.931 h = 0.0001 0.004 y[1] (numeric) = 0.223876022062 1.02522664309 y[1] (closed_form) = 0.223876022062 1.02522664309 absolute error = 1.077e-31 relative error = 1.026e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.9529 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.9529 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.9529 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2968 0.935 h = 0.003 0.006 y[1] (numeric) = 0.221951520982 1.02128283523 y[1] (closed_form) = 0.221951520982 1.02128283523 absolute error = 1.044e-31 relative error = 9.990e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.9568 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.9568 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.9568 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2998 0.941 h = 0.0001 0.005 y[1] (numeric) = 0.2163012393 1.01668065026 y[1] (closed_form) = 0.2163012393 1.01668065026 absolute error = 1.077e-31 relative error = 1.036e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.9621 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.9621 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.9621 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2999 0.946 h = 0.0001 0.003 y[1] (numeric) = 0.214020764464 1.01181230976 y[1] (closed_form) = 0.214020764464 1.01181230976 absolute error = 1.044e-31 relative error = 1.010e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.9669 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.9669 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.9669 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3 0.949 h = 0.001 0.001 y[1] (numeric) = 0.212630009962 1.00892939727 y[1] (closed_form) = 0.212630009962 1.00892939727 absolute error = 2.022e-31 relative error = 1.961e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.9698 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.9698 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.9698 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.301 0.95 h = 0.001 0.003 y[1] (numeric) = 0.211230006125 1.00838445135 y[1] (closed_form) = 0.211230006125 1.00838445135 absolute error = 2.022e-31 relative error = 1.963e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.9706 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.9706 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.9706 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.302 0.953 h = 0.0001 0.004 y[1] (numeric) = 0.208990165852 1.0058971114 y[1] (closed_form) = 0.208990165852 1.0058971114 absolute error = 1.077e-31 relative error = 1.048e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.9734 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.9734 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.9734 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3021 0.957 h = 0.003 0.006 y[1] (numeric) = 0.207222221099 1.00208016974 y[1] (closed_form) = 0.207222221099 1.00208016974 absolute error = 1.077e-31 relative error = 1.053e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.9772 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.9772 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.9772 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3051 0.963 h = 0.0001 0.005 y[1] (numeric) = 0.201894637704 0.997560472598 y[1] (closed_form) = 0.201894637704 0.997560472598 absolute error = 1.360e-31 relative error = 1.336e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.9825 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.9825 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.9825 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3052 0.968 h = 0.0001 0.003 y[1] (numeric) = 0.199800806391 0.992850003011 y[1] (closed_form) = 0.199800806391 0.992850003011 absolute error = 1.360e-31 relative error = 1.343e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.9874 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.9874 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.9874 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3053 0.971 h = 0.001 0.001 y[1] (numeric) = 0.198521723839 0.990059547239 y[1] (closed_form) = 0.198521723839 0.990059547239 absolute error = 1.265e-31 relative error = 1.253e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.9903 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.9903 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.9903 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=527.6MB, alloc=52.3MB, time=6.21 x[1] = 0.3063 0.972 h = 0.0001 0.004 y[1] (numeric) = 0.197189526999 0.989510687881 y[1] (closed_form) = 0.197189526999 0.989510687881 absolute error = 1.393e-31 relative error = 1.380e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.9911 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.9911 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.9911 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3064 0.976 h = 0.003 0.006 y[1] (numeric) = 0.195544304845 0.9858018674 y[1] (closed_form) = 0.195544304845 0.9858018674 absolute error = 1.393e-31 relative error = 1.386e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 0.995 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 0.995 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 0.995 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3094 0.982 h = 0.0001 0.005 y[1] (numeric) = 0.190475741245 0.981359800121 y[1] (closed_form) = 0.190475741245 0.981359800121 absolute error = 1.300e-31 relative error = 1.300e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3095 0.987 h = 0.0001 0.003 y[1] (numeric) = 0.188528137082 0.976783576379 y[1] (closed_form) = 0.188528137082 0.976783576379 absolute error = 1.432e-31 relative error = 1.439e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.005 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.005 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.005 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3096 0.99 h = 0.001 0.001 y[1] (numeric) = 0.187336641268 0.97407182172 y[1] (closed_form) = 0.187336641268 0.97407182172 absolute error = 1.393e-31 relative error = 1.404e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.008 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.008 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.008 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3106 0.991 h = 0.001 0.003 y[1] (numeric) = 0.186059604931 0.973522008906 y[1] (closed_form) = 0.186059604931 0.973522008906 absolute error = 1.432e-31 relative error = 1.445e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.009 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.009 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.009 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3116 0.994 h = 0.0001 0.004 y[1] (numeric) = 0.184068759022 0.971148335815 y[1] (closed_form) = 0.184068759022 0.971148335815 absolute error = 1.342e-31 relative error = 1.357e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.012 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.012 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.012 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3117 0.998 h = 0.003 0.006 y[1] (numeric) = 0.182556606679 0.967559710383 y[1] (closed_form) = 0.182556606679 0.967559710383 absolute error = 1.342e-31 relative error = 1.363e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.016 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.016 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.016 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3147 1.004 h = 0.0001 0.005 y[1] (numeric) = 0.177771025527 0.963206204153 y[1] (closed_form) = 0.177771025527 0.963206204153 absolute error = 1.253e-31 relative error = 1.279e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.021 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.021 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.021 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3148 1.009 h = 0.0001 0.003 y[1] (numeric) = 0.175982053023 0.958779111774 y[1] (closed_form) = 0.175982053023 0.958779111774 absolute error = 1.300e-31 relative error = 1.334e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.026 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.026 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.026 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3149 1.012 h = 0.001 0.001 y[1] (numeric) = 0.174885628248 0.956154812462 y[1] (closed_form) = 0.174885628248 0.956154812462 absolute error = 1.300e-31 relative error = 1.337e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.029 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.029 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.029 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3159 1.013 h = 0.001 0.003 y[1] (numeric) = 0.173669118407 0.955604654789 y[1] (closed_form) = 0.173669118407 0.955604654789 absolute error = 1.342e-31 relative error = 1.381e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.03 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.03 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.03 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3169 1.016 h = 0.0001 0.004 y[1] (numeric) = 0.171798798442 0.953290984257 y[1] (closed_form) = 0.171798798442 0.953290984257 absolute error = 1.300e-31 relative error = 1.342e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.032 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.032 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.032 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.317 1.02 h = 0.003 0.006 y[1] (numeric) = 0.170408673522 0.949818836025 y[1] (closed_form) = 0.170408673522 0.949818836025 absolute error = 1.300e-31 relative error = 1.347e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.036 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.036 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.036 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.32 1.026 h = 0.0001 0.005 y[1] (numeric) = 0.165886997777 0.94555588733 y[1] (closed_form) = 0.165886997777 0.94555588733 absolute error = 1.300e-31 relative error = 1.354e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.042 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.042 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.042 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3201 1.031 h = 0.0001 0.003 y[1] (numeric) = 0.164243487876 0.941273129516 y[1] (closed_form) = 0.164243487876 0.941273129516 absolute error = 1.300e-31 relative error = 1.361e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.047 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.047 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.047 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3202 1.034 h = 0.001 0.001 y[1] (numeric) = 0.163234321579 0.938733528994 y[1] (closed_form) = 0.163234321579 0.938733528994 absolute error = 1.300e-31 relative error = 1.364e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.05 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.05 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.05 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3212 1.035 h = 0.001 0.003 y[1] (numeric) = 0.162074783481 0.938184568805 y[1] (closed_form) = 0.162074783481 0.938184568805 absolute error = 1.300e-31 relative error = 1.365e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.05 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.05 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.05 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3222 1.038 h = 0.0001 0.004 y[1] (numeric) = 0.160316400014 0.935930389285 y[1] (closed_form) = 0.160316400014 0.935930389285 absolute error = 1.265e-31 relative error = 1.332e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.053 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.053 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.053 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3223 1.042 h = 0.003 0.006 y[1] (numeric) = 0.159038246944 0.932570924681 y[1] (closed_form) = 0.159038246944 0.932570924681 absolute error = 1.208e-31 relative error = 1.277e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.057 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.057 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.057 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3253 1.048 h = 0.0001 0.005 y[1] (numeric) = 0.154762820485 0.928399747387 y[1] (closed_form) = 0.154762820485 0.928399747387 absolute error = 1.170e-31 relative error = 1.244e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.062 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.062 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.062 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=572.7MB, alloc=52.3MB, time=6.74 x[1] = 0.3254 1.053 h = 0.0001 0.003 y[1] (numeric) = 0.153252782407 0.924256471217 y[1] (closed_form) = 0.153252782407 0.924256471217 absolute error = 1.170e-31 relative error = 1.249e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.067 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.067 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.067 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3255 1.056 h = 0.001 0.001 y[1] (numeric) = 0.152323755632 0.921798773335 y[1] (closed_form) = 0.152323755632 0.921798773335 absolute error = 1.170e-31 relative error = 1.253e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.07 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.07 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.07 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3265 1.057 h = 0.001 0.003 y[1] (numeric) = 0.151217859396 0.9212523192 y[1] (closed_form) = 0.151217859396 0.9212523192 absolute error = 1.170e-31 relative error = 1.254e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.071 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.071 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.071 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3275 1.06 h = 0.0001 0.004 y[1] (numeric) = 0.14956350217 0.919056882902 y[1] (closed_form) = 0.14956350217 0.919056882902 absolute error = 1.170e-31 relative error = 1.257e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.074 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.074 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.074 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3276 1.064 h = 0.003 0.006 y[1] (numeric) = 0.148388160291 0.915806279291 y[1] (closed_form) = 0.148388160291 0.915806279291 absolute error = 1.170e-31 relative error = 1.262e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.078 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.078 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.078 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3306 1.07 h = 0.0001 0.005 y[1] (numeric) = 0.144342642644 0.911727435828 y[1] (closed_form) = 0.144342642644 0.911727435828 absolute error = 1.044e-31 relative error = 1.131e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.083 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.083 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.083 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3307 1.075 h = 0.0001 0.003 y[1] (numeric) = 0.142955153567 0.907718783722 y[1] (closed_form) = 0.142955153567 0.907718783722 absolute error = 1.044e-31 relative error = 1.136e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.088 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.088 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.088 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3308 1.078 h = 0.001 0.001 y[1] (numeric) = 0.142099776483 0.905340183506 y[1] (closed_form) = 0.142099776483 0.905340183506 absolute error = 1.044e-31 relative error = 1.139e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.091 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.091 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.091 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3318 1.079 h = 0.0001 0.004 y[1] (numeric) = 0.141044404804 0.90479734116 y[1] (closed_form) = 0.141044404804 0.90479734116 absolute error = 1.044e-31 relative error = 1.140e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.092 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.092 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.092 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3319 1.083 h = 0.003 0.006 y[1] (numeric) = 0.139949610314 0.901638476922 y[1] (closed_form) = 0.139949610314 0.901638476922 absolute error = 1.020e-31 relative error = 1.118e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.096 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.096 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.096 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3349 1.089 h = 0.0001 0.005 y[1] (numeric) = 0.136088737638 0.897641643174 y[1] (closed_form) = 0.136088737638 0.897641643174 absolute error = 9.220e-32 relative error = 1.015e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.101 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.101 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.101 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.335 1.094 h = 0.0001 0.003 y[1] (numeric) = 0.134797203734 0.893746308395 y[1] (closed_form) = 0.134797203734 0.893746308395 absolute error = 9.487e-32 relative error = 1.050e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.106 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.106 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.106 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3351 1.097 h = 0.001 0.001 y[1] (numeric) = 0.133999564977 0.891434340689 y[1] (closed_form) = 0.133999564977 0.891434340689 absolute error = 9.487e-32 relative error = 1.052e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.109 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.109 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.109 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3361 1.098 h = 0.001 0.003 y[1] (numeric) = 0.132985282424 0.89089591276 y[1] (closed_form) = 0.132985282424 0.89089591276 absolute error = 9.487e-32 relative error = 1.053e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.11 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.11 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.11 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3371 1.101 h = 0.0001 0.004 y[1] (numeric) = 0.131504868332 0.888808226111 y[1] (closed_form) = 0.131504868332 0.888808226111 absolute error = 9.487e-32 relative error = 1.056e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.113 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.113 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.113 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3372 1.105 h = 0.003 0.006 y[1] (numeric) = 0.130497985121 0.885751066084 y[1] (closed_form) = 0.130497985121 0.885751066084 absolute error = 9.487e-32 relative error = 1.060e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.117 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.117 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.117 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3402 1.111 h = 0.0001 0.005 y[1] (numeric) = 0.126839788108 0.881846086283 y[1] (closed_form) = 0.126839788108 0.881846086283 absolute error = 8.544e-32 relative error = 9.590e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.122 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.122 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.122 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3403 1.116 h = 0.0001 0.003 y[1] (numeric) = 0.125653040765 0.8780763525 y[1] (closed_form) = 0.125653040765 0.8780763525 absolute error = 8.246e-32 relative error = 9.297e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.127 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.127 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.127 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3404 1.119 h = 0.001 0.001 y[1] (numeric) = 0.124918485992 0.875838257047 y[1] (closed_form) = 0.124918485992 0.875838257047 absolute error = 8.246e-32 relative error = 9.321e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.13 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.13 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.13 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3414 1.12 h = 0.001 0.003 y[1] (numeric) = 0.123949442507 0.875305016445 y[1] (closed_form) = 0.123949442507 0.875305016445 absolute error = 8.246e-32 relative error = 9.328e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.131 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.131 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.131 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3424 1.123 h = 0.0001 0.004 y[1] (numeric) = 0.122553712042 0.873272960803 y[1] (closed_form) = 0.122553712042 0.873272960803 absolute error = 7.280e-32 relative error = 8.256e-30 % Correct digits = 31 memory used=618.1MB, alloc=52.3MB, time=7.26 Radius of convergence (given) for eq 1 = 1.134 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.134 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.134 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3425 1.127 h = 0.003 0.006 y[1] (numeric) = 0.121627703007 0.87031378596 y[1] (closed_form) = 0.121627703007 0.87031378596 absolute error = 7.280e-32 relative error = 8.284e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.138 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.138 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.138 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3455 1.133 h = 0.0001 0.005 y[1] (numeric) = 0.11815908151 0.866499931074 y[1] (closed_form) = 0.11815908151 0.866499931074 absolute error = 7.616e-32 relative error = 8.709e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.143 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.143 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.143 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3456 1.138 h = 0.0001 0.003 y[1] (numeric) = 0.11706873002 0.862851131885 y[1] (closed_form) = 0.11706873002 0.862851131885 absolute error = 7.616e-32 relative error = 8.746e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.148 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.148 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.148 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3457 1.141 h = 0.001 0.001 y[1] (numeric) = 0.116392263169 0.860684201396 y[1] (closed_form) = 0.116392263169 0.860684201396 absolute error = 7.616e-32 relative error = 8.769e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.151 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.151 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.151 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3467 1.142 h = 0.001 0.003 y[1] (numeric) = 0.115465883865 0.860156812613 y[1] (closed_form) = 0.115465883865 0.860156812613 absolute error = 8.544e-32 relative error = 9.845e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.152 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.152 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.152 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3477 1.145 h = 0.0001 0.004 y[1] (numeric) = 0.114149066044 0.858179124228 y[1] (closed_form) = 0.114149066044 0.858179124228 absolute error = 8.246e-32 relative error = 9.525e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.155 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.155 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.155 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3478 1.149 h = 0.003 0.006 y[1] (numeric) = 0.113297506508 0.855314290261 y[1] (closed_form) = 0.113297506508 0.855314290261 absolute error = 8.544e-32 relative error = 9.903e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.159 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.159 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.159 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3508 1.155 h = 0.0001 0.005 y[1] (numeric) = 0.110006325806 0.85159052484 y[1] (closed_form) = 0.110006325806 0.85159052484 absolute error = 8.544e-32 relative error = 9.950e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.165 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.165 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.165 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3509 1.16 h = 0.0001 0.003 y[1] (numeric) = 0.109004709435 0.848058101572 y[1] (closed_form) = 0.109004709435 0.848058101572 absolute error = 8.544e-32 relative error = 9.993e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.17 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.17 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.17 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.351 1.163 h = 0.001 0.001 y[1] (numeric) = 0.108381765677 0.845959687802 y[1] (closed_form) = 0.108381765677 0.845959687802 absolute error = 8.944e-32 relative error = 1.049e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.173 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.173 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.173 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.352 1.164 h = 0.001 0.003 y[1] (numeric) = 0.107495642069 0.845438698431 y[1] (closed_form) = 0.107495642069 0.845438698431 absolute error = 8.944e-32 relative error = 1.049e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.173 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.173 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.173 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.353 1.167 h = 0.0001 0.004 y[1] (numeric) = 0.106252412363 0.843514049171 y[1] (closed_form) = 0.106252412363 0.843514049171 absolute error = 9.849e-32 relative error = 1.158e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.176 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.176 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.176 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3531 1.171 h = 0.003 0.006 y[1] (numeric) = 0.105469432995 0.84074000025 y[1] (closed_form) = 0.105469432995 0.84074000025 absolute error = 8.944e-32 relative error = 1.056e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.18 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.18 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.18 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3561 1.177 h = 0.0001 0.005 y[1] (numeric) = 0.102344448156 0.837105041555 y[1] (closed_form) = 0.102344448156 0.837105041555 absolute error = 8.944e-32 relative error = 1.061e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.186 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.186 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.186 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3562 1.182 h = 0.0001 0.003 y[1] (numeric) = 0.10142456801 0.833684557631 y[1] (closed_form) = 0.10142456801 0.833684557631 absolute error = 8.944e-32 relative error = 1.065e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.191 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.191 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.191 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3563 1.185 h = 0.001 0.001 y[1] (numeric) = 0.100850973779 0.831652080226 y[1] (closed_form) = 0.100850973779 0.831652080226 absolute error = 8.944e-32 relative error = 1.068e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.194 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.194 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.194 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3573 1.186 h = 0.0001 0.004 y[1] (numeric) = 0.10000285292 0.831137936668 y[1] (closed_form) = 0.10000285292 0.831137936668 absolute error = 8.944e-32 relative error = 1.068e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.195 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.195 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.195 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3574 1.19 h = 0.003 0.006 y[1] (numeric) = 0.0992735653376 0.828439991246 y[1] (closed_form) = 0.0992735653376 0.828439991246 absolute error = 8.989e-32 relative error = 1.077e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.199 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.199 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.199 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3604 1.196 h = 0.0001 0.005 y[1] (numeric) = 0.0962822259921 0.82488210807 y[1] (closed_form) = 0.0962822259921 0.82488210807 absolute error = 8.062e-32 relative error = 9.708e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.204 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.204 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.204 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3605 1.201 h = 0.0001 0.003 y[1] (numeric) = 0.095426293022 0.821555397272 y[1] (closed_form) = 0.095426293022 0.821555397272 absolute error = 8.944e-32 relative error = 1.081e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.209 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.209 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.209 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=663.3MB, alloc=52.3MB, time=7.79 x[1] = 0.3606 1.204 h = 0.001 0.001 y[1] (numeric) = 0.0948913621877 0.819578192783 y[1] (closed_form) = 0.0948913621877 0.819578192783 absolute error = 8.062e-32 relative error = 9.772e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.212 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.212 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.212 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3616 1.205 h = 0.001 0.003 y[1] (numeric) = 0.0940741726999 0.819070651036 y[1] (closed_form) = 0.0940741726999 0.819070651036 absolute error = 8.062e-32 relative error = 9.779e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.213 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.213 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.213 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3626 1.208 h = 0.0001 0.004 y[1] (numeric) = 0.0929544856682 0.817241766282 y[1] (closed_form) = 0.0929544856682 0.817241766282 absolute error = 8.062e-32 relative error = 9.802e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.216 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.216 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.216 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3627 1.212 h = 0.003 0.006 y[1] (numeric) = 0.0922842012761 0.814628200631 y[1] (closed_form) = 0.0922842012761 0.814628200631 absolute error = 8.013e-32 relative error = 9.774e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.22 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.22 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.22 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3657 1.218 h = 0.0001 0.005 y[1] (numeric) = 0.0894402862185 0.811156132644 y[1] (closed_form) = 0.0894402862185 0.811156132644 absolute error = 8.013e-32 relative error = 9.819e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.225 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.225 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.225 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3658 1.223 h = 0.0001 0.003 y[1] (numeric) = 0.0886546702673 0.807933395953 y[1] (closed_form) = 0.0886546702673 0.807933395953 absolute error = 7.965e-32 relative error = 9.800e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.23 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.23 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.23 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3659 1.226 h = 0.001 0.001 y[1] (numeric) = 0.0881622716481 0.806017487253 y[1] (closed_form) = 0.0881622716481 0.806017487253 absolute error = 7.965e-32 relative error = 9.823e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.233 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.233 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.233 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3669 1.227 h = 0.001 0.003 y[1] (numeric) = 0.0873792686521 0.805517375177 y[1] (closed_form) = 0.0873792686521 0.805517375177 absolute error = 7.965e-32 relative error = 9.830e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.234 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.234 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.234 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3679 1.23 h = 0.0001 0.004 y[1] (numeric) = 0.0863200997215 0.803737491729 y[1] (closed_form) = 0.0863200997215 0.803737491729 absolute error = 8.857e-32 relative error = 1.096e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.237 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.237 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.237 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.368 1.234 h = 0.003 0.006 y[1] (numeric) = 0.0857042683323 0.801205053955 y[1] (closed_form) = 0.0857042683323 0.801205053955 absolute error = 8.814e-32 relative error = 1.094e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.241 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.241 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.241 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.371 1.24 h = 0.0001 0.005 y[1] (numeric) = 0.0829987112681 0.797817069554 y[1] (closed_form) = 0.0829987112681 0.797817069554 absolute error = 8.773e-32 relative error = 1.094e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.247 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.247 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.247 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3711 1.245 h = 0.0001 0.003 y[1] (numeric) = 0.0822779851923 0.794694271252 y[1] (closed_form) = 0.0822779851923 0.794694271252 absolute error = 8.732e-32 relative error = 1.093e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.252 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.252 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.252 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3712 1.248 h = 0.001 0.001 y[1] (numeric) = 0.0818248756567 0.7928373045 y[1] (closed_form) = 0.0818248756567 0.7928373045 absolute error = 8.732e-32 relative error = 1.096e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.255 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.255 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.255 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3722 1.249 h = 0.001 0.003 y[1] (numeric) = 0.0810741968212 0.792344849997 y[1] (closed_form) = 0.0810741968212 0.792344849997 absolute error = 9.657e-32 relative error = 1.212e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.256 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.256 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.256 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3732 1.252 h = 0.0001 0.004 y[1] (numeric) = 0.08007162293 0.790612554483 y[1] (closed_form) = 0.08007162293 0.790612554483 absolute error = 9.657e-32 relative error = 1.215e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.258 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.258 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.258 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3733 1.256 h = 0.003 0.006 y[1] (numeric) = 0.0795060763758 0.788158105194 y[1] (closed_form) = 0.0795060763758 0.788158105194 absolute error = 8.693e-32 relative error = 1.097e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.262 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.262 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.262 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3763 1.262 h = 0.0001 0.005 y[1] (numeric) = 0.0769304590132 0.784852378938 y[1] (closed_form) = 0.0769304590132 0.784852378938 absolute error = 9.621e-32 relative error = 1.220e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.268 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.268 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.268 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3764 1.267 h = 0.0001 0.003 y[1] (numeric) = 0.0762696508817 0.781825628375 y[1] (closed_form) = 0.0762696508817 0.781825628375 absolute error = 8.693e-32 relative error = 1.107e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.273 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.273 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.273 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3765 1.27 h = 0.001 0.001 y[1] (numeric) = 0.0758528571268 0.780025332398 y[1] (closed_form) = 0.0758528571268 0.780025332398 absolute error = 8.654e-32 relative error = 1.104e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.276 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.276 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.276 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3775 1.271 h = 0.001 0.003 y[1] (numeric) = 0.0751327588182 0.779540705779 y[1] (closed_form) = 0.0751327588182 0.779540705779 absolute error = 8.616e-32 relative error = 1.100e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.277 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.277 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.277 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3785 1.274 h = 0.0001 0.004 y[1] (numeric) = 0.0741831496486 0.777854589731 y[1] (closed_form) = 0.0741831496486 0.777854589731 absolute error = 8.616e-32 relative error = 1.103e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.28 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.28 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.28 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=708.5MB, alloc=52.3MB, time=8.32 x[1] = 0.3786 1.278 h = 0.003 0.006 y[1] (numeric) = 0.0736640669521 0.775475103499 y[1] (closed_form) = 0.0736640669521 0.775475103499 absolute error = 8.580e-32 relative error = 1.101e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.284 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.284 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.284 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3816 1.284 h = 0.0001 0.005 y[1] (numeric) = 0.0712105681102 0.772249742006 y[1] (closed_form) = 0.0712105681102 0.772249742006 absolute error = 8.580e-32 relative error = 1.106e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.289 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.289 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.289 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3817 1.289 h = 0.0001 0.003 y[1] (numeric) = 0.0706051197163 0.769315294288 y[1] (closed_form) = 0.0706051197163 0.769315294288 absolute error = 8.544e-32 relative error = 1.106e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.294 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.294 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.294 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3818 1.292 h = 0.001 0.001 y[1] (numeric) = 0.0702219138425 0.767569481257 y[1] (closed_form) = 0.0702219138425 0.767569481257 absolute error = 8.544e-32 relative error = 1.108e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.297 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.297 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.297 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3828 1.293 h = 0.0001 0.004 y[1] (numeric) = 0.0695307629843 0.767092803231 y[1] (closed_form) = 0.0695307629843 0.767092803231 absolute error = 8.544e-32 relative error = 1.109e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.298 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.298 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.298 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3829 1.297 h = 0.003 0.006 y[1] (numeric) = 0.0690480108981 0.764776004567 y[1] (closed_form) = 0.0690480108981 0.764776004567 absolute error = 9.487e-32 relative error = 1.235e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.302 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.302 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.302 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3859 1.303 h = 0.0001 0.005 y[1] (numeric) = 0.0666928602242 0.761619604488 y[1] (closed_form) = 0.0666928602242 0.761619604488 absolute error = 9.456e-32 relative error = 1.237e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.308 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.308 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.308 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.386 1.308 h = 0.0001 0.003 y[1] (numeric) = 0.0661306602624 0.758762312485 y[1] (closed_form) = 0.0661306602624 0.758762312485 absolute error = 9.456e-32 relative error = 1.241e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.313 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.313 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.313 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3861 1.311 h = 0.001 0.001 y[1] (numeric) = 0.0657737372697 0.757062068135 y[1] (closed_form) = 0.0657737372697 0.757062068135 absolute error = 8.509e-32 relative error = 1.120e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.316 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.316 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.316 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3871 1.312 h = 0.001 0.003 y[1] (numeric) = 0.0651061786334 0.756592616183 y[1] (closed_form) = 0.0651061786334 0.756592616183 absolute error = 8.509e-32 relative error = 1.121e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.317 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.317 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.317 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3881 1.315 h = 0.0001 0.004 y[1] (numeric) = 0.0642458549123 0.754989269076 y[1] (closed_form) = 0.0642458549123 0.754989269076 absolute error = 8.509e-32 relative error = 1.123e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.32 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.32 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.32 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3882 1.319 h = 0.003 0.006 y[1] (numeric) = 0.0638033081205 0.752742069865 y[1] (closed_form) = 0.0638033081205 0.752742069865 absolute error = 9.456e-32 relative error = 1.252e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.324 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.324 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.324 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3912 1.325 h = 0.0001 0.005 y[1] (numeric) = 0.0615571779845 0.7496623238 y[1] (closed_form) = 0.0615571779845 0.7496623238 absolute error = 8.476e-32 relative error = 1.127e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.329 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.329 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.329 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3913 1.33 h = 0.0001 0.003 y[1] (numeric) = 0.0610428720376 0.746890706624 y[1] (closed_form) = 0.0610428720376 0.746890706624 absolute error = 8.443e-32 relative error = 1.127e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.334 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.334 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.334 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3914 1.333 h = 0.001 0.001 y[1] (numeric) = 0.0607150637808 0.745241068322 y[1] (closed_form) = 0.0607150637808 0.745241068322 absolute error = 8.443e-32 relative error = 1.129e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.337 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.337 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.337 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3924 1.334 h = 0.001 0.003 y[1] (numeric) = 0.0600736820459 0.744779664027 y[1] (closed_form) = 0.0600736820459 0.744779664027 absolute error = 8.443e-32 relative error = 1.130e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.338 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.338 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.338 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3934 1.337 h = 0.0001 0.004 y[1] (numeric) = 0.0592573631554 0.743218522878 y[1] (closed_form) = 0.0592573631554 0.743218522878 absolute error = 8.412e-32 relative error = 1.128e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.341 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.341 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.341 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3935 1.341 h = 0.003 0.006 y[1] (numeric) = 0.0588520290066 0.741038224393 y[1] (closed_form) = 0.0588520290066 0.741038224393 absolute error = 8.412e-32 relative error = 1.132e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.345 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.345 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.345 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3965 1.347 h = 0.0001 0.005 y[1] (numeric) = 0.0567085611435 0.738033158071 y[1] (closed_form) = 0.0567085611435 0.738033158071 absolute error = 8.412e-32 relative error = 1.136e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.351 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.351 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.351 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3966 1.352 h = 0.0001 0.003 y[1] (numeric) = 0.0562385781025 0.735343883894 y[1] (closed_form) = 0.0562385781025 0.735343883894 absolute error = 8.412e-32 relative error = 1.141e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.356 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.356 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.356 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3967 1.355 h = 0.001 0.001 y[1] (numeric) = 0.0559377429491 0.73374290122 y[1] (closed_form) = 0.0559377429491 0.73374290122 absolute error = 8.382e-32 relative error = 1.139e-29 % Correct digits = 31 memory used=753.8MB, alloc=52.3MB, time=8.85 Radius of convergence (given) for eq 1 = 1.359 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.359 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.359 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3977 1.356 h = 0.001 0.003 y[1] (numeric) = 0.055321181395 0.73328955984 y[1] (closed_form) = 0.055321181395 0.73328955984 absolute error = 8.412e-32 relative error = 1.144e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.36 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.36 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.36 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3987 1.359 h = 0.0001 0.004 y[1] (numeric) = 0.0545461587553 0.731769296628 y[1] (closed_form) = 0.0545461587553 0.731769296628 absolute error = 8.382e-32 relative error = 1.142e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.363 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.363 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.363 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3988 1.363 h = 0.003 0.006 y[1] (numeric) = 0.0541752860867 0.729653309646 y[1] (closed_form) = 0.0541752860867 0.729653309646 absolute error = 8.382e-32 relative error = 1.146e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.367 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.367 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.367 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4018 1.369 h = 0.0001 0.005 y[1] (numeric) = 0.0521285587509 0.726720946334 y[1] (closed_form) = 0.0521285587509 0.726720946334 absolute error = 8.352e-32 relative error = 1.146e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.373 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.373 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.373 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4019 1.374 h = 0.0001 0.003 y[1] (numeric) = 0.0516996153691 0.724110820766 y[1] (closed_form) = 0.0516996153691 0.724110820766 absolute error = 8.352e-32 relative error = 1.151e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.377 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.377 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.377 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.402 1.377 h = 0.001 0.001 y[1] (numeric) = 0.0514237828699 0.72255662257 y[1] (closed_form) = 0.0514237828699 0.72255662257 absolute error = 8.352e-32 relative error = 1.153e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.38 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.38 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.38 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.403 1.378 h = 0.001 0.003 y[1] (numeric) = 0.0508307686503 0.72211133196 y[1] (closed_form) = 0.0508307686503 0.72211133196 absolute error = 8.382e-32 relative error = 1.158e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.381 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.381 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.381 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.404 1.381 h = 0.0001 0.004 y[1] (numeric) = 0.0500945273294 0.720630648354 y[1] (closed_form) = 0.0500945273294 0.720630648354 absolute error = 8.382e-32 relative error = 1.160e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.384 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.384 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.384 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4041 1.385 h = 0.003 0.006 y[1] (numeric) = 0.0497555851565 0.71857649053 y[1] (closed_form) = 0.0497555851565 0.71857649053 absolute error = 8.352e-32 relative error = 1.160e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.388 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.388 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.388 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4071 1.391 h = 0.0001 0.005 y[1] (numeric) = 0.0478000795478 0.715714861689 y[1] (closed_form) = 0.0478000795478 0.715714861689 absolute error = 7.400e-32 relative error = 1.032e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.394 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.394 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.394 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4072 1.396 h = 0.0001 0.003 y[1] (numeric) = 0.0474091550675 0.713180824076 y[1] (closed_form) = 0.0474091550675 0.713180824076 absolute error = 7.400e-32 relative error = 1.035e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.399 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.399 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.399 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4073 1.399 h = 0.001 0.001 y[1] (numeric) = 0.0471565109694 0.711671616464 y[1] (closed_form) = 0.0471565109694 0.711671616464 absolute error = 8.324e-32 relative error = 1.167e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.402 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.402 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.402 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4083 1.4 h = 0.003 0.006 y[1] (numeric) = 0.0465858493456 0.711234341154 y[1] (closed_form) = 0.0465858493456 0.711234341154 absolute error = 7.368e-32 relative error = 1.034e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.403 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.403 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.403 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4113 1.406 h = 0.0001 0.005 y[1] (numeric) = 0.0446918098893 0.708418091368 y[1] (closed_form) = 0.0446918098893 0.708418091368 absolute error = 7.368e-32 relative error = 1.038e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.409 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.409 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.409 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4114 1.411 h = 0.0001 0.003 y[1] (numeric) = 0.0443272399755 0.705933810445 y[1] (closed_form) = 0.0443272399755 0.705933810445 absolute error = 7.368e-32 relative error = 1.042e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.414 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.414 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.414 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4115 1.414 h = 0.001 0.001 y[1] (numeric) = 0.0440906508764 0.704454015133 y[1] (closed_form) = 0.0440906508764 0.704454015133 absolute error = 7.338e-32 relative error = 1.040e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.417 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.417 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.417 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4125 1.415 h = 0.001 0.003 y[1] (numeric) = 0.0435349103336 0.704021692824 y[1] (closed_form) = 0.0435349103336 0.704021692824 absolute error = 7.368e-32 relative error = 1.045e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.418 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.418 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.418 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4135 1.418 h = 0.0001 0.004 y[1] (numeric) = 0.0428598415053 0.702604106989 y[1] (closed_form) = 0.0428598415053 0.702604106989 absolute error = 7.338e-32 relative error = 1.042e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.421 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.421 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.421 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4136 1.422 h = 0.003 0.006 y[1] (numeric) = 0.0425710350934 0.700648285913 y[1] (closed_form) = 0.0425710350934 0.700648285913 absolute error = 8.297e-32 relative error = 1.182e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.425 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.425 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.425 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4166 1.428 h = 0.0001 0.005 y[1] (numeric) = 0.0407596830785 0.697899609546 y[1] (closed_form) = 0.0407596830785 0.697899609546 absolute error = 8.271e-32 relative error = 1.183e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.43 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.43 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.43 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=798.8MB, alloc=52.3MB, time=9.38 x[1] = 0.4167 1.433 h = 0.0001 0.003 y[1] (numeric) = 0.0404284956558 0.69548660594 y[1] (closed_form) = 0.0404284956558 0.69548660594 absolute error = 7.308e-32 relative error = 1.049e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.435 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.435 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.435 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4168 1.436 h = 0.001 0.001 y[1] (numeric) = 0.0402123086165 0.694048980448 y[1] (closed_form) = 0.0402123086165 0.694048980448 absolute error = 8.271e-32 relative error = 1.190e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.438 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.438 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.438 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4178 1.437 h = 0.001 0.003 y[1] (numeric) = 0.0396770646062 0.693624596583 y[1] (closed_form) = 0.0396770646062 0.693624596583 absolute error = 8.271e-32 relative error = 1.190e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.439 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.439 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.439 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4188 1.44 h = 0.0001 0.004 y[1] (numeric) = 0.0390348312992 0.69224331368 y[1] (closed_form) = 0.0390348312992 0.69224331368 absolute error = 8.271e-32 relative error = 1.193e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.442 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.442 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.442 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4189 1.444 h = 0.003 0.006 y[1] (numeric) = 0.038772045619 0.690343204363 y[1] (closed_form) = 0.038772045619 0.690343204363 absolute error = 7.308e-32 relative error = 1.057e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.446 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.446 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.446 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4219 1.45 h = 0.0001 0.005 y[1] (numeric) = 0.0370388003629 0.687660185994 y[1] (closed_form) = 0.0370388003629 0.687660185994 absolute error = 7.280e-32 relative error = 1.057e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.452 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.452 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.452 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.422 1.455 h = 0.0001 0.003 y[1] (numeric) = 0.0367385753628 0.68531573273 y[1] (closed_form) = 0.0367385753628 0.68531573273 absolute error = 7.280e-32 relative error = 1.061e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.457 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.457 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.457 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4221 1.458 h = 0.001 0.001 y[1] (numeric) = 0.036541333941 0.683918676328 y[1] (closed_form) = 0.036541333941 0.683918676328 absolute error = 7.280e-32 relative error = 1.063e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.46 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.46 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.46 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4231 1.459 h = 0.001 0.003 y[1] (numeric) = 0.0360255758352 0.683502147511 y[1] (closed_form) = 0.0360255758352 0.683502147511 absolute error = 7.280e-32 relative error = 1.064e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.461 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.461 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.461 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4241 1.462 h = 0.0001 0.004 y[1] (numeric) = 0.0354142542261 0.682155990495 y[1] (closed_form) = 0.0354142542261 0.682155990495 absolute error = 7.253e-32 relative error = 1.062e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.464 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.464 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.464 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4242 1.466 h = 0.003 0.006 y[1] (numeric) = 0.0351756194311 0.680309473429 y[1] (closed_form) = 0.0351756194311 0.680309473429 absolute error = 7.253e-32 relative error = 1.065e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.468 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.468 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.468 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4272 1.472 h = 0.0001 0.005 y[1] (numeric) = 0.0335162016582 0.677690231331 y[1] (closed_form) = 0.0335162016582 0.677690231331 absolute error = 7.253e-32 relative error = 1.069e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.474 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.474 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.474 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4273 1.477 h = 0.0001 0.003 y[1] (numeric) = 0.0332447068471 0.675411719575 y[1] (closed_form) = 0.0332447068471 0.675411719575 absolute error = 7.228e-32 relative error = 1.069e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.479 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.479 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.479 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4274 1.48 h = 0.001 0.001 y[1] (numeric) = 0.0330650666405 0.674053700109 y[1] (closed_form) = 0.0330650666405 0.674053700109 absolute error = 7.228e-32 relative error = 1.071e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.482 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.482 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.482 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4284 1.481 h = 0.0001 0.004 y[1] (numeric) = 0.03256784405 0.6736449307 y[1] (closed_form) = 0.03256784405 0.6736449307 absolute error = 6.264e-32 relative error = 9.288e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.483 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.483 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.483 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4285 1.485 h = 0.003 0.006 y[1] (numeric) = 0.0323480048124 0.671843176873 y[1] (closed_form) = 0.0323480048124 0.671843176873 absolute error = 7.228e-32 relative error = 1.075e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.487 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.487 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.487 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4315 1.491 h = 0.0001 0.005 y[1] (numeric) = 0.030748192169 0.669278168234 y[1] (closed_form) = 0.030748192169 0.669278168234 absolute error = 7.228e-32 relative error = 1.079e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.493 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.493 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.493 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4316 1.496 h = 0.0001 0.003 y[1] (numeric) = 0.0304990261358 0.667054723671 y[1] (closed_form) = 0.0304990261358 0.667054723671 absolute error = 7.228e-32 relative error = 1.082e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.498 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.498 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.498 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4317 1.499 h = 0.001 0.001 y[1] (numeric) = 0.0303330970653 0.665729319193 y[1] (closed_form) = 0.0303330970653 0.665729319193 absolute error = 7.228e-32 relative error = 1.085e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.501 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.501 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.501 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4327 1.5 h = 0.001 0.003 y[1] (numeric) = 0.0298510204762 0.665327350881 y[1] (closed_form) = 0.0298510204762 0.665327350881 absolute error = 7.228e-32 relative error = 1.085e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.502 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.502 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.502 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4337 1.503 h = 0.0001 0.004 y[1] (numeric) = 0.029292154555 0.664043865704 y[1] (closed_form) = 0.029292154555 0.664043865704 absolute error = 8.179e-32 relative error = 1.230e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.504 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.504 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.504 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=843.9MB, alloc=52.3MB, time=9.91 x[1] = 0.4338 1.507 h = 0.003 0.006 y[1] (numeric) = 0.0290933837145 0.662291982746 y[1] (closed_form) = 0.0290933837145 0.662291982746 absolute error = 8.200e-32 relative error = 1.237e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.508 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.508 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.508 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4368 1.513 h = 0.0001 0.005 y[1] (numeric) = 0.0275601836352 0.659787307597 y[1] (closed_form) = 0.0275601836352 0.659787307597 absolute error = 7.203e-32 relative error = 1.091e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.514 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.514 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.514 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4369 1.518 h = 0.0001 0.003 y[1] (numeric) = 0.0273360683813 0.65762522667 y[1] (closed_form) = 0.0273360683813 0.65762522667 absolute error = 7.203e-32 relative error = 1.094e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.519 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.519 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.519 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.437 1.521 h = 0.001 0.001 y[1] (numeric) = 0.0271855217678 0.656336168395 y[1] (closed_form) = 0.0271855217678 0.656336168395 absolute error = 7.203e-32 relative error = 1.097e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.522 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.522 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.522 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.438 1.522 h = 0.001 0.003 y[1] (numeric) = 0.0267203602249 0.655941746167 y[1] (closed_form) = 0.0267203602249 0.655941746167 absolute error = 6.236e-32 relative error = 9.499e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.523 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.523 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.523 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.439 1.525 h = 0.0001 0.004 y[1] (numeric) = 0.0261876080239 0.654690200597 y[1] (closed_form) = 0.0261876080239 0.654690200597 absolute error = 7.203e-32 relative error = 1.099e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.526 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.526 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.526 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4391 1.529 h = 0.003 0.006 y[1] (numeric) = 0.0260084153409 0.652986322764 y[1] (closed_form) = 0.0260084153409 0.652986322764 absolute error = 7.181e-32 relative error = 1.099e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.53 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.53 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.53 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4421 1.535 h = 0.0001 0.005 y[1] (numeric) = 0.024538292219 0.65054021686 y[1] (closed_form) = 0.024538292219 0.65054021686 absolute error = 7.181e-32 relative error = 1.103e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.536 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.536 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.536 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4422 1.54 h = 0.0001 0.003 y[1] (numeric) = 0.0243374483383 0.648437204861 y[1] (closed_form) = 0.0243374483383 0.648437204861 absolute error = 7.159e-32 relative error = 1.103e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.541 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.541 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.541 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4423 1.543 h = 0.001 0.001 y[1] (numeric) = 0.0242012102207 0.647183143338 y[1] (closed_form) = 0.0242012102207 0.647183143338 absolute error = 7.159e-32 relative error = 1.105e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.544 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.544 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.544 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4433 1.544 h = 0.001 0.003 y[1] (numeric) = 0.0237521642379 0.646796147855 y[1] (closed_form) = 0.0237521642379 0.646796147855 absolute error = 7.159e-32 relative error = 1.106e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.545 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.545 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.545 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4443 1.547 h = 0.0001 0.004 y[1] (numeric) = 0.0232440566397 0.645575504877 y[1] (closed_form) = 0.0232440566397 0.645575504877 absolute error = 7.159e-32 relative error = 1.108e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.548 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.548 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.548 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4444 1.551 h = 0.003 0.006 y[1] (numeric) = 0.0230830640406 0.643917847608 y[1] (closed_form) = 0.0230830640406 0.643917847608 absolute error = 7.159e-32 relative error = 1.111e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.552 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.552 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.552 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4474 1.557 h = 0.0001 0.005 y[1] (numeric) = 0.0216727064022 0.641528590651 y[1] (closed_form) = 0.0216727064022 0.641528590651 absolute error = 7.159e-32 relative error = 1.115e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.558 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.558 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.558 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4475 1.562 h = 0.0001 0.003 y[1] (numeric) = 0.021493488343 0.639482453177 y[1] (closed_form) = 0.021493488343 0.639482453177 absolute error = 8.122e-32 relative error = 1.269e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.563 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.563 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.563 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4476 1.565 h = 0.001 0.001 y[1] (numeric) = 0.0213705647942 0.638262097383 y[1] (closed_form) = 0.0213705647942 0.638262097383 absolute error = 8.122e-32 relative error = 1.272e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.566 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.566 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.566 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4486 1.566 h = 0.001 0.003 y[1] (numeric) = 0.0209368809414 0.63788240378 y[1] (closed_form) = 0.0209368809414 0.63788240378 absolute error = 8.105e-32 relative error = 1.270e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.567 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.567 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.567 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4496 1.569 h = 0.0001 0.004 y[1] (numeric) = 0.0204520457232 0.636691661501 y[1] (closed_form) = 0.0204520457232 0.636691661501 absolute error = 8.105e-32 relative error = 1.272e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.57 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.57 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.57 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4497 1.573 h = 0.003 0.006 y[1] (numeric) = 0.0203079780368 0.635078517931 y[1] (closed_form) = 0.0203079780368 0.635078517931 absolute error = 8.105e-32 relative error = 1.276e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.574 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.574 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.574 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4527 1.579 h = 0.0001 0.005 y[1] (numeric) = 0.0189542823071 0.632744434735 y[1] (closed_form) = 0.0189542823071 0.632744434735 absolute error = 8.105e-32 relative error = 1.280e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.58 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.58 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.58 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=889.0MB, alloc=52.3MB, time=10.43 x[1] = 0.4528 1.584 h = 0.0001 0.003 y[1] (numeric) = 0.0187951673356 0.630753073297 y[1] (closed_form) = 0.0187951673356 0.630753073297 absolute error = 8.105e-32 relative error = 1.284e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.585 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.585 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.585 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4529 1.587 h = 0.001 0.001 y[1] (numeric) = 0.0186846379084 0.629565188125 y[1] (closed_form) = 0.0186846379084 0.629565188125 absolute error = 7.120e-32 relative error = 1.130e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.588 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.588 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.588 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4539 1.588 h = 0.0001 0.004 y[1] (numeric) = 0.0182656057681 0.629192667238 y[1] (closed_form) = 0.0182656057681 0.629192667238 absolute error = 7.120e-32 relative error = 1.131e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.589 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.589 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.589 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.454 1.592 h = 0.003 0.006 y[1] (numeric) = 0.0181346537464 0.627616712266 y[1] (closed_form) = 0.0181346537464 0.627616712266 absolute error = 6.139e-32 relative error = 9.778e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.593 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.593 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.593 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.457 1.598 h = 0.0001 0.005 y[1] (numeric) = 0.0168267622218 0.625329442568 y[1] (closed_form) = 0.0168267622218 0.625329442568 absolute error = 7.102e-32 relative error = 1.135e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.599 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.599 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.599 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4571 1.603 h = 0.0001 0.003 y[1] (numeric) = 0.0166831981345 0.623383837056 y[1] (closed_form) = 0.0166831981345 0.623383837056 absolute error = 6.119e-32 relative error = 9.812e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.604 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.604 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.604 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4572 1.606 h = 0.001 0.001 y[1] (numeric) = 0.0165822840209 0.622223087325 y[1] (closed_form) = 0.0165822840209 0.622223087325 absolute error = 7.102e-32 relative error = 1.141e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.607 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.607 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.607 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4582 1.607 h = 0.001 0.003 y[1] (numeric) = 0.0161752421712 0.621856798306 y[1] (closed_form) = 0.0161752421712 0.621856798306 absolute error = 6.100e-32 relative error = 9.806e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.608 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.608 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.608 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4592 1.61 h = 0.0001 0.004 y[1] (numeric) = 0.0157300316963 0.620719388017 y[1] (closed_form) = 0.0157300316963 0.620719388017 absolute error = 6.119e-32 relative error = 9.854e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.611 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.611 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.611 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4593 1.614 h = 0.003 0.006 y[1] (numeric) = 0.0156138956597 0.619184953189 y[1] (closed_form) = 0.0156138956597 0.619184953189 absolute error = 6.100e-32 relative error = 9.849e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.615 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.615 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.615 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4623 1.62 h = 0.0001 0.005 y[1] (numeric) = 0.014357412724 0.61694983058 y[1] (closed_form) = 0.014357412724 0.61694983058 absolute error = 6.100e-32 relative error = 9.885e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.62 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.62 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.62 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4624 1.625 h = 0.0001 0.003 y[1] (numeric) = 0.0142314339098 0.615055321898 y[1] (closed_form) = 0.0142314339098 0.615055321898 absolute error = 6.100e-32 relative error = 9.915e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.625 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.625 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.625 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4625 1.628 h = 0.001 0.001 y[1] (numeric) = 0.0141413899534 0.613924875846 y[1] (closed_form) = 0.0141413899534 0.613924875846 absolute error = 6.100e-32 relative error = 9.933e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.628 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.628 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.628 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4635 1.629 h = 0.001 0.003 y[1] (numeric) = 0.0137477844645 0.613565503909 y[1] (closed_form) = 0.0137477844645 0.613565503909 absolute error = 6.083e-32 relative error = 9.911e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.629 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.629 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.629 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4645 1.632 h = 0.0001 0.004 y[1] (numeric) = 0.0133224039584 0.6124553031 y[1] (closed_form) = 0.0133224039584 0.6124553031 absolute error = 7.086e-32 relative error = 1.157e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.632 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.632 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.632 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4646 1.636 h = 0.003 0.006 y[1] (numeric) = 0.013220058297 0.610960886269 y[1] (closed_form) = 0.013220058297 0.610960886269 absolute error = 7.071e-32 relative error = 1.157e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.636 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.636 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.636 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4676 1.642 h = 0.0001 0.005 y[1] (numeric) = 0.0120123960809 0.608776369286 y[1] (closed_form) = 0.0120123960809 0.608776369286 absolute error = 7.071e-32 relative error = 1.161e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.642 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.642 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.642 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4677 1.647 h = 0.0001 0.003 y[1] (numeric) = 0.0119027777136 0.606931111281 y[1] (closed_form) = 0.0119027777136 0.606931111281 absolute error = 7.071e-32 relative error = 1.165e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.647 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.647 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.647 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4678 1.65 h = 0.001 0.001 y[1] (numeric) = 0.0118228619224 0.605829881119 y[1] (closed_form) = 0.0118228619224 0.605829881119 absolute error = 7.071e-32 relative error = 1.167e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.65 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.65 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.65 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4688 1.651 h = 0.001 0.003 y[1] (numeric) = 0.011442090531 0.605477290597 y[1] (closed_form) = 0.011442090531 0.605477290597 absolute error = 7.071e-32 relative error = 1.168e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.651 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.651 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.651 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4698 1.654 h = 0.0001 0.004 y[1] (numeric) = 0.0110354785373 0.604393427175 y[1] (closed_form) = 0.0110354785373 0.604393427175 absolute error = 6.067e-32 relative error = 1.004e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.654 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.654 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.654 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=934.0MB, alloc=52.3MB, time=10.96 x[1] = 0.4699 1.658 h = 0.003 0.006 y[1] (numeric) = 0.0109459719516 0.602937591221 y[1] (closed_form) = 0.0109459719516 0.602937591221 absolute error = 6.067e-32 relative error = 1.006e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.658 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.658 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.658 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4729 1.664 h = 0.0001 0.005 y[1] (numeric) = 0.00978469903499 0.600802184289 y[1] (closed_form) = 0.00978469903499 0.600802184289 absolute error = 5.068e-32 relative error = 8.435e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.664 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.664 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.664 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.473 1.669 h = 0.0001 0.003 y[1] (numeric) = 0.00969030502927 0.599004410883 y[1] (closed_form) = 0.00969030502927 0.599004410883 absolute error = 6.057e-32 relative error = 1.011e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.669 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.669 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.669 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4731 1.672 h = 0.001 0.001 y[1] (numeric) = 0.00961982862822 0.597931355628 y[1] (closed_form) = 0.00961982862822 0.597931355628 absolute error = 5.067e-32 relative error = 8.473e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.672 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.672 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.672 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4741 1.673 h = 0.001 0.003 y[1] (numeric) = 0.00925132224523 0.597585409895 y[1] (closed_form) = 0.00925132224523 0.597585409895 absolute error = 5.067e-32 relative error = 8.478e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.673 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.673 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.673 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4751 1.676 h = 0.0001 0.004 y[1] (numeric) = 0.00886248411208 0.596527043046 y[1] (closed_form) = 0.00886248411208 0.596527043046 absolute error = 5.067e-32 relative error = 8.493e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.676 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.676 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.676 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4752 1.68 h = 0.003 0.006 y[1] (numeric) = 0.00878493371399 0.595108412883 y[1] (closed_form) = 0.00878493371399 0.595108412883 absolute error = 5.065e-32 relative error = 8.510e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.68 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.68 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.68 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4782 1.686 h = 0.0001 0.005 y[1] (numeric) = 0.00766776424498 0.593020665919 y[1] (closed_form) = 0.00766776424498 0.593020665919 absolute error = 5.060e-32 relative error = 8.533e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.686 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.686 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.686 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4783 1.691 h = 0.0001 0.003 y[1] (numeric) = 0.00758754022257 0.59126868739 y[1] (closed_form) = 0.00758754022257 0.59126868739 absolute error = 5.060e-32 relative error = 8.558e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.691 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.691 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.691 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4784 1.694 h = 0.001 0.001 y[1] (numeric) = 0.00752586346601 0.590222810714 y[1] (closed_form) = 0.00752586346601 0.590222810714 absolute error = 5.059e-32 relative error = 8.571e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.694 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.694 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.694 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4794 1.695 h = 0.0001 0.004 y[1] (numeric) = 0.00716908405861 0.589883372784 y[1] (closed_form) = 0.00716908405861 0.589883372784 absolute error = 5.059e-32 relative error = 8.576e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.695 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.695 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.695 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4795 1.699 h = 0.003 0.006 y[1] (numeric) = 0.00710074440914 0.588495841518 y[1] (closed_form) = 0.00710074440914 0.588495841518 absolute error = 5.057e-32 relative error = 8.593e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.699 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.699 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.699 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4825 1.705 h = 0.0001 0.005 y[1] (numeric) = 0.00601926595052 0.586448482608 y[1] (closed_form) = 0.00601926595052 0.586448482608 absolute error = 5.054e-32 relative error = 8.618e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.705 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.705 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.705 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4826 1.71 h = 0.0001 0.003 y[1] (numeric) = 0.00594993283347 0.584734778461 y[1] (closed_form) = 0.00594993283347 0.584734778461 absolute error = 6.044e-32 relative error = 1.034e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.71 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.71 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.71 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4827 1.713 h = 0.001 0.001 y[1] (numeric) = 0.0058950444447 0.583711626229 y[1] (closed_form) = 0.0058950444447 0.583711626229 absolute error = 6.044e-32 relative error = 1.035e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.713 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.713 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.713 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4837 1.714 h = 0.001 0.003 y[1] (numeric) = 0.0055478753409 0.583377811921 y[1] (closed_form) = 0.0055478753409 0.583377811921 absolute error = 6.043e-32 relative error = 1.036e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.714 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.714 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.714 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4847 1.717 h = 0.0001 0.004 y[1] (numeric) = 0.00518939055624 0.582364940201 y[1] (closed_form) = 0.00518939055624 0.582364940201 absolute error = 6.042e-32 relative error = 1.037e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.717 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.717 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.717 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4848 1.721 h = 0.003 0.006 y[1] (numeric) = 0.0051315429857 0.581012202526 y[1] (closed_form) = 0.0051315429857 0.581012202526 absolute error = 5.049e-32 relative error = 8.689e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.721 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.721 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.721 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4878 1.727 h = 0.0001 0.005 y[1] (numeric) = 0.0040902841857 0.579009900714 y[1] (closed_form) = 0.0040902841857 0.579009900714 absolute error = 5.046e-32 relative error = 8.715e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.727 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.727 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.727 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4879 1.732 h = 0.0001 0.003 y[1] (numeric) = 0.00403337311584 0.577339027821 y[1] (closed_form) = 0.00403337311584 0.577339027821 absolute error = 5.045e-32 relative error = 8.738e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.732 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.732 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.732 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=979.0MB, alloc=52.3MB, time=11.48 x[1] = 0.488 1.735 h = 0.001 0.001 y[1] (numeric) = 0.00398622228704 0.576341305667 y[1] (closed_form) = 0.00398622228704 0.576341305667 absolute error = 5.045e-32 relative error = 8.753e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.735 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.735 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.735 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.489 1.736 h = 0.001 0.003 y[1] (numeric) = 0.00364985664359 0.576013739388 y[1] (closed_form) = 0.00364985664359 0.576013739388 absolute error = 5.043e-32 relative error = 8.755e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.736 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.736 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.736 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.49 1.739 h = 0.0001 0.004 y[1] (numeric) = 0.00330663665122 0.575024113648 y[1] (closed_form) = 0.00330663665122 0.575024113648 absolute error = 5.042e-32 relative error = 8.768e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.739 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.739 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.739 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4901 1.743 h = 0.003 0.006 y[1] (numeric) = 0.00325856516074 0.573704957088 y[1] (closed_form) = 0.00325856516074 0.573704957088 absolute error = 5.041e-32 relative error = 8.786e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.743 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.743 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.743 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4931 1.749 h = 0.0001 0.005 y[1] (numeric) = 0.00225560325437 0.57174639013 y[1] (closed_form) = 0.00225560325437 0.57174639013 absolute error = 4.048e-32 relative error = 7.080e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.749 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.749 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.749 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4932 1.754 h = 0.0001 0.003 y[1] (numeric) = 0.00221025920152 0.570116858744 y[1] (closed_form) = 0.00221025920152 0.570116858744 absolute error = 5.038e-32 relative error = 8.837e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.754 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.754 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.754 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4933 1.757 h = 0.001 0.001 y[1] (numeric) = 0.00217032595662 0.569143687431 y[1] (closed_form) = 0.00217032595662 0.569143687431 absolute error = 4.048e-32 relative error = 7.112e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.757 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.757 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.757 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4943 1.758 h = 0.001 0.003 y[1] (numeric) = 0.00184430417185 0.568822234054 y[1] (closed_form) = 0.00184430417185 0.568822234054 absolute error = 5.038e-32 relative error = 8.857e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.758 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.758 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.758 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4953 1.761 h = 0.0001 0.004 y[1] (numeric) = 0.00151557018286 0.567855125963 y[1] (closed_form) = 0.00151557018286 0.567855125963 absolute error = 5.037e-32 relative error = 8.870e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.761 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.761 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.761 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4954 1.765 h = 0.003 0.006 y[1] (numeric) = 0.00147660883402 0.566568389575 y[1] (closed_form) = 0.00147660883402 0.566568389575 absolute error = 4.046e-32 relative error = 7.142e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.765 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.765 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.765 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4984 1.771 h = 0.0001 0.005 y[1] (numeric) = 0.000510131927896 0.56465227769 y[1] (closed_form) = 0.000510131927896 0.56465227769 absolute error = 4.044e-32 relative error = 7.161e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.771 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.771 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.771 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4985 1.776 h = 0.0001 0.003 y[1] (numeric) = 0.000475559680243 0.563062661408 y[1] (closed_form) = 0.000475559680243 0.563062661408 absolute error = 5.034e-32 relative error = 8.941e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.776 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.776 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.776 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4986 1.779 h = 0.001 0.001 y[1] (numeric) = 0.000442360021554 0.562113198817 y[1] (closed_form) = 0.000442360021554 0.562113198817 absolute error = 5.034e-32 relative error = 8.956e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.779 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.779 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.779 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4996 1.78 h = 0.001 0.003 y[1] (numeric) = 0.000126246679649 0.561797724439 y[1] (closed_form) = 0.000126246679649 0.561797724439 absolute error = 5.033e-32 relative error = 8.959e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.78 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.78 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.78 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5006 1.783 h = 0.0001 0.004 y[1] (numeric) = -0.000188733291851 0.560852432283 y[1] (closed_form) = -0.000188733291851 0.560852432283 absolute error = 5.033e-32 relative error = 8.973e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.783 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.783 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.783 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5007 1.787 h = 0.003 0.006 y[1] (numeric) = -0.000219204198635 0.559597004229 y[1] (closed_form) = -0.000219204198635 0.559597004229 absolute error = 6.027e-32 relative error = 1.077e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.787 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.787 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.787 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5037 1.793 h = 0.0001 0.005 y[1] (numeric) = -0.00115090451966 0.557722109121 y[1] (closed_form) = -0.00115090451966 0.557722109121 absolute error = 6.025e-32 relative error = 1.080e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.793 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.793 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.793 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5038 1.798 h = 0.0001 0.003 y[1] (numeric) = -0.00117544491611 0.556171041885 y[1] (closed_form) = -0.00117544491611 0.556171041885 absolute error = 6.024e-32 relative error = 1.083e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.798 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.798 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.798 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5039 1.801 h = 0.001 0.001 y[1] (numeric) = -0.00120236173071 0.555244481282 y[1] (closed_form) = -0.00120236173071 0.555244481282 absolute error = 6.024e-32 relative error = 1.085e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.801 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.801 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.801 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5049 1.802 h = 0.0001 0.004 y[1] (numeric) = -0.00150897934636 0.554934853497 y[1] (closed_form) = -0.00150897934636 0.554934853497 absolute error = 6.023e-32 relative error = 1.085e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.802 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.802 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.802 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.505 1.806 h = 0.003 0.006 y[1] (numeric) = -0.00153296127341 0.553705611957 y[1] (closed_form) = -0.00153296127341 0.553705611957 absolute error = 5.027e-32 relative error = 9.079e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.806 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.806 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.806 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1024.1MB, alloc=52.3MB, time=12.02 x[1] = 0.508 1.812 h = 0.0001 0.005 y[1] (numeric) = -0.00243649281478 0.551865622548 y[1] (closed_form) = -0.00243649281478 0.551865622548 absolute error = 6.020e-32 relative error = 1.091e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.812 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.812 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.812 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5081 1.817 h = 0.0001 0.003 y[1] (numeric) = -0.00245338967754 0.550346795566 y[1] (closed_form) = -0.00245338967754 0.550346795566 absolute error = 6.019e-32 relative error = 1.094e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.817 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.817 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.817 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5082 1.82 h = 0.001 0.001 y[1] (numeric) = -0.0024754961803 0.549439396116 y[1] (closed_form) = -0.0024754961803 0.549439396116 absolute error = 6.019e-32 relative error = 1.095e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.82 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.82 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.82 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5092 1.821 h = 0.001 0.003 y[1] (numeric) = -0.00277432190416 0.549134802987 y[1] (closed_form) = -0.00277432190416 0.549134802987 absolute error = 5.023e-32 relative error = 9.147e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.821 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.821 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.821 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5102 1.824 h = 0.0001 0.004 y[1] (numeric) = -0.00306575131267 0.548228470031 y[1] (closed_form) = -0.00306575131267 0.548228470031 absolute error = 6.018e-32 relative error = 1.098e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.824 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.824 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.824 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5103 1.828 h = 0.003 0.006 y[1] (numeric) = -0.00308227265922 0.547028584569 y[1] (closed_form) = -0.00308227265922 0.547028584569 absolute error = 6.018e-32 relative error = 1.100e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.828 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.828 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.828 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5133 1.834 h = 0.0001 0.005 y[1] (numeric) = -0.00395394058771 0.545227596832 y[1] (closed_form) = -0.00395394058771 0.545227596832 absolute error = 5.019e-32 relative error = 9.206e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.834 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.834 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.834 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5134 1.839 h = 0.0001 0.003 y[1] (numeric) = -0.00396203476576 0.543744920464 y[1] (closed_form) = -0.00396203476576 0.543744920464 absolute error = 6.016e-32 relative error = 1.106e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.839 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.839 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.839 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5135 1.842 h = 0.001 0.001 y[1] (numeric) = -0.00397860834911 0.542859005856 y[1] (closed_form) = -0.00397860834911 0.542859005856 absolute error = 6.015e-32 relative error = 1.108e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.842 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.842 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.842 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5145 1.843 h = 0.001 0.003 y[1] (numeric) = -0.00426864904691 0.542560013342 y[1] (closed_form) = -0.00426864904691 0.542560013342 absolute error = 6.015e-32 relative error = 1.109e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.843 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.843 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.843 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5155 1.846 h = 0.0001 0.004 y[1] (numeric) = -0.00454818045273 0.54167362037 y[1] (closed_form) = -0.00454818045273 0.54167362037 absolute error = 6.015e-32 relative error = 1.110e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.846 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.846 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.846 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5156 1.85 h = 0.003 0.006 y[1] (numeric) = -0.00455774750228 0.540502107643 y[1] (closed_form) = -0.00455774750228 0.540502107643 absolute error = 6.015e-32 relative error = 1.113e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.85 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.85 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.85 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5186 1.856 h = 0.0001 0.005 y[1] (numeric) = -0.00539900072508 0.538738997083 y[1] (closed_form) = -0.00539900072508 0.538738997083 absolute error = 6.013e-32 relative error = 1.116e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.856 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.856 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.856 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5187 1.861 h = 0.0001 0.003 y[1] (numeric) = -0.00539889662548 0.537291263102 y[1] (closed_form) = -0.00539889662548 0.537291263102 absolute error = 6.013e-32 relative error = 1.119e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.861 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.861 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.861 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5188 1.864 h = 0.001 0.001 y[1] (numeric) = -0.00541030635273 0.536426119228 y[1] (closed_form) = -0.00541030635273 0.536426119228 absolute error = 6.013e-32 relative error = 1.121e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.864 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.864 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.864 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5198 1.865 h = 0.001 0.003 y[1] (numeric) = -0.00569191715338 0.536132600558 y[1] (closed_form) = -0.00569191715338 0.536132600558 absolute error = 6.013e-32 relative error = 1.121e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.865 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.865 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.865 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5208 1.868 h = 0.0001 0.004 y[1] (numeric) = -0.00596013021326 0.535265540306 y[1] (closed_form) = -0.00596013021326 0.535265540306 absolute error = 5.014e-32 relative error = 9.368e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.868 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.868 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.868 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5209 1.872 h = 0.003 0.006 y[1] (numeric) = -0.00596321499244 0.534121457696 y[1] (closed_form) = -0.00596321499244 0.534121457696 absolute error = 5.014e-32 relative error = 9.388e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.872 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.872 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.872 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5239 1.878 h = 0.0001 0.005 y[1] (numeric) = -0.00677542267078 0.53239513706 y[1] (closed_form) = -0.00677542267078 0.53239513706 absolute error = 5.014e-32 relative error = 9.416e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.878 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.878 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.878 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.524 1.883 h = 0.0001 0.003 y[1] (numeric) = -0.00676768374614 0.530981187249 y[1] (closed_form) = -0.00676768374614 0.530981187249 absolute error = 6.011e-32 relative error = 1.132e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.883 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.883 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.883 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1069.1MB, alloc=52.3MB, time=12.54 x[1] = 0.5241 1.886 h = 0.001 0.001 y[1] (numeric) = -0.00677427397555 0.530136129373 y[1] (closed_form) = -0.00677427397555 0.530136129373 absolute error = 5.014e-32 relative error = 9.457e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.886 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.886 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.886 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5251 1.887 h = 0.001 0.003 y[1] (numeric) = -0.00704779215402 0.529847959945 y[1] (closed_form) = -0.00704779215402 0.529847959945 absolute error = 5.013e-32 relative error = 9.460e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.887 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.887 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.887 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5261 1.89 h = 0.0001 0.004 y[1] (numeric) = -0.00730523322473 0.528999647308 y[1] (closed_form) = -0.00730523322473 0.528999647308 absolute error = 5.013e-32 relative error = 9.475e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.89 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.89 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.89 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5262 1.894 h = 0.003 0.006 y[1] (numeric) = -0.00730227602133 0.527882091008 y[1] (closed_form) = -0.00730227602133 0.527882091008 absolute error = 5.013e-32 relative error = 9.495e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.894 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.894 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.894 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5292 1.9 h = 0.0001 0.005 y[1] (numeric) = -0.00808673266711 0.526191509161 y[1] (closed_form) = -0.00808673266711 0.526191509161 absolute error = 5.012e-32 relative error = 9.523e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.9 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.9 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.9 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5293 1.905 h = 0.0001 0.003 y[1] (numeric) = -0.00807188442294 0.524810232959 y[1] (closed_form) = -0.00807188442294 0.524810232959 absolute error = 5.012e-32 relative error = 9.548e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.905 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.905 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.905 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5294 1.908 h = 0.001 0.001 y[1] (numeric) = -0.00807397660781 0.523984604344 y[1] (closed_form) = -0.00807397660781 0.523984604344 absolute error = 5.012e-32 relative error = 9.563e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.908 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.908 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.908 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5304 1.909 h = 0.0001 0.004 y[1] (numeric) = -0.00833972263992 0.523701661829 y[1] (closed_form) = -0.00833972263992 0.523701661829 absolute error = 5.012e-32 relative error = 9.568e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.909 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.909 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.909 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5305 1.913 h = 0.003 0.006 y[1] (numeric) = -0.0083321967625 0.522606308415 y[1] (closed_form) = -0.0083321967625 0.522606308415 absolute error = 5.012e-32 relative error = 9.588e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.913 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.913 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.913 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5335 1.919 h = 0.0001 0.005 y[1] (numeric) = -0.00909415867936 0.520945985245 y[1] (closed_form) = -0.00909415867936 0.520945985245 absolute error = 5.011e-32 relative error = 9.617e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.919 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.919 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.919 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5336 1.924 h = 0.0001 0.003 y[1] (numeric) = -0.0090739568968 0.519592055638 y[1] (closed_form) = -0.0090739568968 0.519592055638 absolute error = 5.010e-32 relative error = 9.641e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.924 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.924 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.924 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5337 1.927 h = 0.001 0.001 y[1] (numeric) = -0.00907263975095 0.518782694365 y[1] (closed_form) = -0.00907263975095 0.518782694365 absolute error = 5.010e-32 relative error = 9.656e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.927 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.927 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.927 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5347 1.928 h = 0.001 0.003 y[1] (numeric) = -0.00933200063041 0.51850424252 y[1] (closed_form) = -0.00933200063041 0.51850424252 absolute error = 6.008e-32 relative error = 1.159e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.928 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.928 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.928 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5357 1.931 h = 0.0001 0.004 y[1] (numeric) = -0.00957095451121 0.51768944429 y[1] (closed_form) = -0.00957095451121 0.51768944429 absolute error = 6.008e-32 relative error = 1.160e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.931 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.931 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.931 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5358 1.935 h = 0.003 0.006 y[1] (numeric) = -0.00955811948581 0.516619028074 y[1] (closed_form) = -0.00955811948581 0.516619028074 absolute error = 6.008e-32 relative error = 1.163e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.935 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.935 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.935 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5388 1.941 h = 0.0001 0.005 y[1] (numeric) = -0.0102945448644 0.514992566543 y[1] (closed_form) = -0.0102945448644 0.514992566543 absolute error = 6.007e-32 relative error = 1.166e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.941 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.941 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.941 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5389 1.946 h = 0.0001 0.003 y[1] (numeric) = -0.0102681079265 0.513669357966 y[1] (closed_form) = -0.0102681079265 0.513669357966 absolute error = 5.004e-32 relative error = 9.740e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.946 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.946 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.946 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.539 1.949 h = 0.001 0.001 y[1] (numeric) = -0.0102628284039 0.51287827075 y[1] (closed_form) = -0.0102628284039 0.51287827075 absolute error = 5.009e-32 relative error = 9.764e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.949 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.949 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.949 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.54 1.95 h = 0.001 0.003 y[1] (numeric) = -0.0105149706895 0.512604821114 y[1] (closed_form) = -0.0105149706895 0.512604821114 absolute error = 5.009e-32 relative error = 9.770e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.95 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.95 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.95 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.541 1.953 h = 0.0001 0.004 y[1] (numeric) = -0.010744544523 0.511807206183 y[1] (closed_form) = -0.010744544523 0.511807206183 absolute error = 5.004e-32 relative error = 9.775e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.953 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.953 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.953 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5411 1.957 h = 0.003 0.006 y[1] (numeric) = -0.0107267623986 0.510760924918 y[1] (closed_form) = -0.0107267623986 0.510760924918 absolute error = 5.009e-32 relative error = 9.805e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.957 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.957 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.957 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1114.2MB, alloc=52.3MB, time=13.08 x[1] = 0.5441 1.963 h = 0.0001 0.005 y[1] (numeric) = -0.0114387575625 0.509167371774 y[1] (closed_form) = -0.0114387575625 0.509167371774 absolute error = 5.004e-32 relative error = 9.825e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.963 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.963 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.963 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5442 1.968 h = 0.0001 0.003 y[1] (numeric) = -0.0114065174322 0.507873898338 y[1] (closed_form) = -0.0114065174322 0.507873898338 absolute error = 5.004e-32 relative error = 9.850e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.968 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.968 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.968 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5443 1.971 h = 0.001 0.001 y[1] (numeric) = -0.0113975404504 0.507100501754 y[1] (closed_form) = -0.0113975404504 0.507100501754 absolute error = 5.004e-32 relative error = 9.865e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.971 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.971 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.971 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5453 1.972 h = 0.001 0.003 y[1] (numeric) = -0.0116427418046 0.506831939045 y[1] (closed_form) = -0.0116427418046 0.506831939045 absolute error = 5.001e-32 relative error = 9.865e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.973 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.973 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.973 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5463 1.975 h = 0.0001 0.004 y[1] (numeric) = -0.0118633728201 0.506051000425 y[1] (closed_form) = -0.0118633728201 0.506051000425 absolute error = 5.001e-32 relative error = 9.880e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.976 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.976 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.976 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5464 1.979 h = 0.003 0.006 y[1] (numeric) = -0.0118409818607 0.505028084104 y[1] (closed_form) = -0.0118409818607 0.505028084104 absolute error = 5.001e-32 relative error = 9.900e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.98 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.98 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.98 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5494 1.985 h = 0.0001 0.005 y[1] (numeric) = -0.012529594954 0.503466517889 y[1] (closed_form) = -0.012529594954 0.503466517889 absolute error = 5.001e-32 relative error = 9.930e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.986 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.986 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.986 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5495 1.99 h = 0.0001 0.003 y[1] (numeric) = -0.0124919551493 0.502201833276 y[1] (closed_form) = -0.0124919551493 0.502201833276 absolute error = 5.001e-32 relative error = 9.955e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.991 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.991 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.991 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5496 1.993 h = 0.001 0.001 y[1] (numeric) = -0.0124795284155 0.50144556718 y[1] (closed_form) = -0.0124795284155 0.50144556718 absolute error = 4e-32 relative error = 7.974e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.994 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.994 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.994 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5506 1.994 h = 0.001 0.003 y[1] (numeric) = -0.0127180531578 0.501181778591 y[1] (closed_form) = -0.0127180531578 0.501181778591 absolute error = 5e-32 relative error = 9.973e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.995 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.995 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.995 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5516 1.997 h = 0.0001 0.004 y[1] (numeric) = -0.0129301545427 0.500417027554 y[1] (closed_form) = -0.0129301545427 0.500417027554 absolute error = 5e-32 relative error = 9.988e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 1.998 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 1.998 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 1.998 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5517 2.001 h = 0.003 0.006 y[1] (numeric) = -0.0129034709136 0.499416736908 y[1] (closed_form) = -0.0129034709136 0.499416736908 absolute error = 4e-32 relative error = 8.007e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.002 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.002 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.002 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5547 2.007 h = 0.0001 0.005 y[1] (numeric) = -0.0135696954654 0.497886266895 y[1] (closed_form) = -0.0135696954654 0.497886266895 absolute error = 4e-32 relative error = 8.031e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.008 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.008 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.008 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5548 2.012 h = 0.0001 0.003 y[1] (numeric) = -0.0135270330746 0.496649462519 y[1] (closed_form) = -0.0135270330746 0.496649462519 absolute error = 4e-32 relative error = 8.051e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.013 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.013 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.013 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5549 2.015 h = 0.001 0.001 y[1] (numeric) = -0.0135113882951 0.495909788974 y[1] (closed_form) = -0.0135113882951 0.495909788974 absolute error = 4e-32 relative error = 8.063e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.016 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.016 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.016 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5559 2.016 h = 0.0001 0.004 y[1] (numeric) = -0.0137434881589 0.495650664192 y[1] (closed_form) = -0.0137434881589 0.495650664192 absolute error = 5e-32 relative error = 1.008e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.017 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.017 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.017 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.556 2.02 h = 0.003 0.006 y[1] (numeric) = -0.0137136050717 0.4946693258 y[1] (closed_form) = -0.0137136050717 0.4946693258 absolute error = 5.001e-32 relative error = 1.011e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.021 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.021 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.021 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.559 2.026 h = 0.0001 0.005 y[1] (numeric) = -0.0143616711825 0.493165183317 y[1] (closed_form) = -0.0143616711825 0.493165183317 absolute error = 4.001e-32 relative error = 8.110e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.027 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.027 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.027 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5591 2.031 h = 0.0001 0.003 y[1] (numeric) = -0.0143152867199 0.49195173144 y[1] (closed_form) = -0.0143152867199 0.49195173144 absolute error = 4.001e-32 relative error = 8.130e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.032 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.032 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.032 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5592 2.034 h = 0.001 0.001 y[1] (numeric) = -0.0142972354286 0.491225960503 y[1] (closed_form) = -0.0142972354286 0.491225960503 absolute error = 5.001e-32 relative error = 1.018e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.035 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.035 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.035 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1159.4MB, alloc=52.3MB, time=13.60 x[1] = 0.5602 2.035 h = 0.001 0.003 y[1] (numeric) = -0.0145240512788 0.490970836419 y[1] (closed_form) = -0.0145240512788 0.490970836419 absolute error = 5.001e-32 relative error = 1.018e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.036 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.036 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.036 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5612 2.038 h = 0.0001 0.004 y[1] (numeric) = -0.014721484523 0.4902350565 y[1] (closed_form) = -0.014721484523 0.4902350565 absolute error = 5.001e-32 relative error = 1.020e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.039 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.039 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.039 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5613 2.042 h = 0.003 0.006 y[1] (numeric) = -0.0146878354908 0.489275041961 y[1] (closed_form) = -0.0146878354908 0.489275041961 absolute error = 5.001e-32 relative error = 1.022e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.043 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.043 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.043 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5643 2.048 h = 0.0001 0.005 y[1] (numeric) = -0.0153152178252 0.487800406003 y[1] (closed_form) = -0.0153152178252 0.487800406003 absolute error = 5.001e-32 relative error = 1.025e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.049 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.049 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.049 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5644 2.053 h = 0.0001 0.003 y[1] (numeric) = -0.0152644385257 0.486613234369 y[1] (closed_form) = -0.0152644385257 0.486613234369 absolute error = 5e-32 relative error = 1.027e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.054 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.054 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.054 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5645 2.056 h = 0.001 0.001 y[1] (numeric) = -0.0152435556834 0.485903108297 y[1] (closed_form) = -0.0152435556834 0.485903108297 absolute error = 5e-32 relative error = 1.029e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.057 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.057 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.057 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5655 2.057 h = 0.001 0.003 y[1] (numeric) = -0.0154643827229 0.485652446734 y[1] (closed_form) = -0.0154643827229 0.485652446734 absolute error = 5e-32 relative error = 1.029e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.058 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.058 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.058 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5665 2.06 h = 0.0001 0.004 y[1] (numeric) = -0.0156543436184 0.484931546674 y[1] (closed_form) = -0.0156543436184 0.484931546674 absolute error = 5e-32 relative error = 1.031e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.061 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.061 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.061 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5666 2.064 h = 0.003 0.006 y[1] (numeric) = -0.0156171900859 0.483992197258 y[1] (closed_form) = -0.0156171900859 0.483992197258 absolute error = 5.001e-32 relative error = 1.033e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.065 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.065 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.065 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5696 2.07 h = 0.0001 0.005 y[1] (numeric) = -0.0162247438085 0.482546259822 y[1] (closed_form) = -0.0162247438085 0.482546259822 absolute error = 5.001e-32 relative error = 1.036e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.071 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.071 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.071 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5697 2.075 h = 0.0001 0.003 y[1] (numeric) = -0.0161698813207 0.481384558685 y[1] (closed_form) = -0.0161698813207 0.481384558685 absolute error = 5.001e-32 relative error = 1.038e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.076 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.076 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.076 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5698 2.078 h = 0.001 0.001 y[1] (numeric) = -0.0161463589623 0.48068959776 y[1] (closed_form) = -0.0161463589623 0.48068959776 absolute error = 5e-32 relative error = 1.040e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.079 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.079 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.079 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5708 2.079 h = 0.001 0.003 y[1] (numeric) = -0.0163614167068 0.48044329567 y[1] (closed_form) = -0.0163614167068 0.48044329567 absolute error = 4e-32 relative error = 8.321e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.08 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.08 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.08 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5718 2.082 h = 0.0001 0.004 y[1] (numeric) = -0.0165442391434 0.479736850927 y[1] (closed_form) = -0.0165442391434 0.479736850927 absolute error = 5.001e-32 relative error = 1.042e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.083 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.083 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.083 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5719 2.086 h = 0.003 0.006 y[1] (numeric) = -0.0165038258198 0.47881753352 y[1] (closed_form) = -0.0165038258198 0.47881753352 absolute error = 4e-32 relative error = 8.349e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.087 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.087 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.087 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5749 2.092 h = 0.0001 0.005 y[1] (numeric) = -0.0170923630749 0.477399513387 y[1] (closed_form) = -0.0170923630749 0.477399513387 absolute error = 5e-32 relative error = 1.047e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.093 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.093 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.093 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.575 2.097 h = 0.0001 0.003 y[1] (numeric) = -0.0170337090288 0.476262504446 y[1] (closed_form) = -0.0170337090288 0.476262504446 absolute error = 4e-32 relative error = 8.393e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.098 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.098 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.098 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5751 2.1 h = 0.001 0.001 y[1] (numeric) = -0.0170077270407 0.475582247476 y[1] (closed_form) = -0.0170077270407 0.475582247476 absolute error = 4e-32 relative error = 8.405e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.101 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.101 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.101 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5761 2.101 h = 0.001 0.003 y[1] (numeric) = -0.0172172249145 0.475340204276 y[1] (closed_form) = -0.0172172249145 0.475340204276 absolute error = 4e-32 relative error = 8.410e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.102 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.102 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.102 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5771 2.104 h = 0.0001 0.004 y[1] (numeric) = -0.0173932251845 0.474647805294 y[1] (closed_form) = -0.0173932251845 0.474647805294 absolute error = 4.001e-32 relative error = 8.424e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.105 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.105 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.105 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5772 2.108 h = 0.003 0.006 y[1] (numeric) = -0.0173497811896 0.473747911239 y[1] (closed_form) = -0.0173497811896 0.473747911239 absolute error = 4.001e-32 relative error = 8.440e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.109 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.109 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.109 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1204.6MB, alloc=52.3MB, time=14.13 x[1] = 0.5802 2.114 h = 0.0001 0.005 y[1] (numeric) = -0.0179200736294 0.472357053025 y[1] (closed_form) = -0.0179200736294 0.472357053025 absolute error = 5.001e-32 relative error = 1.058e-29 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.116 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.116 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.116 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5803 2.119 h = 0.0001 0.003 y[1] (numeric) = -0.0178579010078 0.471243987989 y[1] (closed_form) = -0.0178579010078 0.471243987989 absolute error = 4.001e-32 relative error = 8.485e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.121 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.121 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.121 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5804 2.122 h = 0.001 0.001 y[1] (numeric) = -0.0178296279523 0.470577991476 y[1] (closed_form) = -0.0178296279523 0.470577991476 absolute error = 4.001e-32 relative error = 8.497e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.124 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.124 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.124 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5814 2.123 h = 0.0001 0.004 y[1] (numeric) = -0.0180337658383 0.470340109025 y[1] (closed_form) = -0.0180337658383 0.470340109025 absolute error = 3.007e-32 relative error = 6.388e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.125 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.125 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.125 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5815 2.127 h = 0.003 0.006 y[1] (numeric) = -0.0179881074331 0.469456497059 y[1] (closed_form) = -0.0179881074331 0.469456497059 absolute error = 4.001e-32 relative error = 8.517e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.129 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.129 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.129 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5845 2.133 h = 0.0001 0.005 y[1] (numeric) = -0.0185435958567 0.468088638608 y[1] (closed_form) = -0.0185435958567 0.468088638608 absolute error = 4.001e-32 relative error = 8.541e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.135 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.135 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.135 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5846 2.138 h = 0.0001 0.003 y[1] (numeric) = -0.0184788734796 0.466995644202 y[1] (closed_form) = -0.0184788734796 0.466995644202 absolute error = 3.002e-32 relative error = 6.423e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.14 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.14 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.14 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5847 2.141 h = 0.001 0.001 y[1] (numeric) = -0.018448918242 0.466341605149 y[1] (closed_form) = -0.018448918242 0.466341605149 absolute error = 3.007e-32 relative error = 6.442e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.143 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.143 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.143 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5857 2.142 h = 0.001 0.003 y[1] (numeric) = -0.018648643602 0.466107288162 y[1] (closed_form) = -0.018648643602 0.466107288162 absolute error = 3.007e-32 relative error = 6.445e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.144 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.144 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.144 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5867 2.145 h = 0.0001 0.004 y[1] (numeric) = -0.0188128918147 0.465440057007 y[1] (closed_form) = -0.0188128918147 0.465440057007 absolute error = 3.002e-32 relative error = 6.444e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.147 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.147 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.147 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5868 2.149 h = 0.003 0.006 y[1] (numeric) = -0.0187645845463 0.464574794817 y[1] (closed_form) = -0.0187645845463 0.464574794817 absolute error = 4.001e-32 relative error = 8.606e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.151 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.151 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.151 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5898 2.155 h = 0.0001 0.005 y[1] (numeric) = -0.0193031559 0.463232750162 y[1] (closed_form) = -0.0193031559 0.463232750162 absolute error = 3.002e-32 relative error = 6.474e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.157 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.157 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.157 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5899 2.16 h = 0.0001 0.003 y[1] (numeric) = -0.019235369417 0.462162379764 y[1] (closed_form) = -0.019235369417 0.462162379764 absolute error = 3.002e-32 relative error = 6.489e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.162 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.162 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.162 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.59 2.163 h = 0.001 0.001 y[1] (numeric) = -0.0192034043795 0.461521818588 y[1] (closed_form) = -0.0192034043795 0.461521818588 absolute error = 3e-32 relative error = 6.495e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.165 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.165 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.165 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.591 2.164 h = 0.001 0.003 y[1] (numeric) = -0.0193981169331 0.461291483992 y[1] (closed_form) = -0.0193981169331 0.461291483992 absolute error = 2.002e-32 relative error = 4.337e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.166 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.166 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.166 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.592 2.167 h = 0.0001 0.004 y[1] (numeric) = -0.0195563555711 0.460637201332 y[1] (closed_form) = -0.0195563555711 0.460637201332 absolute error = 3.002e-32 relative error = 6.510e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.169 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.169 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.169 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5921 2.171 h = 0.003 0.006 y[1] (numeric) = -0.0195055898033 0.45978974444 y[1] (closed_form) = -0.0195055898033 0.45978974444 absolute error = 3.002e-32 relative error = 6.522e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.173 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.173 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.173 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5951 2.177 h = 0.0001 0.005 y[1] (numeric) = -0.0200279126766 0.458472827517 y[1] (closed_form) = -0.0200279126766 0.458472827517 absolute error = 3.002e-32 relative error = 6.541e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.179 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.179 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.179 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5952 2.182 h = 0.0001 0.003 y[1] (numeric) = -0.0199572887188 0.457424411601 y[1] (closed_form) = -0.0199572887188 0.457424411601 absolute error = 3.002e-32 relative error = 6.556e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.184 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.184 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.184 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5953 2.185 h = 0.001 0.001 y[1] (numeric) = -0.019923454256 0.456796931263 y[1] (closed_form) = -0.019923454256 0.456796931263 absolute error = 3.002e-32 relative error = 6.565e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.187 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.187 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.187 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1249.7MB, alloc=52.3MB, time=14.66 x[1] = 0.5963 2.186 h = 0.001 0.003 y[1] (numeric) = -0.0201133293584 0.456570487824 y[1] (closed_form) = -0.0201133293584 0.456570487824 absolute error = 3.002e-32 relative error = 6.568e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.188 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.188 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.188 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5973 2.189 h = 0.0001 0.004 y[1] (numeric) = -0.0202658163194 0.455928796744 y[1] (closed_form) = -0.0202658163194 0.455928796744 absolute error = 3.002e-32 relative error = 6.577e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.191 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.191 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.191 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5974 2.193 h = 0.003 0.006 y[1] (numeric) = -0.0202127704965 0.455098621137 y[1] (closed_form) = -0.0202127704965 0.455098621137 absolute error = 3.002e-32 relative error = 6.589e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.195 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.195 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.195 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6004 2.199 h = 0.0001 0.005 y[1] (numeric) = -0.0207194812628 0.453806168295 y[1] (closed_form) = -0.0207194812628 0.453806168295 absolute error = 3.002e-32 relative error = 6.608e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.201 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.201 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.201 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6005 2.204 h = 0.0001 0.003 y[1] (numeric) = -0.0206462322039 0.452779062461 y[1] (closed_form) = -0.0206462322039 0.452779062461 absolute error = 4.001e-32 relative error = 8.828e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.206 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.206 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.206 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6006 2.207 h = 0.001 0.001 y[1] (numeric) = -0.0206106600104 0.452164280744 y[1] (closed_form) = -0.0206106600104 0.452164280744 absolute error = 4e-32 relative error = 8.837e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.209 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.209 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.209 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6016 2.208 h = 0.001 0.003 y[1] (numeric) = -0.0207958652973 0.451941639532 y[1] (closed_form) = -0.0207958652973 0.451941639532 absolute error = 3.002e-32 relative error = 6.635e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.21 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.21 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.21 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6026 2.211 h = 0.0001 0.004 y[1] (numeric) = -0.0209428454317 0.451312195413 y[1] (closed_form) = -0.0209428454317 0.451312195413 absolute error = 3.002e-32 relative error = 6.644e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.213 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.213 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.213 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6027 2.215 h = 0.003 0.006 y[1] (numeric) = -0.0208876868691 0.45049879664 y[1] (closed_form) = -0.0208876868691 0.45049879664 absolute error = 2.002e-32 relative error = 4.440e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.217 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.217 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.217 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6057 2.221 h = 0.0001 0.005 y[1] (numeric) = -0.0213793915032 0.449230165834 y[1] (closed_form) = -0.0213793915032 0.449230165834 absolute error = 2.002e-32 relative error = 4.453e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.224 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.224 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.224 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6058 2.226 h = 0.0001 0.003 y[1] (numeric) = -0.0213037164047 0.448223749688 y[1] (closed_form) = -0.0213037164047 0.448223749688 absolute error = 2.002e-32 relative error = 4.463e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.229 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.229 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.229 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6059 2.229 h = 0.001 0.001 y[1] (numeric) = -0.0212665300657 0.447621298549 y[1] (closed_form) = -0.0212665300657 0.447621298549 absolute error = 2.002e-32 relative error = 4.469e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.232 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.232 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.232 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6069 2.23 h = 0.0001 0.004 y[1] (numeric) = -0.0214472258576 0.447402372895 y[1] (closed_form) = -0.0214472258576 0.447402372895 absolute error = 1.005e-32 relative error = 2.244e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.233 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.233 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.233 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.607 2.234 h = 0.003 0.006 y[1] (numeric) = -0.0213905667601 0.446603048056 y[1] (closed_form) = -0.0213905667601 0.446603048056 absolute error = 1e-32 relative error = 2.237e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.237 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.237 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.237 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.61 2.24 h = 0.0001 0.005 y[1] (numeric) = -0.0218700916556 0.445354593713 y[1] (closed_form) = -0.0218700916556 0.445354593713 absolute error = 1.005e-32 relative error = 2.254e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.243 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.243 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.243 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6101 2.245 h = 0.0001 0.003 y[1] (numeric) = -0.0217927150144 0.444365533219 y[1] (closed_form) = -0.0217927150144 0.444365533219 absolute error = 1.005e-32 relative error = 2.259e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.248 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.248 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.248 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6102 2.248 h = 0.001 0.001 y[1] (numeric) = -0.0217543736023 0.443773428839 y[1] (closed_form) = -0.0217543736023 0.443773428839 absolute error = 1.020e-32 relative error = 2.295e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.251 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.251 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.251 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6112 2.249 h = 0.001 0.003 y[1] (numeric) = -0.0219313537426 0.443557684955 y[1] (closed_form) = -0.0219313537426 0.443557684955 absolute error = 1.020e-32 relative error = 2.296e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.252 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.252 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.252 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6122 2.252 h = 0.0001 0.004 y[1] (numeric) = -0.0220688338178 0.442950211743 y[1] (closed_form) = -0.0220688338178 0.442950211743 absolute error = 1.020e-32 relative error = 2.299e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.255 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.255 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.255 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6123 2.256 h = 0.003 0.006 y[1] (numeric) = -0.0220103406697 0.442166772492 y[1] (closed_form) = -0.0220103406697 0.442166772492 absolute error = 1.005e-32 relative error = 2.270e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.259 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.259 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.259 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6153 2.262 h = 0.0001 0.005 y[1] (numeric) = -0.0224759047726 0.44094099389 y[1] (closed_form) = -0.0224759047726 0.44094099389 absolute error = 1.020e-32 relative error = 2.310e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.265 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.265 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.265 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1294.8MB, alloc=52.3MB, time=15.18 x[1] = 0.6154 2.267 h = 0.0001 0.003 y[1] (numeric) = -0.0223964332644 0.439971526952 y[1] (closed_form) = -0.0223964332644 0.439971526952 absolute error = 1.020e-32 relative error = 2.315e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.27 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.27 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.27 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6155 2.27 h = 0.001 0.001 y[1] (numeric) = -0.0223566838573 0.43939110265 y[1] (closed_form) = -0.0223566838573 0.43939110265 absolute error = 1.020e-32 relative error = 2.318e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.273 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.273 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.273 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6165 2.271 h = 0.001 0.003 y[1] (numeric) = -0.0225294336656 0.439178917207 y[1] (closed_form) = -0.0225294336656 0.439178917207 absolute error = 1.020e-32 relative error = 2.319e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.274 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.274 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.274 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6175 2.274 h = 0.0001 0.004 y[1] (numeric) = -0.0226620382748 0.438582766272 y[1] (closed_form) = -0.0226620382748 0.438582766272 absolute error = 1.020e-32 relative error = 2.322e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.277 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.277 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.277 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6176 2.278 h = 0.003 0.006 y[1] (numeric) = -0.0226018506272 0.437814759599 y[1] (closed_form) = -0.0226018506272 0.437814759599 absolute error = 1.020e-32 relative error = 2.326e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.281 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.281 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.281 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6206 2.284 h = 0.0001 0.005 y[1] (numeric) = -0.023053982203 0.436611072568 y[1] (closed_form) = -0.023053982203 0.436611072568 absolute error = 1.020e-32 relative error = 2.332e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.287 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.287 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.287 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6207 2.289 h = 0.0001 0.003 y[1] (numeric) = -0.022972581687 0.435660641936 y[1] (closed_form) = -0.022972581687 0.435660641936 absolute error = 1.020e-32 relative error = 2.338e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.292 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.292 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.292 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6208 2.292 h = 0.001 0.001 y[1] (numeric) = -0.0229315276127 0.435091566957 y[1] (closed_form) = -0.0229315276127 0.435091566957 absolute error = 1.020e-32 relative error = 2.341e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.295 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.295 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.295 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6218 2.293 h = 0.001 0.003 y[1] (numeric) = -0.0231001885294 0.434882859589 y[1] (closed_form) = -0.0231001885294 0.434882859589 absolute error = 1.044e-32 relative error = 2.397e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.296 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.296 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.296 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6228 2.296 h = 0.0001 0.004 y[1] (numeric) = -0.0232281189833 0.434297729525 y[1] (closed_form) = -0.0232281189833 0.434297729525 absolute error = 1.020e-32 relative error = 2.345e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.299 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.299 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.299 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6229 2.3 h = 0.003 0.006 y[1] (numeric) = -0.0231663678039 0.433544718868 y[1] (closed_form) = -0.0231663678039 0.433544718868 absolute error = 1.020e-32 relative error = 2.349e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.303 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.303 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.303 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6259 2.306 h = 0.0001 0.005 y[1] (numeric) = -0.0236055707054 0.432362557957 y[1] (closed_form) = -0.0236055707054 0.432362557957 absolute error = 1.044e-32 relative error = 2.411e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.309 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.309 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.309 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.626 2.311 h = 0.0001 0.003 y[1] (numeric) = -0.0235223967754 0.431430626571 y[1] (closed_form) = -0.0235223967754 0.431430626571 absolute error = 1.020e-32 relative error = 2.360e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.314 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.314 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.314 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6261 2.314 h = 0.001 0.001 y[1] (numeric) = -0.0234801350916 0.430872582094 y[1] (closed_form) = -0.0234801350916 0.430872582094 absolute error = 1.020e-32 relative error = 2.363e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.317 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.317 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.317 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6271 2.315 h = 0.001 0.003 y[1] (numeric) = -0.023644842588 0.430667274517 y[1] (closed_form) = -0.023644842588 0.430667274517 absolute error = 1.020e-32 relative error = 2.364e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.318 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.318 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.318 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6281 2.318 h = 0.0001 0.004 y[1] (numeric) = -0.0237682904069 0.430092874029 y[1] (closed_form) = -0.0237682904069 0.430092874029 absolute error = 2.010e-32 relative error = 4.666e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.322 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.322 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.322 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6282 2.322 h = 0.003 0.006 y[1] (numeric) = -0.0237050986324 0.429354438568 y[1] (closed_form) = -0.0237050986324 0.429354438568 absolute error = 1.020e-32 relative error = 2.372e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.326 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.326 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.326 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6312 2.328 h = 0.0001 0.005 y[1] (numeric) = -0.024131853623 0.428193256359 y[1] (closed_form) = -0.024131853623 0.428193256359 absolute error = 1.020e-32 relative error = 2.378e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.332 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.332 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.332 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6313 2.333 h = 0.0001 0.003 y[1] (numeric) = -0.0240470522683 0.427279306488 y[1] (closed_form) = -0.0240470522683 0.427279306488 absolute error = 1.020e-32 relative error = 2.383e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.337 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.337 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.337 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6314 2.336 h = 0.001 0.001 y[1] (numeric) = -0.0240036741624 0.426731985109 y[1] (closed_form) = -0.0240036741624 0.426731985109 absolute error = 1.020e-32 relative error = 2.386e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.34 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.34 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.34 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6324 2.337 h = 0.0001 0.004 y[1] (numeric) = -0.0241645580413 0.426530001076 y[1] (closed_form) = -0.0241645580413 0.426530001076 absolute error = 1.020e-32 relative error = 2.387e-30 % Correct digits = 32 memory used=1340.1MB, alloc=52.3MB, time=15.71 Radius of convergence (given) for eq 1 = 2.341 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.341 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.341 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6325 2.341 h = 0.003 0.006 y[1] (numeric) = -0.02410038602 0.425803801304 y[1] (closed_form) = -0.02410038602 0.425803801304 absolute error = 2e-33 relative error = 4.689e-31 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.345 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.345 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.345 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6355 2.347 h = 0.0001 0.005 y[1] (numeric) = -0.0245170358795 0.424660392688 y[1] (closed_form) = -0.0245170358795 0.424660392688 absolute error = 1.005e-32 relative error = 2.363e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.351 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.351 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.351 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6356 2.352 h = 0.0001 0.003 y[1] (numeric) = -0.0244311498631 0.423761537448 y[1] (closed_form) = -0.0244311498631 0.423761537448 absolute error = 1.005e-32 relative error = 2.368e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.356 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.356 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.356 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6357 2.355 h = 0.001 0.001 y[1] (numeric) = -0.0243870025443 0.423223220278 y[1] (closed_form) = -0.0243870025443 0.423223220278 absolute error = 1.005e-32 relative error = 2.371e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.359 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.359 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.359 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6367 2.356 h = 0.001 0.003 y[1] (numeric) = -0.0245447333952 0.423024081046 y[1] (closed_form) = -0.0245447333952 0.423024081046 absolute error = 1.005e-32 relative error = 2.372e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.36 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.36 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.36 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6377 2.359 h = 0.0001 0.004 y[1] (numeric) = -0.0246604386099 0.42246895193 y[1] (closed_form) = -0.0246604386099 0.42246895193 absolute error = 1.005e-32 relative error = 2.375e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.363 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.363 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.363 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6378 2.363 h = 0.003 0.006 y[1] (numeric) = -0.0245950305073 0.421756582648 y[1] (closed_form) = -0.0245950305073 0.421756582648 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 2.367 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.367 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.367 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6408 2.369 h = 0.0001 0.005 y[1] (numeric) = -0.0250000637431 0.420633174768 y[1] (closed_form) = -0.0250000637431 0.420633174768 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 2.373 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.373 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.373 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6409 2.374 h = 0.0001 0.003 y[1] (numeric) = -0.0249127928042 0.419751384791 y[1] (closed_form) = -0.0249127928042 0.419751384791 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 2.378 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.378 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.378 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.641 2.377 h = 0.001 0.001 y[1] (numeric) = -0.0248676810094 0.41922324652 y[1] (closed_form) = -0.0248676810094 0.41922324652 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 2.381 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.381 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.381 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.642 2.378 h = 0.001 0.003 y[1] (numeric) = -0.0250218147935 0.419027292809 y[1] (closed_form) = -0.0250218147935 0.419027292809 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 2.382 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.382 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.382 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.643 2.381 h = 0.0001 0.004 y[1] (numeric) = -0.0251335328784 0.418482110373 y[1] (closed_form) = -0.0251335328784 0.418482110373 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 2.385 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.385 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.385 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6431 2.385 h = 0.003 0.006 y[1] (numeric) = -0.0250669915349 0.417783192248 y[1] (closed_form) = -0.0250669915349 0.417783192248 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 2.389 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.389 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.389 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6461 2.391 h = 0.0001 0.005 y[1] (numeric) = -0.0254608296455 0.416679285984 y[1] (closed_form) = -0.0254608296455 0.416679285984 absolute error = 1e-32 relative error = 2.395e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.395 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.395 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.395 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6462 2.396 h = 0.0001 0.003 y[1] (numeric) = -0.025372295748 0.415814094475 y[1] (closed_form) = -0.025372295748 0.415814094475 absolute error = 1e-32 relative error = 2.400e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.4 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.4 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.4 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6463 2.399 h = 0.001 0.001 y[1] (numeric) = -0.025326295956 0.415295857816 y[1] (closed_form) = -0.025326295956 0.415295857816 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 2.403 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.403 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.403 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6473 2.4 h = 0.001 0.003 y[1] (numeric) = -0.0254769477909 0.415103018996 y[1] (closed_form) = -0.0254769477909 0.415103018996 absolute error = 1e-33 relative error = 2.405e-31 % Correct digits = 33 Radius of convergence (given) for eq 1 = 2.405 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.405 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.405 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6483 2.403 h = 0.0001 0.004 y[1] (numeric) = -0.025584837424 0.414567527511 y[1] (closed_form) = -0.025584837424 0.414567527511 absolute error = 1e-33 relative error = 2.408e-31 % Correct digits = 33 Radius of convergence (given) for eq 1 = 2.408 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.408 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.408 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6484 2.407 h = 0.003 0.006 y[1] (numeric) = -0.0255172594375 0.413881694516 y[1] (closed_form) = -0.0255172594375 0.413881694516 absolute error = 1e-33 relative error = 2.412e-31 % Correct digits = 33 Radius of convergence (given) for eq 1 = 2.412 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.412 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.412 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6514 2.413 h = 0.0001 0.005 y[1] (numeric) = -0.0259003052158 0.412796806378 y[1] (closed_form) = -0.0259003052158 0.412796806378 absolute error = 1e-33 relative error = 2.418e-31 % Correct digits = 33 Radius of convergence (given) for eq 1 = 2.418 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.418 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.418 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1385.2MB, alloc=52.3MB, time=16.24 x[1] = 0.6515 2.418 h = 0.0001 0.003 y[1] (numeric) = -0.0258106228602 0.411947762877 y[1] (closed_form) = -0.0258106228602 0.411947762877 absolute error = 1e-33 relative error = 2.423e-31 % Correct digits = 33 Radius of convergence (given) for eq 1 = 2.423 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.423 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.423 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6516 2.421 h = 0.001 0.001 y[1] (numeric) = -0.0257638069754 0.411439160208 y[1] (closed_form) = -0.0257638069754 0.411439160208 absolute error = 1e-33 relative error = 2.426e-31 % Correct digits = 33 Radius of convergence (given) for eq 1 = 2.426 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.426 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.426 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6526 2.422 h = 0.001 0.003 y[1] (numeric) = -0.0259110873162 0.411249367496 y[1] (closed_form) = -0.0259110873162 0.411249367496 absolute error = 1.005e-32 relative error = 2.439e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.427 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.427 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.427 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6536 2.425 h = 0.0001 0.004 y[1] (numeric) = -0.0260152997468 0.410723319571 y[1] (closed_form) = -0.0260152997468 0.410723319571 absolute error = 1e-32 relative error = 2.430e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.43 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.43 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.43 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6537 2.429 h = 0.003 0.006 y[1] (numeric) = -0.0259467758632 0.410050218423 y[1] (closed_form) = -0.0259467758632 0.410050218423 absolute error = 1e-32 relative error = 2.434e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.434 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.434 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.434 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6567 2.435 h = 0.0001 0.005 y[1] (numeric) = -0.0263194143712 0.408983879987 y[1] (closed_form) = -0.0263194143712 0.408983879987 absolute error = 1e-32 relative error = 2.440e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.44 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.44 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.44 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6568 2.44 h = 0.0001 0.003 y[1] (numeric) = -0.026228691062 0.408150549689 y[1] (closed_form) = -0.026228691062 0.408150549689 absolute error = 1e-32 relative error = 2.445e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.445 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.445 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.445 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6569 2.443 h = 0.001 0.001 y[1] (numeric) = -0.0261811266979 0.407651322645 y[1] (closed_form) = -0.0261811266979 0.407651322645 absolute error = 1e-32 relative error = 2.448e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.448 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.448 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.448 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6579 2.444 h = 0.0001 0.004 y[1] (numeric) = -0.0263251415634 0.407464509062 y[1] (closed_form) = -0.0263251415634 0.407464509062 absolute error = 1e-33 relative error = 2.449e-31 % Correct digits = 33 Radius of convergence (given) for eq 1 = 2.449 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.449 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.449 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.658 2.448 h = 0.003 0.006 y[1] (numeric) = -0.026256018112 0.406802103406 y[1] (closed_form) = -0.026256018112 0.406802103406 absolute error = 1e-33 relative error = 2.453e-31 % Correct digits = 33 Radius of convergence (given) for eq 1 = 2.453 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.453 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.453 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.661 2.454 h = 0.0001 0.005 y[1] (numeric) = -0.0266202075153 0.405751485978 y[1] (closed_form) = -0.0266202075153 0.405751485978 absolute error = 1e-33 relative error = 2.459e-31 % Correct digits = 33 Radius of convergence (given) for eq 1 = 2.459 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.459 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.459 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6611 2.459 h = 0.0001 0.003 y[1] (numeric) = -0.0265288496605 0.404931355152 y[1] (closed_form) = -0.0265288496605 0.404931355152 absolute error = 1.005e-32 relative error = 2.477e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.464 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.464 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.464 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6612 2.462 h = 0.001 0.001 y[1] (numeric) = -0.0264807997512 0.404440006125 y[1] (closed_form) = -0.0264807997512 0.404440006125 absolute error = 1e-33 relative error = 2.467e-31 % Correct digits = 33 Radius of convergence (given) for eq 1 = 2.467 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.467 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.467 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6622 2.463 h = 0.001 0.003 y[1] (numeric) = -0.0266221199052 0.40425574184 y[1] (closed_form) = -0.0266221199052 0.40425574184 absolute error = 1e-32 relative error = 2.468e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.468 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.468 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.468 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6632 2.466 h = 0.0001 0.004 y[1] (numeric) = -0.0267199745877 0.403746674837 y[1] (closed_form) = -0.0267199745877 0.403746674837 absolute error = 1e-32 relative error = 2.471e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.471 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.471 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.471 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6633 2.47 h = 0.003 0.006 y[1] (numeric) = -0.0266500558756 0.403096374848 y[1] (closed_form) = -0.0266500558756 0.403096374848 absolute error = 1e-32 relative error = 2.475e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.475 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.475 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.475 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6663 2.476 h = 0.0001 0.005 y[1] (numeric) = -0.0270045052495 0.402063469619 y[1] (closed_form) = -0.0270045052495 0.402063469619 absolute error = 1.005e-32 relative error = 2.494e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.482 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.482 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.482 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6664 2.481 h = 0.0001 0.003 y[1] (numeric) = -0.0269122845645 0.401258281277 y[1] (closed_form) = -0.0269122845645 0.401258281277 absolute error = 1.005e-32 relative error = 2.499e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.487 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.487 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.487 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6665 2.484 h = 0.001 0.001 y[1] (numeric) = -0.0268635986259 0.40077584977 y[1] (closed_form) = -0.0268635986259 0.40077584977 absolute error = 1.005e-32 relative error = 2.502e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.49 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.49 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.49 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6675 2.485 h = 0.001 0.003 y[1] (numeric) = -0.0270018387446 0.400594443465 y[1] (closed_form) = -0.0270018387446 0.400594443465 absolute error = 1.005e-32 relative error = 2.503e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.491 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.491 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.491 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6685 2.488 h = 0.0001 0.004 y[1] (numeric) = -0.0270964087409 0.40009415399 y[1] (closed_form) = -0.0270964087409 0.40009415399 absolute error = 1.005e-32 relative error = 2.506e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.494 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.494 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.494 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1430.2MB, alloc=52.3MB, time=16.76 x[1] = 0.6686 2.492 h = 0.003 0.006 y[1] (numeric) = -0.0270257708325 0.399455640063 y[1] (closed_form) = -0.0270257708325 0.399455640063 absolute error = 1.005e-32 relative error = 2.510e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.498 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.498 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.498 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6716 2.498 h = 0.0001 0.005 y[1] (numeric) = -0.0273708195571 0.398440018961 y[1] (closed_form) = -0.0273708195571 0.398440018961 absolute error = 1.020e-32 relative error = 2.553e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.504 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.504 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.504 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6717 2.503 h = 0.0001 0.003 y[1] (numeric) = -0.0272778260035 0.397649379654 y[1] (closed_form) = -0.0272778260035 0.397649379654 absolute error = 1.005e-32 relative error = 2.521e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.509 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.509 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.509 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6718 2.506 h = 0.001 0.001 y[1] (numeric) = -0.0272285608699 0.397175631781 y[1] (closed_form) = -0.0272285608699 0.397175631781 absolute error = 2.002e-32 relative error = 5.030e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.512 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.512 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.512 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6728 2.507 h = 0.001 0.003 y[1] (numeric) = -0.0273638154371 0.396997021417 y[1] (closed_form) = -0.0273638154371 0.396997021417 absolute error = 1.005e-32 relative error = 2.525e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.513 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.513 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.513 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6738 2.51 h = 0.0001 0.004 y[1] (numeric) = -0.0274552269542 0.396505291456 y[1] (closed_form) = -0.0274552269542 0.396505291456 absolute error = 1.005e-32 relative error = 2.529e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.516 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.516 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.516 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6739 2.514 h = 0.003 0.006 y[1] (numeric) = -0.0273839413334 0.395878254814 y[1] (closed_form) = -0.0273839413334 0.395878254814 absolute error = 2.002e-32 relative error = 5.046e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.52 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.52 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.52 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6769 2.52 h = 0.0001 0.005 y[1] (numeric) = -0.0277199143066 0.394879502841 y[1] (closed_form) = -0.0277199143066 0.394879502841 absolute error = 2.002e-32 relative error = 5.059e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.526 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.526 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.526 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.677 2.525 h = 0.0001 0.003 y[1] (numeric) = -0.0276262323719 0.394103032424 y[1] (closed_form) = -0.0276262323719 0.394103032424 absolute error = 2.002e-32 relative error = 5.069e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.531 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.531 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.531 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6771 2.528 h = 0.001 0.001 y[1] (numeric) = -0.0275764415105 0.393637742171 y[1] (closed_form) = -0.0275764415105 0.393637742171 absolute error = 2.002e-32 relative error = 5.075e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.534 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.534 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.534 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6781 2.529 h = 0.001 0.003 y[1] (numeric) = -0.0277088013333 0.393461867332 y[1] (closed_form) = -0.0277088013333 0.393461867332 absolute error = 1e-32 relative error = 2.535e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.535 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.535 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.535 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6791 2.532 h = 0.0001 0.004 y[1] (numeric) = -0.0277971748823 0.392978485774 y[1] (closed_form) = -0.0277971748823 0.392978485774 absolute error = 1e-32 relative error = 2.538e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.538 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.538 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.538 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6792 2.536 h = 0.003 0.006 y[1] (numeric) = -0.0277253087312 0.392362628027 y[1] (closed_form) = -0.0277253087312 0.392362628027 absolute error = 1e-32 relative error = 2.542e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.542 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.542 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.542 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6822 2.542 h = 0.0001 0.005 y[1] (numeric) = -0.0280525170957 0.391380342795 y[1] (closed_form) = -0.0280525170957 0.391380342795 absolute error = 1e-32 relative error = 2.549e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.549 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.549 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.549 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6823 2.547 h = 0.0001 0.003 y[1] (numeric) = -0.0279582261282 0.390617673882 y[1] (closed_form) = -0.0279582261282 0.390617673882 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 2.554 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.554 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.554 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6824 2.55 h = 0.001 0.001 y[1] (numeric) = -0.0279079598422 0.390160622794 y[1] (closed_form) = -0.0279079598422 0.390160622794 absolute error = 1e-32 relative error = 2.557e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.557 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.557 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.557 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6834 2.551 h = 0.0001 0.004 y[1] (numeric) = -0.0280375122223 0.389987424641 y[1] (closed_form) = -0.0280375122223 0.389987424641 absolute error = 1e-32 relative error = 2.558e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.558 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.558 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.558 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6835 2.555 h = 0.003 0.006 y[1] (numeric) = -0.0279653255871 0.389380963896 y[1] (closed_form) = -0.0279653255871 0.389380963896 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 2.562 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.562 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.562 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6865 2.561 h = 0.0001 0.005 y[1] (numeric) = -0.0282854186809 0.388412639366 y[1] (closed_form) = -0.0282854186809 0.388412639366 absolute error = 1e-33 relative error = 2.568e-31 % Correct digits = 33 Radius of convergence (given) for eq 1 = 2.568 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.568 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.568 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6866 2.566 h = 0.0001 0.003 y[1] (numeric) = -0.0281908220002 0.387661571557 y[1] (closed_form) = -0.0281908220002 0.387661571557 absolute error = 1e-32 relative error = 2.573e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.573 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.573 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.573 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1475.4MB, alloc=52.3MB, time=17.29 x[1] = 0.6867 2.569 h = 0.001 0.001 y[1] (numeric) = -0.0281402792287 0.387211447983 y[1] (closed_form) = -0.0281402792287 0.387211447983 absolute error = 1e-32 relative error = 2.576e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.576 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.576 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.576 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6877 2.57 h = 0.001 0.003 y[1] (numeric) = -0.0282675133672 0.387040539977 y[1] (closed_form) = -0.0282675133672 0.387040539977 absolute error = 1e-32 relative error = 2.577e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.577 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.577 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.577 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6887 2.573 h = 0.0001 0.004 y[1] (numeric) = -0.0283506302401 0.386572186581 y[1] (closed_form) = -0.0283506302401 0.386572186581 absolute error = 1e-32 relative error = 2.580e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.58 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.58 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.58 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6888 2.577 h = 0.003 0.006 y[1] (numeric) = -0.0282779742361 0.385976375035 y[1] (closed_form) = -0.0282779742361 0.385976375035 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 2.584 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.584 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.584 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6918 2.583 h = 0.0001 0.005 y[1] (numeric) = -0.0285898429345 0.385023797184 y[1] (closed_form) = -0.0285898429345 0.385023797184 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 2.59 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.59 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.59 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6919 2.588 h = 0.0001 0.003 y[1] (numeric) = -0.0284947682054 0.384285878664 y[1] (closed_form) = -0.0284947682054 0.384285878664 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 2.595 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.595 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.595 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.692 2.591 h = 0.001 0.001 y[1] (numeric) = -0.0284438334288 0.383843606323 y[1] (closed_form) = -0.0284438334288 0.383843606323 absolute error = 1e-33 relative error = 2.598e-31 % Correct digits = 33 Radius of convergence (given) for eq 1 = 2.598 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.598 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.598 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.693 2.592 h = 0.001 0.003 y[1] (numeric) = -0.0285684131342 0.383675268621 y[1] (closed_form) = -0.0285684131342 0.383675268621 absolute error = 1e-32 relative error = 2.599e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.599 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.599 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.599 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.694 2.595 h = 0.0001 0.004 y[1] (numeric) = -0.0286488056623 0.383214694297 y[1] (closed_form) = -0.0286488056623 0.383214694297 absolute error = 1e-32 relative error = 2.602e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.602 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.602 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.602 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6941 2.599 h = 0.003 0.006 y[1] (numeric) = -0.0285757366576 0.382629261068 y[1] (closed_form) = -0.0285757366576 0.382629261068 absolute error = 1.005e-32 relative error = 2.619e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.606 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.606 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.606 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6971 2.605 h = 0.0001 0.005 y[1] (numeric) = -0.0288796565386 0.381692061304 y[1] (closed_form) = -0.0288796565386 0.381692061304 absolute error = 1.005e-32 relative error = 2.625e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.612 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.612 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.612 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6972 2.61 h = 0.0001 0.003 y[1] (numeric) = -0.0287841701964 0.380966958482 y[1] (closed_form) = -0.0287841701964 0.380966958482 absolute error = 1.005e-32 relative error = 2.630e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.617 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.617 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.617 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6973 2.613 h = 0.001 0.001 y[1] (numeric) = -0.0287328857528 0.380532338936 y[1] (closed_form) = -0.0287328857528 0.380532338936 absolute error = 1.005e-32 relative error = 2.634e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.62 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.62 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.62 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6983 2.614 h = 0.001 0.003 y[1] (numeric) = -0.0288548891828 0.380366517014 y[1] (closed_form) = -0.0288548891828 0.380366517014 absolute error = 1e-33 relative error = 2.622e-31 % Correct digits = 33 Radius of convergence (given) for eq 1 = 2.622 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.622 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.622 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6993 2.617 h = 0.0001 0.004 y[1] (numeric) = -0.0289326585897 0.379913535018 y[1] (closed_form) = -0.0289326585897 0.379913535018 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 2.625 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.625 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.625 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6994 2.621 h = 0.003 0.006 y[1] (numeric) = -0.0288592295643 0.379338218094 y[1] (closed_form) = -0.0288592295643 0.379338218094 absolute error = 1e-33 relative error = 2.629e-31 % Correct digits = 33 Radius of convergence (given) for eq 1 = 2.629 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.629 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.629 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7024 2.627 h = 0.0001 0.005 y[1] (numeric) = -0.0291554648845 0.378416038792 y[1] (closed_form) = -0.0291554648845 0.378416038792 absolute error = 1e-33 relative error = 2.635e-31 % Correct digits = 33 Radius of convergence (given) for eq 1 = 2.635 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.635 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.635 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7025 2.632 h = 0.0001 0.003 y[1] (numeric) = -0.029059629319 0.377703428975 y[1] (closed_form) = -0.029059629319 0.377703428975 absolute error = 2e-33 relative error = 5.280e-31 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.64 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.64 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.64 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7026 2.635 h = 0.001 0.001 y[1] (numeric) = -0.0290080350482 0.377276270246 y[1] (closed_form) = -0.0290080350482 0.377276270246 absolute error = 1.005e-32 relative error = 2.656e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.643 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.643 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.643 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7036 2.636 h = 0.001 0.003 y[1] (numeric) = -0.0291275374348 0.377112910993 y[1] (closed_form) = -0.0291275374348 0.377112910993 absolute error = 1e-33 relative error = 2.644e-31 % Correct digits = 33 Radius of convergence (given) for eq 1 = 2.644 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.644 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.644 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7046 2.639 h = 0.0001 0.004 y[1] (numeric) = -0.029202780534 0.376667340319 y[1] (closed_form) = -0.029202780534 0.376667340319 absolute error = 1.020e-32 relative error = 2.699e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.647 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.647 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.647 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1520.5MB, alloc=52.3MB, time=17.81 x[1] = 0.7047 2.643 h = 0.003 0.006 y[1] (numeric) = -0.0291290412815 0.376101886209 y[1] (closed_form) = -0.0291290412815 0.376101886209 absolute error = 1e-33 relative error = 2.651e-31 % Correct digits = 33 Radius of convergence (given) for eq 1 = 2.651 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.651 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.651 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7077 2.649 h = 0.0001 0.005 y[1] (numeric) = -0.0294178455243 0.375194380326 y[1] (closed_form) = -0.0294178455243 0.375194380326 absolute error = 1e-33 relative error = 2.657e-31 % Correct digits = 33 Radius of convergence (given) for eq 1 = 2.657 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.657 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.657 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7078 2.654 h = 0.0001 0.003 y[1] (numeric) = -0.0293217193211 0.374493951291 y[1] (closed_form) = -0.0293217193211 0.374493951291 absolute error = 1e-33 relative error = 2.662e-31 % Correct digits = 33 Radius of convergence (given) for eq 1 = 2.662 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.662 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.662 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7079 2.657 h = 0.001 0.001 y[1] (numeric) = -0.0292698527116 0.374074067603 y[1] (closed_form) = -0.0292698527116 0.374074067603 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 2.665 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.665 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.665 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7089 2.658 h = 0.0001 0.004 y[1] (numeric) = -0.029386926493 0.373913119284 y[1] (closed_form) = -0.029386926493 0.373913119284 absolute error = 1e-33 relative error = 2.666e-31 % Correct digits = 33 Radius of convergence (given) for eq 1 = 2.666 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.666 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.666 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.709 2.662 h = 0.003 0.006 y[1] (numeric) = -0.0293130713156 0.373355960967 y[1] (closed_form) = -0.0293130713156 0.373355960967 absolute error = 1e-33 relative error = 2.670e-31 % Correct digits = 33 Radius of convergence (given) for eq 1 = 2.67 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.67 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.67 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.712 2.668 h = 0.0001 0.005 y[1] (numeric) = -0.0295958436267 0.372460899982 y[1] (closed_form) = -0.0295958436267 0.372460899982 absolute error = 1e-33 relative error = 2.676e-31 % Correct digits = 33 Radius of convergence (given) for eq 1 = 2.676 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.676 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.676 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7121 2.673 h = 0.0001 0.003 y[1] (numeric) = -0.0294996516517 0.371770716006 y[1] (closed_form) = -0.0294996516517 0.371770716006 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 2.681 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.681 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.681 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7122 2.676 h = 0.001 0.001 y[1] (numeric) = -0.0294476627079 0.371356952905 y[1] (closed_form) = -0.0294476627079 0.371356952905 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 2.684 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.684 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.684 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7132 2.677 h = 0.001 0.003 y[1] (numeric) = -0.029562729897 0.371198067234 y[1] (closed_form) = -0.029562729897 0.371198067234 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 2.685 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.685 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.685 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7142 2.68 h = 0.0001 0.004 y[1] (numeric) = -0.0296335990583 0.370765851896 y[1] (closed_form) = -0.0296335990583 0.370765851896 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 2.689 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.689 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.689 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7143 2.684 h = 0.003 0.006 y[1] (numeric) = -0.0295595156702 0.370218105735 y[1] (closed_form) = -0.0295595156702 0.370218105735 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 2.693 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.693 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.693 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7173 2.69 h = 0.0001 0.005 y[1] (numeric) = -0.0298352978014 0.369337096575 y[1] (closed_form) = -0.0298352978014 0.369337096575 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 2.699 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.699 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.699 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7174 2.695 h = 0.0001 0.003 y[1] (numeric) = -0.0297389113996 0.368658538279 y[1] (closed_form) = -0.0297389113996 0.368658538279 absolute error = 1e-33 relative error = 2.704e-31 % Correct digits = 33 Radius of convergence (given) for eq 1 = 2.704 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.704 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.704 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7175 2.698 h = 0.001 0.001 y[1] (numeric) = -0.0296867120332 0.368251719842 y[1] (closed_form) = -0.0296867120332 0.368251719842 absolute error = 1e-33 relative error = 2.707e-31 % Correct digits = 33 Radius of convergence (given) for eq 1 = 2.707 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.707 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.707 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7185 2.699 h = 0.001 0.003 y[1] (numeric) = -0.0297994778136 0.368095151574 y[1] (closed_form) = -0.0297994778136 0.368095151574 absolute error = 1e-33 relative error = 2.708e-31 % Correct digits = 33 Radius of convergence (given) for eq 1 = 2.708 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.708 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.708 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7195 2.702 h = 0.0001 0.004 y[1] (numeric) = -0.0298680732647 0.367669858593 y[1] (closed_form) = -0.0298680732647 0.367669858593 absolute error = 1e-33 relative error = 2.711e-31 % Correct digits = 33 Radius of convergence (given) for eq 1 = 2.711 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.711 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.711 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7196 2.706 h = 0.003 0.006 y[1] (numeric) = -0.0297938034359 0.367131293705 y[1] (closed_form) = -0.0297938034359 0.367131293705 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 2.715 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.715 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.715 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7226 2.712 h = 0.0001 0.005 y[1] (numeric) = -0.0300628209237 0.366264017722 y[1] (closed_form) = -0.0300628209237 0.366264017722 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 2.721 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.721 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.721 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7227 2.717 h = 0.0001 0.003 y[1] (numeric) = -0.0299662891089 0.365596800668 y[1] (closed_form) = -0.0299662891089 0.365596800668 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 2.726 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.726 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.726 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7228 2.72 h = 0.001 0.001 y[1] (numeric) = -0.0299139108794 0.365196757594 y[1] (closed_form) = -0.0299139108794 0.365196757594 absolute error = 1e-33 relative error = 2.729e-31 % Correct digits = 33 Radius of convergence (given) for eq 1 = 2.729 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.729 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.729 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1565.8MB, alloc=52.3MB, time=18.34 x[1] = 0.7238 2.721 h = 0.001 0.003 y[1] (numeric) = -0.0300244403774 0.365042458744 y[1] (closed_form) = -0.0300244403774 0.365042458744 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 2.73 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.73 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.73 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7248 2.724 h = 0.0001 0.004 y[1] (numeric) = -0.0300908439366 0.364623927417 y[1] (closed_form) = -0.0300908439366 0.364623927417 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 2.733 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.733 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.733 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7249 2.728 h = 0.003 0.006 y[1] (numeric) = -0.0300164269134 0.36409432023 y[1] (closed_form) = -0.0300164269134 0.36409432023 absolute error = 1e-33 relative error = 2.737e-31 % Correct digits = 33 Radius of convergence (given) for eq 1 = 2.737 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.737 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.737 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7279 2.734 h = 0.0001 0.005 y[1] (numeric) = -0.0302788963635 0.363240468002 y[1] (closed_form) = -0.0302788963635 0.363240468002 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 2.743 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.743 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.743 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.728 2.739 h = 0.0001 0.003 y[1] (numeric) = -0.0301822651393 0.362584316739 y[1] (closed_form) = -0.0301822651393 0.362584316739 absolute error = 1e-32 relative error = 2.748e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.748 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.748 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.748 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7281 2.742 h = 0.001 0.001 y[1] (numeric) = -0.0301297377393 0.362190885055 y[1] (closed_form) = -0.0301297377393 0.362190885055 absolute error = 1e-32 relative error = 2.751e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.751 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.751 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.751 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7291 2.743 h = 0.001 0.003 y[1] (numeric) = -0.0302380937338 0.362038808868 y[1] (closed_form) = -0.0302380937338 0.362038808868 absolute error = 1e-32 relative error = 2.753e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.753 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.753 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.753 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7301 2.746 h = 0.0001 0.004 y[1] (numeric) = -0.030302383774 0.361626883282 y[1] (closed_form) = -0.030302383774 0.361626883282 absolute error = 1e-32 relative error = 2.756e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.756 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.756 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.756 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7302 2.75 h = 0.003 0.006 y[1] (numeric) = -0.0302278564262 0.361106017255 y[1] (closed_form) = -0.0302278564262 0.361106017255 absolute error = 1.005e-32 relative error = 2.773e-30 % Correct digits = 32 Radius of convergence (given) for eq 1 = 2.76 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.76 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.76 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7332 2.756 h = 0.0001 0.005 y[1] (numeric) = -0.0304839859308 0.360265288273 y[1] (closed_form) = -0.0304839859308 0.360265288273 absolute error = 2.002e-32 relative error = 5.539e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.766 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.766 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.766 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7333 2.761 h = 0.0001 0.003 y[1] (numeric) = -0.0303872984666 0.35961993599 y[1] (closed_form) = -0.0303872984666 0.35961993599 absolute error = 2.002e-32 relative error = 5.549e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.771 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.771 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.771 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7334 2.764 h = 0.001 0.001 y[1] (numeric) = -0.0303346498294 0.359232956849 y[1] (closed_form) = -0.0303346498294 0.359232956849 absolute error = 2.002e-32 relative error = 5.555e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.774 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.774 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.774 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7344 2.765 h = 0.0001 0.004 y[1] (numeric) = -0.0304408928534 0.359083057763 y[1] (closed_form) = -0.0304408928534 0.359083057763 absolute error = 2.002e-32 relative error = 5.557e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.775 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.775 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.775 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7345 2.769 h = 0.003 0.006 y[1] (numeric) = -0.0303663990938 0.358569548361 y[1] (closed_form) = -0.0303663990938 0.358569548361 absolute error = 2e-32 relative error = 5.558e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.779 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.779 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.779 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7375 2.775 h = 0.0001 0.005 y[1] (numeric) = -0.0306173834223 0.357739953671 y[1] (closed_form) = -0.0306173834223 0.357739953671 absolute error = 2.002e-32 relative error = 5.577e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.785 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.785 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.785 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7376 2.78 h = 0.0001 0.003 y[1] (numeric) = -0.0305208045424 0.357103689511 y[1] (closed_form) = -0.0305208045424 0.357103689511 absolute error = 2.002e-32 relative error = 5.587e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.79 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.79 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.79 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7377 2.783 h = 0.001 0.001 y[1] (numeric) = -0.030468147027 0.356722142095 y[1] (closed_form) = -0.030468147027 0.356722142095 absolute error = 2.002e-32 relative error = 5.593e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.793 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.793 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.793 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7387 2.784 h = 0.001 0.003 y[1] (numeric) = -0.0305726433229 0.356574105617 y[1] (closed_form) = -0.0305726433229 0.356574105617 absolute error = 2.002e-32 relative error = 5.595e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.794 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.794 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.794 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7397 2.787 h = 0.0001 0.004 y[1] (numeric) = -0.0306332725963 0.356174095644 y[1] (closed_form) = -0.0306332725963 0.356174095644 absolute error = 2e-32 relative error = 5.595e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.797 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.797 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.797 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7398 2.791 h = 0.003 0.006 y[1] (numeric) = -0.0305587288662 0.355668941891 y[1] (closed_form) = -0.0305587288662 0.355668941891 absolute error = 2e-32 relative error = 5.603e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.801 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.801 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.801 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7428 2.797 h = 0.0001 0.005 y[1] (numeric) = -0.0308037357939 0.354851931694 y[1] (closed_form) = -0.0308037357939 0.354851931694 absolute error = 2e-32 relative error = 5.615e-30 % Correct digits = 31 memory used=1611.0MB, alloc=52.3MB, time=18.87 Radius of convergence (given) for eq 1 = 2.808 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.808 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.808 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7429 2.802 h = 0.0001 0.003 y[1] (numeric) = -0.0307071710679 0.354225991487 y[1] (closed_form) = -0.0307071710679 0.354225991487 absolute error = 2.002e-32 relative error = 5.632e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.813 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.813 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.813 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.743 2.805 h = 0.001 0.001 y[1] (numeric) = -0.030654438195 0.353850613732 y[1] (closed_form) = -0.030654438195 0.353850613732 absolute error = 2.002e-32 relative error = 5.638e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.816 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.816 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.816 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.744 2.806 h = 0.001 0.003 y[1] (numeric) = -0.030756927998 0.353704671977 y[1] (closed_form) = -0.030756927998 0.353704671977 absolute error = 2.002e-32 relative error = 5.640e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.817 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.817 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.817 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.745 2.809 h = 0.0001 0.004 y[1] (numeric) = -0.0308156487147 0.353310845876 y[1] (closed_form) = -0.0308156487147 0.353310845876 absolute error = 2e-32 relative error = 5.639e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.82 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.82 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.82 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7451 2.813 h = 0.003 0.006 y[1] (numeric) = -0.0307410858931 0.352813849928 y[1] (closed_form) = -0.0307410858931 0.352813849928 absolute error = 3e-32 relative error = 8.471e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.824 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.824 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.824 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7481 2.819 h = 0.0001 0.005 y[1] (numeric) = -0.0309803013596 0.352009147653 y[1] (closed_form) = -0.0309803013596 0.352009147653 absolute error = 3e-32 relative error = 8.490e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.83 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.83 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.83 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7482 2.824 h = 0.0001 0.003 y[1] (numeric) = -0.0308837868187 0.351393287575 y[1] (closed_form) = -0.0308837868187 0.351393287575 absolute error = 3.002e-32 relative error = 8.509e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.835 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.835 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.835 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7483 2.827 h = 0.001 0.001 y[1] (numeric) = -0.0308310020797 0.351023934271 y[1] (closed_form) = -0.0308310020797 0.351023934271 absolute error = 2.002e-32 relative error = 5.683e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.838 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.838 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.838 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7493 2.828 h = 0.001 0.003 y[1] (numeric) = -0.0309315400289 0.350880044933 y[1] (closed_form) = -0.0309315400289 0.350880044933 absolute error = 2.010e-32 relative error = 5.706e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.839 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.839 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.839 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7503 2.831 h = 0.0001 0.004 y[1] (numeric) = -0.0309884188009 0.350492263785 y[1] (closed_form) = -0.0309884188009 0.350492263785 absolute error = 2.002e-32 relative error = 5.691e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.842 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.842 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.842 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7504 2.835 h = 0.003 0.006 y[1] (numeric) = -0.0309138658758 0.350003233857 y[1] (closed_form) = -0.0309138658758 0.350003233857 absolute error = 3.007e-32 relative error = 8.557e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.846 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.846 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.846 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7534 2.841 h = 0.0001 0.005 y[1] (numeric) = -0.0311474687158 0.349210570724 y[1] (closed_form) = -0.0311474687158 0.349210570724 absolute error = 3.002e-32 relative error = 8.562e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.852 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.852 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.852 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7535 2.846 h = 0.0001 0.003 y[1] (numeric) = -0.0310510381382 0.348604554403 y[1] (closed_form) = -0.0310510381382 0.348604554403 absolute error = 3.007e-32 relative error = 8.591e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.857 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.857 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.857 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7536 2.849 h = 0.001 0.001 y[1] (numeric) = -0.0309982236209 0.348241084763 y[1] (closed_form) = -0.0309982236209 0.348241084763 absolute error = 2.010e-32 relative error = 5.749e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.86 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.86 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.86 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7546 2.85 h = 0.001 0.003 y[1] (numeric) = -0.0310968624565 0.348099206603 y[1] (closed_form) = -0.0310968624565 0.348099206603 absolute error = 3.007e-32 relative error = 8.603e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.861 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.861 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.861 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7556 2.853 h = 0.0001 0.004 y[1] (numeric) = -0.0311519631814 0.34771733551 y[1] (closed_form) = -0.0311519631814 0.34771733551 absolute error = 2.010e-32 relative error = 5.757e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.864 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.864 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.864 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7557 2.857 h = 0.003 0.006 y[1] (numeric) = -0.0310774473579 0.347236085653 y[1] (closed_form) = -0.0310774473579 0.347236085653 absolute error = 3.007e-32 relative error = 8.624e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.868 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.868 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.868 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7587 2.863 h = 0.0001 0.005 y[1] (numeric) = -0.0313056096219 0.346455200416 y[1] (closed_form) = -0.0313056096219 0.346455200416 absolute error = 2.022e-32 relative error = 5.814e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.875 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.875 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.875 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7588 2.868 h = 0.0001 0.003 y[1] (numeric) = -0.0312092946624 0.345858798655 y[1] (closed_form) = -0.0312092946624 0.345858798655 absolute error = 2.022e-32 relative error = 5.824e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.88 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.88 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.88 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7589 2.871 h = 0.001 0.001 y[1] (numeric) = -0.0311564711303 0.345501076149 y[1] (closed_form) = -0.0311564711303 0.345501076149 absolute error = 3.015e-32 relative error = 8.691e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.883 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.883 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.883 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1656.0MB, alloc=52.3MB, time=19.39 x[1] = 0.7599 2.872 h = 0.001 0.003 y[1] (numeric) = -0.0312532617736 0.345361168964 y[1] (closed_form) = -0.0312532617736 0.345361168964 absolute error = 3.007e-32 relative error = 8.670e-30 % Correct digits = 31 Radius of convergence (given) for eq 1 = 2.884 Order of pole (given) = 0 0 Radius of convergence (ratio test) for eq 1 = 2.884 Order of pole (ratio test) = 1 0 Radius of convergence (three term test) for eq 1 = 2.884 Order of pole (three term test) = 1 0 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = y * y ; Iterations = 754 Total Elapsed Time = 19 Seconds Expected Time Remaining = 0 Seconds Optimized Time Remaining = 0 Seconds Expected Total Time = 19 Seconds > quit memory used=1659.2MB, alloc=52.3MB, time=19.43