|\^/| 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(cos(c(x)) - sin(c(x))) ; > end; exact_soln_y := proc(x) return cos(c(x)) - sin(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 + 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, 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0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 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_g, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local min_size; > min_size := glob_estimated_size_answer; > if (float_abs(array_y[1]) < min_size) then # if number 3 > min_size := float_abs(array_y[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 3; > if (min_size < glob__1) then # if number 3 > min_size := glob__1; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 3; > min_size; > end; est_size_answer := proc() local min_size; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_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_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; min_size := glob_estimated_size_answer; if float_abs(array_y[1]) < min_size then min_size := float_abs(array_y[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if min_size < glob__1 then min_size := glob__1; omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; min_size end proc # End Function number 4 # Begin Function number 5 > test_suggested_h := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_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_g, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > max_estimated_step_error := glob__small; > no_terms := ATS_MAX_TERMS; > hn_div_ho := glob__0_5; > hn_div_ho_2 := glob__0_25; > hn_div_ho_3 := glob__0_125; > omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""); > omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,""); > omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,""); > est_tmp := float_abs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3); > if (est_tmp >= max_estimated_step_error) then # if number 3 > max_estimated_step_error := est_tmp; > fi;# end if 3; > omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,""); > max_estimated_step_error; > end; test_suggested_h := proc() local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_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_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; max_estimated_step_error := glob__small; no_terms := ATS_MAX_TERMS; hn_div_ho := glob__0_5; hn_div_ho_2 := glob__0_25; hn_div_ho_3 := glob__0_125; omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""); omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""); omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""); est_tmp := float_abs(array_y[no_terms - 3] + array_y[no_terms - 2]*hn_div_ho + array_y[no_terms - 1]*hn_div_ho_2 + array_y[no_terms]*hn_div_ho_3); if max_estimated_step_error <= est_tmp then max_estimated_step_error := est_tmp end if; omniout_float(ALWAYS, "max_estimated_step_error", 32, max_estimated_step_error, 32, ""); max_estimated_step_error end proc # End Function number 5 # Begin Function number 6 > track_estimated_error := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_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_g, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > no_terms := ATS_MAX_TERMS; > hn_div_ho := glob__0_5; > hn_div_ho_2 := glob__0_25; > hn_div_ho_3 := glob__0_125; > est_tmp := c(float_abs(array_y[no_terms-3])) + c(float_abs(array_y[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y[no_terms])) * c(hn_div_ho_3); > if (glob_prec * c(float_abs(array_y[1])) > c(est_tmp)) then # if number 3 > est_tmp := c(glob_prec) * c(float_abs(array_y[1])); > fi;# end if 3; > if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 3 > array_max_est_error[1] := c(est_tmp); > fi;# end if 3 > ; > end; track_estimated_error := proc() local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_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_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; no_terms := ATS_MAX_TERMS; hn_div_ho := glob__0_5; hn_div_ho_2 := glob__0_25; hn_div_ho_3 := glob__0_125; est_tmp := c(float_abs(array_y[no_terms - 3])) + c(float_abs(array_y[no_terms - 2]))*c(hn_div_ho) + c(float_abs(array_y[no_terms - 1]))*c(hn_div_ho_2) + c(float_abs(array_y[no_terms]))*c(hn_div_ho_3); if c(est_tmp) < glob_prec*c(float_abs(array_y[1])) then est_tmp := c(glob_prec)*c(float_abs(array_y[1])) end if; if c(array_max_est_error[1]) <= c(est_tmp) then array_max_est_error[1] := c(est_tmp) end if end proc # End Function number 6 # Begin Function number 7 > reached_interval := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_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_g, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local ret; > if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 3 > ret := true; > else > ret := false; > fi;# end if 3; > return(ret); > end; reached_interval := proc() local ret; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_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_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; if glob_check_sign*glob_next_display - glob_h/glob__10 <= glob_check_sign*array_x[1] then ret := true else ret := false end if; return ret end proc # End Function number 7 # Begin Function number 8 > display_alot := proc(iter) > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_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_g, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err; > #TOP DISPLAY ALOT > 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_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; 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_g, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := (clock_sec1) - (glob_orig_start_sec); > glob_clock_sec := (clock_sec1) - (glob_clock_start_sec); > left_sec := (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1); > expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h) ,( clock_sec1) - (glob_orig_start_sec)); > opt_clock_sec := ( clock_sec1) - (glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec)); > glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec); > percent_done := comp_percent((x_end),(x_start),(array_x[1]) + (glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr((total_clock_sec)); > 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_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := clock_sec1 - glob_orig_start_sec; glob_clock_sec := clock_sec1 - glob_clock_start_sec; left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1; expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h, clock_sec1 - glob_orig_start_sec); opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec; glob_optimal_expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec) ; glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec); percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(total_clock_sec); 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_g, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad, last_no; > #TOP CHECK FOR POLE > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,1] := glob_larger_float; > array_ord_test_poles[1,1] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 3 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 3; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 3 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 4 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 5 > found_sing := 0; > fi;# end if 5; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 5 > if (rad_c < array_rad_test_poles[1,1]) then # if number 6 > array_rad_test_poles[1,1] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,1] := rad_c; > array_ord_test_poles[1,1] := tmp_ord; > fi;# end if 6; > fi;# end if 5; > #BOTTOM general radius test1 > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,2] := glob_larger_float; > array_ord_test_poles[1,2] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 5 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 5; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 6 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 7 > found_sing := 0; > fi;# end if 7; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 7 > if (rad_c < array_rad_test_poles[1,2]) then # if number 8 > array_rad_test_poles[1,2] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,2] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 9 > glob_min_pole_est := rad_c; > fi;# end if 9; > array_ord_test_poles[1,2] := tmp_ord; > fi;# end if 8; > fi;# end if 7; > #BOTTOM general radius test1 > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,3] := glob_larger_float; > array_ord_test_poles[1,3] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 7 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 7; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 8 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 9 > found_sing := 0; > fi;# end if 9; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 9 > if (rad_c < array_rad_test_poles[1,3]) then # if number 10 > array_rad_test_poles[1,3] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,3] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 11 > glob_min_pole_est := rad_c; > fi;# end if 11; > array_ord_test_poles[1,3] := tmp_ord; > fi;# end if 10; > fi;# end if 9; > #BOTTOM general radius test1 > ; > 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_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 1] := glob_larger_float; array_ord_test_poles[1, 1] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do tmp_rad := comp_rad_from_ratio(array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 1] then array_rad_test_poles[1, 1] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_ratio(array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 1] := rad_c; array_ord_test_poles[1, 1] := tmp_ord end if end if; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 2] := glob_larger_float; array_ord_test_poles[1, 2] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do tmp_rad := comp_rad_from_three_terms( array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 2] then array_rad_test_poles[1, 2] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_three_terms( array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 2] := rad_c; if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c end if; array_ord_test_poles[1, 2] := tmp_ord end if end if; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 3] := glob_larger_float; array_ord_test_poles[1, 3] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do tmp_rad := comp_rad_from_six_terms(array_y_higher[1, last_no - 5], array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3], array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 3] then array_rad_test_poles[1, 3] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_six_terms( array_y_higher[1, last_no - 5], array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3], array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 3] := rad_c; if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c end if; array_ord_test_poles[1, 3] := tmp_ord end if end if; 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_g, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > # before write maple main top matter > # before generate constants assign > # before generate globals assign > #END OUTFILE1 > #BEGIN OUTFILE2 > #END OUTFILE2 > #BEGIN ATOMHDR1 > #emit pre sin 1 $eq_no = 1 > array_tmp1[1] := sin(array_x[1]); > array_tmp1_g[1] := cos(array_x[1]); > #emit pre neg FULL $eq_no = 1 > array_tmp2[1] := neg(array_tmp1[1]); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp3[1] := array_const_0D0[1] + array_tmp2[1]; > #emit pre cos 1 $eq_no = 1 > array_tmp4[1] := cos(array_x[1]); > array_tmp4_g[1] := sin(array_x[1]); > #emit pre sub FULL FULL $eq_no = 1 i = 1 > array_tmp5[1] := array_tmp3[1] - array_tmp4[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y_set_initial[1,2]) then # if number 1 > if (1 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp5[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1)); > if (2 <= ATS_MAX_TERMS) then # if number 3 > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(1); > array_y_higher[2,1] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre sin ID_LINEAR iii = 2 $eq_no = 1 > array_tmp1[2] := array_tmp1_g[1] * array_x[2] / c(1); > array_tmp1_g[2] := neg(array_tmp1[1]) * array_x[2] / c(1); > #emit pre neg FULL $eq_no = 1 > array_tmp2[2] := neg(array_tmp1[2]); > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp3[2] := array_tmp2[2]; > #emit pre cos ID_LINEAR iii = 2 $eq_no = 1 > array_tmp4[2] := neg(array_tmp4_g[1]) * array_x[2] / c(1); > array_tmp4_g[2] := array_tmp4[1] * array_x[2] / c(1); > #emit pre sub FULL FULL $eq_no = 1 i = 2 > array_tmp5[2] := array_tmp3[2] - array_tmp4[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y_set_initial[1,3]) then # if number 1 > if (2 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp5[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2)); > if (3 <= ATS_MAX_TERMS) then # if number 3 > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(2); > array_y_higher[2,2] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre sin ID_LINEAR iii = 3 $eq_no = 1 > array_tmp1[3] := array_tmp1_g[2] * array_x[2] / c(2); > array_tmp1_g[3] := neg(array_tmp1[2]) * array_x[2] / c(2); > #emit pre neg FULL $eq_no = 1 > array_tmp2[3] := neg(array_tmp1[3]); > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp3[3] := array_tmp2[3]; > #emit pre cos ID_LINEAR iii = 3 $eq_no = 1 > array_tmp4[3] := neg(array_tmp4_g[2]) * array_x[2] / c(2); > array_tmp4_g[3] := array_tmp4[2] * array_x[2] / c(2); > #emit pre sub FULL FULL $eq_no = 1 i = 3 > array_tmp5[3] := array_tmp3[3] - array_tmp4[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y_set_initial[1,4]) then # if number 1 > if (3 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp5[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3)); > if (4 <= ATS_MAX_TERMS) then # if number 3 > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(3); > array_y_higher[2,3] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre sin ID_LINEAR iii = 4 $eq_no = 1 > array_tmp1[4] := array_tmp1_g[3] * array_x[2] / c(3); > array_tmp1_g[4] := neg(array_tmp1[3]) * array_x[2] / c(3); > #emit pre neg FULL $eq_no = 1 > array_tmp2[4] := neg(array_tmp1[4]); > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp3[4] := array_tmp2[4]; > #emit pre cos ID_LINEAR iii = 4 $eq_no = 1 > array_tmp4[4] := neg(array_tmp4_g[3]) * array_x[2] / c(3); > array_tmp4_g[4] := array_tmp4[3] * array_x[2] / c(3); > #emit pre sub FULL FULL $eq_no = 1 i = 4 > array_tmp5[4] := array_tmp3[4] - array_tmp4[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y_set_initial[1,5]) then # if number 1 > if (4 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp5[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4)); > if (5 <= ATS_MAX_TERMS) then # if number 3 > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(4); > array_y_higher[2,4] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre sin ID_LINEAR iii = 5 $eq_no = 1 > array_tmp1[5] := array_tmp1_g[4] * array_x[2] / c(4); > array_tmp1_g[5] := neg(array_tmp1[4]) * array_x[2] / c(4); > #emit pre neg FULL $eq_no = 1 > array_tmp2[5] := neg(array_tmp1[5]); > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp3[5] := array_tmp2[5]; > #emit pre cos ID_LINEAR iii = 5 $eq_no = 1 > array_tmp4[5] := neg(array_tmp4_g[4]) * array_x[2] / c(4); > array_tmp4_g[5] := array_tmp4[4] * array_x[2] / c(4); > #emit pre sub FULL FULL $eq_no = 1 i = 5 > array_tmp5[5] := array_tmp3[5] - array_tmp4[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y_set_initial[1,6]) then # if number 1 > if (5 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp5[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5)); > if (6 <= ATS_MAX_TERMS) then # if number 3 > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(5); > array_y_higher[2,5] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= ATS_MAX_TERMS) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit sin LINEAR $eq_no = 1 > array_tmp1[kkk] := array_tmp1_g[kkk - 1] * array_x[2] / c(kkk - 1); > array_tmp1_g[kkk] := neg(array_tmp1[kkk - 1]) * array_x[2] / c(kkk - 1); > #emit neg FULL $eq_no = 1 > array_tmp2[kkk] := neg(array_tmp1[kkk]); > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp3[kkk] := array_tmp2[kkk]; > #emit cos LINEAR $eq_no = 1 > array_tmp4[kkk] := neg(array_tmp4_g[kkk - 1]) * array_x[2] / c(kkk - 1); > array_tmp4_g[kkk] := array_tmp4[kkk - 1] * array_x[2] / c(kkk - 1); > #emit FULL - FULL sub $eq_no = 1 > array_tmp5[kkk] := array_tmp3[kkk] - array_tmp4[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1 > if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2 > temporary := c(array_tmp5[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1))); > array_y[kkk + order_d] := c(temporary); > array_y_higher[1,kkk + order_d] := c(temporary); > term := kkk + order_d - 1; > adj2 := kkk + order_d - 1; > adj3 := 2; > while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := c(temporary) / c(glob_h) * c(adj2); > else > temporary := c(temporary); > fi;# end if 4; > array_y_higher[adj3,term] := c(temporary); > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 1 > fi;# end if 2 > fi;# end if 1; > kkk := kkk + 1; > od;# end do number 1; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > #BOTTOM ATOMALL ??? > end; atomall := proc() local kkk, order_d, adj2, adj3, temporary, term; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_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_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; array_tmp1[1] := sin(array_x[1]); array_tmp1_g[1] := cos(array_x[1]); array_tmp2[1] := neg(array_tmp1[1]); array_tmp3[1] := array_const_0D0[1] + array_tmp2[1]; array_tmp4[1] := cos(array_x[1]); array_tmp4_g[1] := sin(array_x[1]); array_tmp5[1] := array_tmp3[1] - array_tmp4[1]; if not array_y_set_initial[1, 2] then if 1 <= ATS_MAX_TERMS then temporary := c(array_tmp5[1])*expt(glob_h, c(1))*c(factorial_3(0, 1)); if 2 <= ATS_MAX_TERMS then array_y[2] := temporary; array_y_higher[1, 2] := temporary end if; temporary := c(temporary)*c(1)/c(glob_h); array_y_higher[2, 1] := c(temporary) end if end if; kkk := 2; array_tmp1[2] := array_tmp1_g[1]*array_x[2]/c(1); array_tmp1_g[2] := neg(array_tmp1[1])*array_x[2]/c(1); array_tmp2[2] := neg(array_tmp1[2]); array_tmp3[2] := array_tmp2[2]; array_tmp4[2] := neg(array_tmp4_g[1])*array_x[2]/c(1); array_tmp4_g[2] := array_tmp4[1]*array_x[2]/c(1); array_tmp5[2] := array_tmp3[2] - array_tmp4[2]; if not array_y_set_initial[1, 3] then if 2 <= ATS_MAX_TERMS then temporary := c(array_tmp5[2])*expt(glob_h, c(1))*c(factorial_3(1, 2)); if 3 <= ATS_MAX_TERMS then array_y[3] := temporary; array_y_higher[1, 3] := temporary end if; temporary := c(temporary)*c(2)/c(glob_h); array_y_higher[2, 2] := c(temporary) end if end if; kkk := 3; array_tmp1[3] := array_tmp1_g[2]*array_x[2]/c(2); array_tmp1_g[3] := neg(array_tmp1[2])*array_x[2]/c(2); array_tmp2[3] := neg(array_tmp1[3]); array_tmp3[3] := array_tmp2[3]; array_tmp4[3] := neg(array_tmp4_g[2])*array_x[2]/c(2); array_tmp4_g[3] := array_tmp4[2]*array_x[2]/c(2); array_tmp5[3] := array_tmp3[3] - array_tmp4[3]; if not array_y_set_initial[1, 4] then if 3 <= ATS_MAX_TERMS then temporary := c(array_tmp5[3])*expt(glob_h, c(1))*c(factorial_3(2, 3)); if 4 <= ATS_MAX_TERMS then array_y[4] := temporary; array_y_higher[1, 4] := temporary end if; temporary := c(temporary)*c(3)/c(glob_h); array_y_higher[2, 3] := c(temporary) end if end if; kkk := 4; array_tmp1[4] := array_tmp1_g[3]*array_x[2]/c(3); array_tmp1_g[4] := neg(array_tmp1[3])*array_x[2]/c(3); array_tmp2[4] := neg(array_tmp1[4]); array_tmp3[4] := array_tmp2[4]; array_tmp4[4] := neg(array_tmp4_g[3])*array_x[2]/c(3); array_tmp4_g[4] := array_tmp4[3]*array_x[2]/c(3); array_tmp5[4] := array_tmp3[4] - array_tmp4[4]; if not array_y_set_initial[1, 5] then if 4 <= ATS_MAX_TERMS then temporary := c(array_tmp5[4])*expt(glob_h, c(1))*c(factorial_3(3, 4)); if 5 <= ATS_MAX_TERMS then array_y[5] := temporary; array_y_higher[1, 5] := temporary end if; temporary := c(temporary)*c(4)/c(glob_h); array_y_higher[2, 4] := c(temporary) end if end if; kkk := 5; array_tmp1[5] := array_tmp1_g[4]*array_x[2]/c(4); array_tmp1_g[5] := neg(array_tmp1[4])*array_x[2]/c(4); array_tmp2[5] := neg(array_tmp1[5]); array_tmp3[5] := array_tmp2[5]; array_tmp4[5] := neg(array_tmp4_g[4])*array_x[2]/c(4); array_tmp4_g[5] := array_tmp4[4]*array_x[2]/c(4); array_tmp5[5] := array_tmp3[5] - array_tmp4[5]; if not array_y_set_initial[1, 6] then if 5 <= ATS_MAX_TERMS then temporary := c(array_tmp5[5])*expt(glob_h, c(1))*c(factorial_3(4, 5)); if 6 <= ATS_MAX_TERMS then array_y[6] := temporary; array_y_higher[1, 6] := temporary end if; temporary := c(temporary)*c(5)/c(glob_h); array_y_higher[2, 5] := c(temporary) end if end if; kkk := 6; while kkk <= ATS_MAX_TERMS do array_tmp1[kkk] := array_tmp1_g[kkk - 1]*array_x[2]/c(kkk - 1); array_tmp1_g[kkk] := neg(array_tmp1[kkk - 1])*array_x[2]/c(kkk - 1) ; array_tmp2[kkk] := neg(array_tmp1[kkk]); array_tmp3[kkk] := array_tmp2[kkk]; array_tmp4[kkk] := neg(array_tmp4_g[kkk - 1])*array_x[2]/c(kkk - 1) ; array_tmp4_g[kkk] := array_tmp4[kkk - 1]*array_x[2]/c(kkk - 1); array_tmp5[kkk] := array_tmp3[kkk] - array_tmp4[kkk]; order_d := 1; if kkk + order_d <= ATS_MAX_TERMS then if not array_y_set_initial[1, kkk + order_d] then temporary := c(array_tmp5[kkk])*expt(glob_h, c(order_d))* c(factorial_3(kkk - 1, kkk + order_d - 1)); array_y[kkk + order_d] := c(temporary); array_y_higher[1, kkk + order_d] := c(temporary); term := kkk + order_d - 1; adj2 := kkk + order_d - 1; adj3 := 2; while 1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1 do if adj3 <= order_d + 1 then if 0 < adj2 then temporary := c(temporary)*c(adj2)/c(glob_h) else temporary := c(temporary) end if; array_y_higher[adj3, term] := c(temporary) end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; kkk := kkk + 1 end do end proc # End Function number 12 #END OUTFILE5 # Begin Function number 12 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it; > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_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_g, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > ATS_MAX_TERMS := 40; > # before first input block > #BEGIN FIRST INPUT BLOCK > #BEGIN BLOCK 1 > #BEGIN FIRST INPUT BLOCK > Digits:=32; > max_terms:=40; > #END BLOCK 1 > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > # before generate arrays > array_y_init:= Array(0..(40),[]); > array_norms:= Array(0..(40),[]); > array_fact_1:= Array(0..(40),[]); > array_1st_rel_error:= Array(0..(2),[]); > array_last_rel_error:= Array(0..(2),[]); > array_est_rel_error:= Array(0..(2),[]); > array_max_est_error:= Array(0..(2),[]); > array_type_pole:= Array(0..(2),[]); > array_type_real_pole:= Array(0..(2),[]); > array_type_complex_pole:= Array(0..(2),[]); > array_est_digits:= Array(0..(2),[]); > array_y:= Array(0..(40),[]); > array_x:= Array(0..(40),[]); > array_tmp0:= Array(0..(40),[]); > array_tmp1_g:= Array(0..(40),[]); > array_tmp1:= Array(0..(40),[]); > array_tmp2:= Array(0..(40),[]); > array_tmp3:= Array(0..(40),[]); > array_tmp4_g:= Array(0..(40),[]); > array_tmp4:= Array(0..(40),[]); > array_tmp5:= Array(0..(40),[]); > array_m1:= Array(0..(40),[]); > array_y_higher := Array(0..(2) ,(0..40+ 1),[]); > array_y_higher_work := Array(0..(2) ,(0..40+ 1),[]); > array_y_higher_work2 := Array(0..(2) ,(0..40+ 1),[]); > array_y_set_initial := Array(0..(2) ,(0..40+ 1),[]); > array_given_rad_poles := Array(0..(2) ,(0..3+ 1),[]); > array_given_ord_poles := Array(0..(2) ,(0..3+ 1),[]); > array_rad_test_poles := Array(0..(2) ,(0..4+ 1),[]); > array_ord_test_poles := Array(0..(2) ,(0..4+ 1),[]); > array_fact_2 := Array(0..(40) ,(0..40+ 1),[]); > # before generate constants > # before generate globals definition > #Top Generate Globals Definition > #Bottom Generate Globals Deninition > # before generate const definition > # before arrays initialized > term := 1; > while (term <= 40) do # do number 1 > array_y_init[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_norms[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_fact_1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_1st_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_last_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_est_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_max_est_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_real_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_complex_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_est_digits[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_y[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_x[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp0[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp1_g[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp2[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp3[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp4_g[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp4[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp5[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_m1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_y_higher[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_y_higher_work[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_y_higher_work2[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_y_set_initial[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_rad_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_ord_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 4) do # do number 2 > array_rad_test_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 4) do # do number 2 > array_ord_test_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=40) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_fact_2[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > # before symbols initialized > #BEGIN SYMBOLS INITIALIZATED > zero_ats_ar(array_y); > zero_ats_ar(array_x); > zero_ats_ar(array_tmp0); > zero_ats_ar(array_tmp1_g); > zero_ats_ar(array_tmp1); > zero_ats_ar(array_tmp2); > zero_ats_ar(array_tmp3); > zero_ats_ar(array_tmp4_g); > zero_ats_ar(array_tmp4); > zero_ats_ar(array_tmp5); > zero_ats_ar(array_m1); > zero_ats_ar(array_const_1); > array_const_1[1] := c(1); > zero_ats_ar(array_const_0D0); > array_const_0D0[1] := c(0.0); > zero_ats_ar(array_m1); > array_m1[1] := glob__m1; > #END SYMBOLS INITIALIZATED > # before generate factorials init > #Initing Factorial Tables > iiif := 0; > while (iiif <= ATS_MAX_TERMS) do # do number 1 > jjjf := 0; > while (jjjf <= ATS_MAX_TERMS) do # do number 2 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 2; > iiif := iiif + 1; > od;# end do number 1; > #Done Initing Factorial Table > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := 5; > glob_yes_pole := 4; > glob_no_pole := 3; > glob_not_given := 0; > glob_no_sing_tests := 4; > glob_ratio_test := 1; > glob_three_term_test := 2; > glob_six_term_test := 3; > glob_log_10 := log(c(10.0)); > MAX_UNCHANGED := 10; > glob__small := c(0.1e-50); > glob_small_float := c(0.1e-50); > glob_smallish_float := c(0.1e-60); > glob_large_float := c(1.0e100); > glob_larger_float := c(1.1e100); > glob__m2 := c(-2); > glob__m1 := c(-1); > glob__0 := c(0); > glob__1 := c(1); > glob__2 := c(2); > glob__3 := c(3); > glob__4 := c(4); > glob__5 := c(5); > glob__8 := c(8); > glob__10 := c(10); > glob__100 := c(100); > glob__pi := c(0.0); > glob__0_5 := c(0.5); > glob__0_8 := c(0.8); > glob__m0_8 := c(-0.8); > glob__0_25 := c(0.25); > glob__0_125 := c(0.125); > glob_h := 0.1; > glob_nxt := 1; > glob_prec := c(1.0e-16); > glob_check_sign := c(1.0); > glob_desired_digits_correct := c(8.0); > glob_max_estimated_step_error := c(0.0); > glob_ratio_of_radius := c(0.1); > glob_percent_done := c(0.0); > glob_total_exp_sec := c(0.1); > glob_optimal_expect_sec := c(0.1); > glob_estimated_size_answer := c(100.0); > glob_almost_1 := c(0.9990); > glob_clock_sec := c(0.0); > glob_clock_start_sec := c(0.0); > glob_disp_incr := c(0.1); > glob_diff_rc_fm := c(0.1); > glob_diff_rc_fmm1 := c(0.1); > glob_diff_rc_fmm2 := c(0.1); > glob_diff_ord_fm := c(0.1); > glob_diff_ord_fmm1 := c(0.1); > glob_diff_ord_fmm2 := c(0.1); > glob_six_term_ord_save := c(0.1); > glob_guess_error_rc := c(0.1); > glob_guess_error_ord := c(0.1); > glob_least_given_sing := c(9.9e200); > glob_least_ratio_sing := c(9.9e200); > glob_least_3_sing := c(9.9e100); > glob_least_6_sing := c(9.9e100); > glob_last_good_h := c(0.1); > glob_max_h := c(0.1); > glob_min_h := c(0.000001); > glob_display_interval := c(0.1); > glob_abserr := c(0.1e-10); > glob_relerr := c(0.1e-10); > glob_min_pole_est := c(0.1e+10); > glob_max_rel_trunc_err := c(0.1e-10); > glob_max_trunc_err := c(0.1e-10); > glob_max_hours := c(0.0); > glob_optimal_clock_start_sec := c(0.0); > glob_optimal_start := c(0.0); > glob_upper_ratio_limit := c(1.0001); > glob_lower_ratio_limit := c(0.9999); > glob_max_sec := c(10000.0); > glob_orig_start_sec := c(0.0); > glob_normmax := c(0.0); > glob_max_minutes := c(0.0); > glob_next_display := c(0.0); > glob_est_digits := 1; > glob_subiter_method := 3; > glob_html_log := true; > glob_min_good_digits := 99999; > glob_good_digits := 0; > glob_min_apfp_est_good_digits := 99999; > glob_apfp_est_good_digits := 0; > glob_max_opt_iter := 10; > glob_dump := false; > glob_djd_debug := true; > glob_display_flag := true; > glob_djd_debug2 := true; > glob_h_reason := 0; > glob_sec_in_minute := 60 ; > glob_min_in_hour := 60; > glob_hours_in_day := 24; > glob_days_in_year := 365; > glob_sec_in_hour := 3600; > glob_sec_in_day := 86400; > glob_sec_in_year := 31536000; > glob_not_yet_finished := true; > glob_initial_pass := true; > glob_not_yet_start_msg := true; > glob_reached_optimal_h := false; > glob_optimal_done := false; > glob_type_given_pole := 0; > glob_optimize := false; > glob_look_poles := false; > glob_dump_closed_form := false; > glob_max_iter := 10000; > glob_no_eqs := 0; > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_start := 0; > glob_iter := 0; > # before generate set diff initial > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > array_y_set_initial[1,31] := false; > array_y_set_initial[1,32] := false; > array_y_set_initial[1,33] := false; > array_y_set_initial[1,34] := false; > array_y_set_initial[1,35] := false; > array_y_set_initial[1,36] := false; > array_y_set_initial[1,37] := false; > array_y_set_initial[1,38] := false; > array_y_set_initial[1,39] := false; > array_y_set_initial[1,40] := false; > # before generate init omniout const > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > ATS_MAX_TERMS := 40; > glob_iolevel := INFO; > # set default block > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > glob_display_flag := true; > glob_no_eqs := 1; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 10000; > glob_max_hours := (0.0); > glob_max_minutes := (15.0); > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/sub_sin_cospostcpx.cpx#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = neg ( sin ( x ) ) - cos ( x ) ; "); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=40;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 0.1 + 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 := 3;"); > 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(cos(c(x)) - sin(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 := 3; > #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 ) = neg ( sin ( x ) ) - cos ( x ) ; "); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 10 > logstart(html_log_file); > logitem_str(html_log_file,"2017-11-26T16:39:03-06:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"sub_sin_cos") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = neg ( sin ( x ) ) - cos ( x ) ; ") > ; > logitem_complex(html_log_file,x_start) > ; > logitem_complex(html_log_file,x_end) > ; > logitem_complex(html_log_file,array_x[1]) > ; > logitem_complex(html_log_file,glob_h) > ; > logitem_h_reason(html_log_file) > ; > logitem_integer(html_log_file,Digits) > ; > ; > glob_desired_digits_correct := 0.0; > logitem_float(html_log_file,glob_desired_digits_correct) > ; > if (array_est_digits[1] <> -16) then # if number 11 > logitem_integer(html_log_file,array_est_digits[1]) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 11; > if (glob_min_good_digits <> -16) then # if number 11 > logitem_integer(html_log_file,glob_min_good_digits) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 11; > if (glob_good_digits <> -16) then # if number 11 > logitem_integer(html_log_file,glob_good_digits) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 11; > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > logitem_integer(html_log_file,ATS_MAX_TERMS) > ; > if (glob_type_given_pole = 0) then # if number 11 > logitem_str(html_log_file,"Not Given") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 4) then # if number 12 > logitem_str(html_log_file,"No Solution") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 5) then # if number 13 > logitem_str(html_log_file,"Some Pole") > ; > logitem_str(html_log_file,"????") > ; > elif > (glob_type_given_pole = 3) then # if number 14 > logitem_str(html_log_file,"No Pole") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 1) then # if number 15 > logitem_str(html_log_file,"Real Sing") > ; > logitem_float(html_log_file,glob_least_given_sing) > ; > elif > (glob_type_given_pole = 2) then # if number 16 > logitem_str(html_log_file,"Complex Sing") > ; > logitem_float(html_log_file,glob_least_given_sing) > ; > fi;# end if 16; > if (glob_least_ratio_sing < glob_large_float) then # if number 16 > glob_least_ratio_sing := 0; > logitem_float(html_log_file,glob_least_ratio_sing) > ; > else > logitem_str(html_log_file,"NONE") > ; > fi;# end if 16; > if (glob_least_3_sing < glob_large_float) then # if number 16 > logitem_float(html_log_file,glob_least_3_sing) > ; > else > logitem_str(html_log_file,"NONE") > ; > fi;# end if 16; > if (glob_least_6_sing < glob_large_float) then # if number 16 > glob_least_6_sing := 0.0; > logitem_float(html_log_file,glob_least_6_sing) > ; > else > logitem_str(html_log_file,"NONE") > ; > fi;# end if 16; > logitem_integer(html_log_file,glob_iter) > ; > logitem_time(html_log_file,(glob_clock_sec)) > ; > if (c(glob_percent_done) < glob__100) then # if number 16 > logitem_time(html_log_file,(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 16; > log_revs(html_log_file," 309 ") > ; > logitem_str(html_log_file,"sub_sin_cos diffeq.mxt") > ; > logitem_str(html_log_file,"sub_sin_cos maple results") > ; > logitem_str(html_log_file,"OK") > ; > logend(html_log_file) > ; > ; > fi;# end if 15; > if (glob_html_log) then # if number 15 > fclose(html_log_file); > fi;# end if 15 > ; > ;; > end; > # End Function number 12 > #END OUTFILEMAIN > end; Warning, `h_new` is implicitly declared local to procedure `main` Warning, `ratio` is implicitly declared local to procedure `main` main := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err, estimated_step_error, min_value, est_answer, found_h, repeat_it, h_new, ratio; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; ATS_MAX_TERMS := 40; Digits := 32; max_terms := 40; glob_html_log := true; array_y_init := Array(0 .. 40, []); array_norms := Array(0 .. 40, []); array_fact_1 := Array(0 .. 40, []); array_1st_rel_error := Array(0 .. 2, []); array_last_rel_error := Array(0 .. 2, []); array_est_rel_error := Array(0 .. 2, []); array_max_est_error := Array(0 .. 2, []); array_type_pole := Array(0 .. 2, []); array_type_real_pole := Array(0 .. 2, []); array_type_complex_pole := Array(0 .. 2, []); array_est_digits := Array(0 .. 2, []); array_y := Array(0 .. 40, []); array_x := Array(0 .. 40, []); array_tmp0 := Array(0 .. 40, []); array_tmp1_g := Array(0 .. 40, []); array_tmp1 := Array(0 .. 40, []); array_tmp2 := Array(0 .. 40, []); array_tmp3 := Array(0 .. 40, []); array_tmp4_g := Array(0 .. 40, []); array_tmp4 := Array(0 .. 40, []); array_tmp5 := Array(0 .. 40, []); array_m1 := Array(0 .. 40, []); array_y_higher := Array(0 .. 2, 0 .. 41, []); array_y_higher_work := Array(0 .. 2, 0 .. 41, []); array_y_higher_work2 := Array(0 .. 2, 0 .. 41, []); array_y_set_initial := Array(0 .. 2, 0 .. 41, []); array_given_rad_poles := Array(0 .. 2, 0 .. 4, []); array_given_ord_poles := Array(0 .. 2, 0 .. 4, []); array_rad_test_poles := Array(0 .. 2, 0 .. 5, []); array_ord_test_poles := Array(0 .. 2, 0 .. 5, []); array_fact_2 := Array(0 .. 40, 0 .. 41, []); term := 1; while term <= 40 do array_y_init[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_norms[term] := c(0.); term := term + 1 end do ; term := 1; while term <= 40 do array_fact_1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_1st_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_last_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_est_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_max_est_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_type_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_type_real_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_type_complex_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_est_digits[term] := 0; term := term + 1 end do ; term := 1; while term <= 40 do array_y[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_x[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp0[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp1_g[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp2[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp3[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp4_g[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp4[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp5[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_m1[term] := c(0.); term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 40 do array_y_higher[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 40 do array_y_higher_work[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 40 do array_y_higher_work2[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 40 do array_y_set_initial[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_rad_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_ord_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 4 do array_rad_test_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 4 do array_ord_test_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 40 do term := 1; while term <= 40 do array_fact_2[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; zero_ats_ar(array_y); zero_ats_ar(array_x); zero_ats_ar(array_tmp0); zero_ats_ar(array_tmp1_g); zero_ats_ar(array_tmp1); zero_ats_ar(array_tmp2); zero_ats_ar(array_tmp3); zero_ats_ar(array_tmp4_g); zero_ats_ar(array_tmp4); zero_ats_ar(array_tmp5); zero_ats_ar(array_m1); zero_ats_ar(array_const_1); array_const_1[1] := c(1); zero_ats_ar(array_const_0D0); array_const_0D0[1] := c(0.); zero_ats_ar(array_m1); array_m1[1] := glob__m1; iiif := 0; while iiif <= ATS_MAX_TERMS do jjjf := 0; while jjjf <= ATS_MAX_TERMS do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := 5; glob_yes_pole := 4; glob_no_pole := 3; glob_not_given := 0; glob_no_sing_tests := 4; glob_ratio_test := 1; glob_three_term_test := 2; glob_six_term_test := 3; glob_log_10 := log(c(10.0)); MAX_UNCHANGED := 10; glob__small := c(0.1*10^(-50)); glob_small_float := c(0.1*10^(-50)); glob_smallish_float := c(0.1*10^(-60)); glob_large_float := c(0.10*10^101); glob_larger_float := c(0.11*10^101); glob__m2 := c(-2); glob__m1 := c(-1); glob__0 := c(0); glob__1 := c(1); glob__2 := c(2); glob__3 := c(3); glob__4 := c(4); glob__5 := c(5); glob__8 := c(8); glob__10 := c(10); glob__100 := c(100); glob__pi := c(0.); glob__0_5 := c(0.5); glob__0_8 := c(0.8); glob__m0_8 := c(-0.8); glob__0_25 := c(0.25); glob__0_125 := c(0.125); glob_h := 0.1; glob_nxt := 1; glob_prec := c(0.10*10^(-15)); glob_check_sign := c(1.0); glob_desired_digits_correct := c(8.0); glob_max_estimated_step_error := c(0.); glob_ratio_of_radius := c(0.1); glob_percent_done := c(0.); glob_total_exp_sec := c(0.1); glob_optimal_expect_sec := c(0.1); glob_estimated_size_answer := c(100.0); glob_almost_1 := c(0.9990); glob_clock_sec := c(0.); glob_clock_start_sec := c(0.); glob_disp_incr := c(0.1); glob_diff_rc_fm := c(0.1); glob_diff_rc_fmm1 := c(0.1); glob_diff_rc_fmm2 := c(0.1); glob_diff_ord_fm := c(0.1); glob_diff_ord_fmm1 := c(0.1); glob_diff_ord_fmm2 := c(0.1); glob_six_term_ord_save := c(0.1); glob_guess_error_rc := c(0.1); glob_guess_error_ord := c(0.1); glob_least_given_sing := c(0.99*10^201); glob_least_ratio_sing := c(0.99*10^201); glob_least_3_sing := c(0.99*10^101); glob_least_6_sing := c(0.99*10^101); glob_last_good_h := c(0.1); glob_max_h := c(0.1); glob_min_h := c(0.1*10^(-5)); glob_display_interval := c(0.1); glob_abserr := c(0.1*10^(-10)); glob_relerr := c(0.1*10^(-10)); glob_min_pole_est := c(0.1*10^10); glob_max_rel_trunc_err := c(0.1*10^(-10)); glob_max_trunc_err := c(0.1*10^(-10)); glob_max_hours := c(0.); glob_optimal_clock_start_sec := c(0.); glob_optimal_start := c(0.); glob_upper_ratio_limit := c(1.0001); glob_lower_ratio_limit := c(0.9999); glob_max_sec := c(10000.0); glob_orig_start_sec := c(0.); glob_normmax := c(0.); glob_max_minutes := c(0.); glob_next_display := c(0.); glob_est_digits := 1; glob_subiter_method := 3; glob_html_log := true; glob_min_good_digits := 99999; glob_good_digits := 0; glob_min_apfp_est_good_digits := 99999; glob_apfp_est_good_digits := 0; glob_max_opt_iter := 10; glob_dump := false; glob_djd_debug := true; glob_display_flag := true; glob_djd_debug2 := true; glob_h_reason := 0; glob_sec_in_minute := 60; glob_min_in_hour := 60; glob_hours_in_day := 24; glob_days_in_year := 365; glob_sec_in_hour := 3600; glob_sec_in_day := 86400; glob_sec_in_year := 31536000; glob_not_yet_finished := true; glob_initial_pass := true; glob_not_yet_start_msg := true; glob_reached_optimal_h := false; glob_optimal_done := false; glob_type_given_pole := 0; glob_optimize := false; glob_look_poles := false; glob_dump_closed_form := false; glob_max_iter := 10000; glob_no_eqs := 0; glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_start := 0; glob_iter := 0; array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 30] := false; array_y_set_initial[1, 31] := false; array_y_set_initial[1, 32] := false; array_y_set_initial[1, 33] := false; array_y_set_initial[1, 34] := false; array_y_set_initial[1, 35] := false; array_y_set_initial[1, 36] := false; array_y_set_initial[1, 37] := false; array_y_set_initial[1, 38] := false; array_y_set_initial[1, 39] := false; array_y_set_initial[1, 40] := false; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; ATS_MAX_TERMS := 40; glob_iolevel := INFO; glob_orig_start_sec := elapsed_time_seconds(); glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 10000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/sub_sin_cospostcpx.cpx#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = neg ( sin ( x ) \ ) - cos ( x ) ; "); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=40;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 0.1 + 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 := 3;"); 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(cos(c(x)) - sin(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,"); 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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 := 3; 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 ) = neg ( sin ( x )\ ) - cos ( x ) ; "); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2017-11-26T16:39:03-06:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "sub_sin_cos"); logitem_str(html_log_file, "diff ( y , x , 1 ) = ne\ g ( sin ( x ) ) - cos ( x ) ; "); logitem_complex(html_log_file, x_start); logitem_complex(html_log_file, x_end); logitem_complex(html_log_file, array_x[1]); logitem_complex(html_log_file, glob_h); logitem_h_reason(html_log_file); logitem_integer(html_log_file, Digits); glob_desired_digits_correct := 0.; logitem_float(html_log_file, glob_desired_digits_correct); if array_est_digits[1] <> -16 then logitem_integer(html_log_file, array_est_digits[1]) else logitem_str(html_log_file, "Unknown") end if; if glob_min_good_digits <> -16 then logitem_integer(html_log_file, glob_min_good_digits) else logitem_str(html_log_file, "Unknown") end if; if glob_good_digits <> -16 then logitem_integer(html_log_file, glob_good_digits) else logitem_str(html_log_file, "Unknown") end if; logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); logitem_integer(html_log_file, ATS_MAX_TERMS); if glob_type_given_pole = 0 then logitem_str(html_log_file, "Not Given"); logitem_str(html_log_file, "NA") elif glob_type_given_pole = 4 then logitem_str(html_log_file, "No Solution"); logitem_str(html_log_file, "NA") elif glob_type_given_pole = 5 then logitem_str(html_log_file, "Some Pole"); logitem_str(html_log_file, "????") elif glob_type_given_pole = 3 then logitem_str(html_log_file, "No Pole"); logitem_str(html_log_file, "NA") elif glob_type_given_pole = 1 then logitem_str(html_log_file, "Real Sing"); logitem_float(html_log_file, glob_least_given_sing) elif glob_type_given_pole = 2 then logitem_str(html_log_file, "Complex Sing"); logitem_float(html_log_file, glob_least_given_sing) end if; if glob_least_ratio_sing < glob_large_float then glob_least_ratio_sing := 0; logitem_float(html_log_file, glob_least_ratio_sing) else logitem_str(html_log_file, "NONE") end if; if glob_least_3_sing < glob_large_float then logitem_float(html_log_file, glob_least_3_sing) else logitem_str(html_log_file, "NONE") end if; if glob_least_6_sing < glob_large_float then glob_least_6_sing := 0.; logitem_float(html_log_file, glob_least_6_sing) else logitem_str(html_log_file, "NONE") end if; logitem_integer(html_log_file, glob_iter); logitem_time(html_log_file, glob_clock_sec); if c(glob_percent_done) < glob__100 then logitem_time(html_log_file, glob_total_exp_sec); 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 309 "); logitem_str(html_log_file, "sub_sin_cos diffeq.mxt"); logitem_str(html_log_file, "sub_sin_cos maple results"); logitem_str(html_log_file, "OK"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end if end proc # End Function number 12 > main(); memory used=3.8MB, alloc=40.3MB, time=0.08 ##############ECHO OF PROBLEM################# ##############temp/sub_sin_cospostcpx.cpx################# diff ( y , x , 1 ) = neg ( sin ( x ) ) - cos ( x ) ; ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=40; ! #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 := 3; #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(cos(c(x)) - sin(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) = 0.899650333496 -0.109666322381 y[1] (closed_form) = 0.899650333496 -0.109666322381 absolute error = 0 relative error = 0 % Correct digits = 30 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6253 Order of pole (three term test) = 32.6 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1001 0.105 h = 0.0001 0.003 y[1] (numeric) = 0.89999757642 -0.115178386372 y[1] (closed_form) = 0.899999820397 -0.1151787138 absolute error = 2.268e-06 relative error = 0.0002499 % Correct digits = 6 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3009 Order of pole (three term test) = 32.6 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1002 0.108 h = 0.001 0.001 y[1] (numeric) = 0.900176641839 -0.118491944166 y[1] (closed_form) = 0.900176197085 -0.118491827211 absolute error = 4.599e-07 relative error = 5.065e-05 % Correct digits = 6 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2365 Order of pole (three term test) = 32.6 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1012 0.109 h = 0.001 0.003 y[1] (numeric) = 0.899173195664 -0.119691764686 y[1] (closed_form) = 0.89917151205 -0.119690978789 absolute error = 1.858e-06 relative error = 0.0002048 % Correct digits = 6 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.122 Order of pole (three term test) = 32.6 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1022 0.112 h = 0.0001 0.004 y[1] (numeric) = 0.898364296751 -0.123098588947 y[1] (closed_form) = 0.898365187613 -0.123099065299 absolute error = 1.010e-06 relative error = 0.0001114 % Correct digits = 6 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6358 Order of pole (three term test) = 32.6 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1023 0.116 h = 0.003 0.006 y[1] (numeric) = 0.898659797414 -0.127526041523 y[1] (closed_form) = 0.898662745084 -0.127525203112 absolute error = 3.065e-06 relative error = 0.0003376 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8439 Order of pole (three term test) = 32.6 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1053 0.122 h = 0.0001 0.005 y[1] (numeric) = 0.89597946866 -0.134470262372 y[1] (closed_form) = 0.895982361401 -0.134480145739 absolute error = 1.030e-05 relative error = 0.001137 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3759 Order of pole (three term test) = 32.61 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1054 0.127 h = 0.0001 0.003 y[1] (numeric) = 0.896424771407 -0.140028951352 y[1] (closed_form) = 0.896426568065 -0.140031972909 absolute error = 3.515e-06 relative error = 0.0003875 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3034 Order of pole (three term test) = 32.61 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=30.5MB, alloc=40.3MB, time=0.38 x[1] = 0.1055 0.13 h = 0.001 0.001 y[1] (numeric) = 0.896660295028 -0.143367304052 y[1] (closed_form) = 0.896659416011 -0.143369806954 absolute error = 2.653e-06 relative error = 0.0002921 % Correct digits = 6 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2385 Order of pole (three term test) = 32.61 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1065 0.131 h = 0.001 0.003 y[1] (numeric) = 0.895668234458 -0.144593867349 y[1] (closed_form) = 0.89566613534 -0.144595667134 absolute error = 2.765e-06 relative error = 0.0003048 % Correct digits = 6 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.132 Order of pole (three term test) = 32.61 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1075 0.134 h = 0.0001 0.004 y[1] (numeric) = 0.894908746245 -0.148042740235 y[1] (closed_form) = 0.894909186218 -0.148045873567 absolute error = 3.164e-06 relative error = 0.0003488 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6415 Order of pole (three term test) = 32.61 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1076 0.138 h = 0.003 0.006 y[1] (numeric) = 0.895279427014 -0.152503171058 y[1] (closed_form) = 0.895281960515 -0.152505046669 absolute error = 3.152e-06 relative error = 0.0003471 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8518 Order of pole (three term test) = 32.61 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1106 0.144 h = 0.0001 0.005 y[1] (numeric) = 0.892689344647 -0.159551640853 y[1] (closed_form) = 0.89269152493 -0.159564240623 absolute error = 1.279e-05 relative error = 0.00141 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3796 Order of pole (three term test) = 32.61 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1107 0.149 h = 0.0001 0.003 y[1] (numeric) = 0.893228083819 -0.165152435996 y[1] (closed_form) = 0.893229359097 -0.165158138347 absolute error = 5.843e-06 relative error = 0.0006433 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3065 Order of pole (three term test) = 32.62 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1108 0.152 h = 0.001 0.001 y[1] (numeric) = 0.893519394459 -0.168517160561 y[1] (closed_form) = 0.893518006019 -0.168522269125 absolute error = 5.294e-06 relative error = 0.0005822 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.241 Order of pole (three term test) = 32.62 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1118 0.153 h = 0.001 0.003 y[1] (numeric) = 0.892537981135 -0.169770794487 y[1] (closed_form) = 0.89253539096 -0.169775165152 absolute error = 5.081e-06 relative error = 0.0005592 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.144 Order of pole (three term test) = 32.62 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1128 0.156 h = 0.0001 0.004 y[1] (numeric) = 0.891826753015 -0.173263111293 y[1] (closed_form) = 0.891826667395 -0.173268888002 absolute error = 5.777e-06 relative error = 0.0006359 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6484 Order of pole (three term test) = 32.62 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1129 0.16 h = 0.003 0.006 y[1] (numeric) = 0.892271742641 -0.177758640423 y[1] (closed_form) = 0.892273788515 -0.17776321637 absolute error = 5.012e-06 relative error = 0.0005509 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8613 Order of pole (three term test) = 32.62 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1159 0.166 h = 0.0001 0.005 y[1] (numeric) = 0.889769081955 -0.184913968669 y[1] (closed_form) = 0.889770473661 -0.184929275964 absolute error = 1.537e-05 relative error = 0.001691 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3841 Order of pole (three term test) = 32.62 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.116 0.171 h = 0.0001 0.003 y[1] (numeric) = 0.890400196971 -0.190559549149 y[1] (closed_form) = 0.890400875945 -0.190567920059 absolute error = 8.398e-06 relative error = 0.0009223 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3102 Order of pole (three term test) = 32.62 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1161 0.174 h = 0.001 0.001 y[1] (numeric) = 0.890746642731 -0.193952247572 y[1] (closed_form) = 0.890744668869 -0.19395994867 absolute error = 7.950e-06 relative error = 0.0008721 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.244 Order of pole (three term test) = 32.62 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1171 0.175 h = 0.001 0.003 y[1] (numeric) = 0.889775136835 -0.195233294805 y[1] (closed_form) = 0.889771979228 -0.195240222606 absolute error = 7.613e-06 relative error = 0.0008358 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.159 Order of pole (three term test) = 32.62 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1181 0.178 h = 0.0001 0.004 y[1] (numeric) = 0.889111030073 -0.198770481886 y[1] (closed_form) = 0.889110343299 -0.198778889454 absolute error = 8.436e-06 relative error = 0.0009259 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6567 Order of pole (three term test) = 32.62 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1182 0.182 h = 0.003 0.006 y[1] (numeric) = 0.889629482999 -0.203303262717 y[1] (closed_form) = 0.889630966937 -0.203310526431 absolute error = 7.414e-06 relative error = 0.0008124 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8726 Order of pole (three term test) = 32.63 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1212 0.188 h = 0.0001 0.005 y[1] (numeric) = 0.887211434225 -0.210568128026 y[1] (closed_form) = 0.887211960244 -0.210586135017 absolute error = 1.801e-05 relative error = 0.001976 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3893 Order of pole (three term test) = 32.63 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1213 0.193 h = 0.0001 0.003 y[1] (numeric) = 0.887933896176 -0.216261214979 y[1] (closed_form) = 0.887933903029 -0.21627224329 absolute error = 1.103e-05 relative error = 0.001207 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3146 Order of pole (three term test) = 32.63 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1214 0.196 h = 0.001 0.001 y[1] (numeric) = 0.888334843772 -0.219683514867 y[1] (closed_form) = 0.888332207616 -0.219693796418 absolute error = 1.061e-05 relative error = 0.00116 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2475 Order of pole (three term test) = 32.63 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=74.1MB, alloc=44.3MB, time=0.90 x[1] = 0.1224 0.197 h = 0.0001 0.004 y[1] (numeric) = 0.887372503608 -0.220992332892 y[1] (closed_form) = 0.88736870134 -0.22100180512 absolute error = 1.021e-05 relative error = 0.001116 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.487 Order of pole (three term test) = 32.63 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1225 0.201 h = 0.003 0.006 y[1] (numeric) = 0.887950487341 -0.225557088088 y[1] (closed_form) = 0.887952416328 -0.22556644416 absolute error = 9.553e-06 relative error = 0.001043 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8838 Order of pole (three term test) = 32.63 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1255 0.207 h = 0.0001 0.005 y[1] (numeric) = 0.885604379216 -0.232917474801 y[1] (closed_form) = 0.885605086692 -0.23293759183 absolute error = 2.013e-05 relative error = 0.002198 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3944 Order of pole (three term test) = 32.64 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1256 0.212 h = 0.0001 0.003 y[1] (numeric) = 0.886405279815 -0.238652593516 y[1] (closed_form) = 0.886405635294 -0.238665690487 absolute error = 1.310e-05 relative error = 0.001427 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3189 Order of pole (three term test) = 32.64 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1257 0.215 h = 0.001 0.001 y[1] (numeric) = 0.88685302686 -0.242101057401 y[1] (closed_form) = 0.886850746032 -0.24211334051 absolute error = 1.249e-05 relative error = 0.001359 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2509 Order of pole (three term test) = 32.64 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1267 0.216 h = 0.001 0.003 y[1] (numeric) = 0.885898317458 -0.243433980047 y[1] (closed_form) = 0.885894884979 -0.243445422105 absolute error = 1.195e-05 relative error = 0.0013 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.191 Order of pole (three term test) = 32.64 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1277 0.219 h = 0.0001 0.004 y[1] (numeric) = 0.885319474955 -0.247058034762 y[1] (closed_form) = 0.885318453528 -0.247071097498 absolute error = 1.310e-05 relative error = 0.001426 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6757 Order of pole (three term test) = 32.64 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1278 0.223 h = 0.003 0.006 y[1] (numeric) = 0.885972965681 -0.251665128648 y[1] (closed_form) = 0.885974191967 -0.251677152904 absolute error = 1.209e-05 relative error = 0.001312 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8984 Order of pole (three term test) = 32.64 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1308 0.229 h = 0.0001 0.005 y[1] (numeric) = 0.883706308239 -0.259140255732 y[1] (closed_form) = 0.883706003727 -0.259163061559 absolute error = 2.281e-05 relative error = 0.002477 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4011 Order of pole (three term test) = 32.64 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1309 0.234 h = 0.0001 0.003 y[1] (numeric) = 0.884596755371 -0.264928070868 y[1] (closed_form) = 0.884596295056 -0.264943808198 absolute error = 1.574e-05 relative error = 0.001705 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3244 Order of pole (three term test) = 32.64 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.131 0.237 h = 0.001 0.001 y[1] (numeric) = 0.885097893246 -0.268409242079 y[1] (closed_form) = 0.885094804539 -0.268424086804 absolute error = 1.516e-05 relative error = 0.001639 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2553 Order of pole (three term test) = 32.65 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.132 0.238 h = 0.001 0.003 y[1] (numeric) = 0.88415096769 -0.269770649009 y[1] (closed_form) = 0.884146744331 -0.269784615457 absolute error = 1.459e-05 relative error = 0.001578 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.212 Order of pole (three term test) = 32.65 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.133 0.241 h = 0.0001 0.004 y[1] (numeric) = 0.883616065081 -0.27344384268 y[1] (closed_form) = 0.883614221216 -0.273459507171 absolute error = 1.577e-05 relative error = 0.001705 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6878 Order of pole (three term test) = 32.65 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1331 0.245 h = 0.003 0.006 y[1] (numeric) = 0.884340761183 -0.278094548925 y[1] (closed_form) = 0.884341207858 -0.278109231879 absolute error = 1.469e-05 relative error = 0.001585 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9147 Order of pole (three term test) = 32.65 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1361 0.251 h = 0.0001 0.005 y[1] (numeric) = 0.882150777671 -0.285687295837 y[1] (closed_form) = 0.88214938105 -0.285712785533 absolute error = 2.553e-05 relative error = 0.002753 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4086 Order of pole (three term test) = 32.65 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1362 0.256 h = 0.0001 0.003 y[1] (numeric) = 0.883129827489 -0.291530653858 y[1] (closed_form) = 0.883128472838 -0.29154902336 absolute error = 1.842e-05 relative error = 0.001981 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3306 Order of pole (three term test) = 32.65 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1363 0.259 h = 0.001 0.001 y[1] (numeric) = 0.883683772803 -0.295046236416 y[1] (closed_form) = 0.883679796685 -0.295063633549 absolute error = 1.785e-05 relative error = 0.001916 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2603 Order of pole (three term test) = 32.65 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1373 0.26 h = 0.001 0.003 y[1] (numeric) = 0.882743881864 -0.296436527486 y[1] (closed_form) = 0.88273878778 -0.296453008452 absolute error = 1.725e-05 relative error = 0.001853 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.236 Order of pole (three term test) = 32.66 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1383 0.263 h = 0.0001 0.004 y[1] (numeric) = 0.882251818621 -0.300160410058 y[1] (closed_form) = 0.882249073163 -0.30017866776 absolute error = 1.846e-05 relative error = 0.001981 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7012 Order of pole (three term test) = 32.66 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=117.8MB, alloc=44.3MB, time=1.42 x[1] = 0.1384 0.267 h = 0.003 0.006 y[1] (numeric) = 0.883046965877 -0.304857018036 y[1] (closed_form) = 0.883046555058 -0.304874351231 absolute error = 1.734e-05 relative error = 0.001856 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9329 Order of pole (three term test) = 32.66 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1414 0.273 h = 0.0001 0.005 y[1] (numeric) = 0.880930887069 -0.312570335739 y[1] (closed_form) = 0.880928317095 -0.312598505345 absolute error = 2.829e-05 relative error = 0.003026 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4169 Order of pole (three term test) = 32.66 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1415 0.278 h = 0.0001 0.003 y[1] (numeric) = 0.88199762317 -0.318472129097 y[1] (closed_form) = 0.881995294618 -0.318493123576 absolute error = 2.112e-05 relative error = 0.002253 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3375 Order of pole (three term test) = 32.66 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1416 0.281 h = 0.001 0.001 y[1] (numeric) = 0.882603808583 -0.322023855025 y[1] (closed_form) = 0.882598864521 -0.322043796316 absolute error = 2.055e-05 relative error = 0.002187 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2657 Order of pole (three term test) = 32.66 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1426 0.282 h = 0.001 0.003 y[1] (numeric) = 0.881670199502 -0.323443444902 y[1] (closed_form) = 0.881664153864 -0.323462431456 absolute error = 1.993e-05 relative error = 0.002122 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.262 Order of pole (three term test) = 32.66 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1436 0.285 h = 0.0001 0.004 y[1] (numeric) = 0.881219882807 -0.327219599421 y[1] (closed_form) = 0.881216155583 -0.327240442762 absolute error = 2.117e-05 relative error = 0.002253 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7162 Order of pole (three term test) = 32.67 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1437 0.289 h = 0.003 0.006 y[1] (numeric) = 0.88208474841 -0.331964435865 y[1] (closed_form) = 0.882083401206 -0.331984411852 absolute error = 2.002e-05 relative error = 0.002124 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9531 Order of pole (three term test) = 32.67 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1467 0.295 h = 0.0001 0.005 y[1] (numeric) = 0.880039810655 -0.339801347529 y[1] (closed_form) = 0.880035984925 -0.339832194034 absolute error = 3.108e-05 relative error = 0.003295 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4261 Order of pole (three term test) = 32.67 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1468 0.3 h = 0.0001 0.003 y[1] (numeric) = 0.881193342986 -0.345764515768 y[1] (closed_form) = 0.881189959913 -0.345788128996 absolute error = 2.385e-05 relative error = 0.00252 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.345 Order of pole (three term test) = 32.67 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1469 0.303 h = 0.001 0.001 y[1] (numeric) = 0.881851216546 -0.349354145752 y[1] (closed_form) = 0.881845222973 -0.349376623884 absolute error = 2.326e-05 relative error = 0.002453 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2717 Order of pole (three term test) = 32.67 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1479 0.304 h = 0.0001 0.004 y[1] (numeric) = 0.880923132597 -0.350803463925 y[1] (closed_form) = 0.880916053559 -0.350824948058 absolute error = 2.262e-05 relative error = 0.002386 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.633 Order of pole (three term test) = 32.67 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.148 0.308 h = 0.003 0.006 y[1] (numeric) = 0.881844564627 -0.355589388814 y[1] (closed_form) = 0.881843393007 -0.355611552741 absolute error = 2.219e-05 relative error = 0.002334 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9721 Order of pole (three term test) = 32.68 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.151 0.314 h = 0.0001 0.005 y[1] (numeric) = 0.879860175086 -0.363534359886 y[1] (closed_form) = 0.879856247583 -0.36356743106 absolute error = 3.330e-05 relative error = 0.003498 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4348 Order of pole (three term test) = 32.68 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1511 0.319 h = 0.0001 0.003 y[1] (numeric) = 0.881088504947 -0.369551728317 y[1] (closed_form) = 0.881085194082 -0.369577511175 absolute error = 2.599e-05 relative error = 0.002721 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3521 Order of pole (three term test) = 32.68 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1512 0.322 h = 0.001 0.001 y[1] (numeric) = 0.881790919815 -0.373174810104 y[1] (closed_form) = 0.881785001027 -0.373199386416 absolute error = 2.528e-05 relative error = 0.00264 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2774 Order of pole (three term test) = 32.68 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1522 0.323 h = 0.001 0.003 y[1] (numeric) = 0.880867343751 -0.374650019191 y[1] (closed_form) = 0.880860352675 -0.374673566957 absolute error = 2.456e-05 relative error = 0.002566 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.318 Order of pole (three term test) = 32.68 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1532 0.326 h = 0.0001 0.004 y[1] (numeric) = 0.880492490615 -0.378527301415 y[1] (closed_form) = 0.880487764363 -0.378552858983 absolute error = 2.599e-05 relative error = 0.002712 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.748 Order of pole (three term test) = 32.69 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1533 0.33 h = 0.003 0.006 y[1] (numeric) = 0.881485846835 -0.383367393328 y[1] (closed_form) = 0.881483589165 -0.383392189766 absolute error = 2.490e-05 relative error = 0.00259 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9959 Order of pole (three term test) = 32.69 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=161.4MB, alloc=44.3MB, time=1.94 x[1] = 0.1563 0.336 h = 0.0001 0.005 y[1] (numeric) = 0.879567502013 -0.391441811351 y[1] (closed_form) = 0.879562162194 -0.391477557289 absolute error = 3.614e-05 relative error = 0.003754 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4456 Order of pole (three term test) = 32.69 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1564 0.341 h = 0.0001 0.003 y[1] (numeric) = 0.880881074709 -0.397526163617 y[1] (closed_form) = 0.880876556326 -0.397554557137 absolute error = 2.875e-05 relative error = 0.002975 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.361 Order of pole (three term test) = 32.69 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1565 0.344 h = 0.001 0.001 y[1] (numeric) = 0.881634211169 -0.401190510465 y[1] (closed_form) = 0.881627088155 -0.401217613415 absolute error = 2.802e-05 relative error = 0.002893 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2845 Order of pole (three term test) = 32.69 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1575 0.345 h = 0.001 0.003 y[1] (numeric) = 0.880714745586 -0.402696295696 y[1] (closed_form) = 0.880706565909 -0.402722329517 absolute error = 2.729e-05 relative error = 0.002818 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.351 Order of pole (three term test) = 32.7 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1585 0.348 h = 0.0001 0.004 y[1] (numeric) = 0.880378567719 -0.406630578416 y[1] (closed_form) = 0.88037262437 -0.406658706132 absolute error = 2.875e-05 relative error = 0.002965 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7672 Order of pole (three term test) = 32.7 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1586 0.352 h = 0.003 0.006 y[1] (numeric) = 0.881439685607 -0.411525777341 y[1] (closed_form) = 0.881436259927 -0.41155320162 absolute error = 2.764e-05 relative error = 0.002841 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.022 Order of pole (three term test) = 32.7 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1616 0.358 h = 0.0001 0.005 y[1] (numeric) = 0.879584627789 -0.419732876235 y[1] (closed_form) = 0.879577789737 -0.41977129654 absolute error = 3.902e-05 relative error = 0.004004 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4574 Order of pole (three term test) = 32.7 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1617 0.363 h = 0.0001 0.003 y[1] (numeric) = 0.880982623229 -0.42588729268 y[1] (closed_form) = 0.8809768135 -0.425918293304 absolute error = 3.154e-05 relative error = 0.003223 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3707 Order of pole (three term test) = 32.7 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1618 0.366 h = 0.001 0.001 y[1] (numeric) = 0.881785970064 -0.429594750893 y[1] (closed_form) = 0.881777558107 -0.429624375728 absolute error = 3.080e-05 relative error = 0.00314 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2921 Order of pole (three term test) = 32.71 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1628 0.367 h = 0.001 0.003 y[1] (numeric) = 0.88086984458 -0.431131584354 y[1] (closed_form) = 0.880860391354 -0.431160098741 absolute error = 3.004e-05 relative error = 0.003063 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.388 Order of pole (three term test) = 32.71 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1638 0.37 h = 0.0001 0.004 y[1] (numeric) = 0.880571271166 -0.435124582895 y[1] (closed_form) = 0.880564026303 -0.435155276749 absolute error = 3.154e-05 relative error = 0.003211 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7881 Order of pole (three term test) = 32.71 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1639 0.374 h = 0.003 0.006 y[1] (numeric) = 0.881699492863 -0.440077368137 y[1] (closed_form) = 0.881694816068 -0.440107416513 absolute error = 3.041e-05 relative error = 0.003086 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.05 Order of pole (three term test) = 32.71 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1669 0.38 h = 0.0001 0.005 y[1] (numeric) = 0.879904962245 -0.448420457073 y[1] (closed_form) = 0.879896538734 -0.448461552217 absolute error = 4.195e-05 relative error = 0.004248 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4701 Order of pole (three term test) = 32.72 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.167 0.385 h = 0.0001 0.003 y[1] (numeric) = 0.881386582488 -0.454648069673 y[1] (closed_form) = 0.881379396386 -0.454681674732 absolute error = 3.436e-05 relative error = 0.003465 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3811 Order of pole (three term test) = 32.72 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1671 0.388 h = 0.001 0.001 y[1] (numeric) = 0.882239641316 -0.45840051692 y[1] (closed_form) = 0.882229854526 -0.458432659736 absolute error = 3.360e-05 relative error = 0.003379 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3004 Order of pole (three term test) = 32.72 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1681 0.389 h = 0.001 0.003 y[1] (numeric) = 0.881326079832 -0.459968885632 y[1] (closed_form) = 0.881315266951 -0.459999875933 absolute error = 3.282e-05 relative error = 0.003302 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.427 Order of pole (three term test) = 32.72 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1691 0.392 h = 0.0001 0.004 y[1] (numeric) = 0.881064043508 -0.464022350862 y[1] (closed_form) = 0.881055411521 -0.464055607708 absolute error = 3.436e-05 relative error = 0.00345 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8105 Order of pole (three term test) = 32.72 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1692 0.396 h = 0.003 0.006 y[1] (numeric) = 0.882258728317 -0.469035243629 y[1] (closed_form) = 0.88225271612 -0.469067913261 absolute error = 3.322e-05 relative error = 0.003324 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.08 Order of pole (three term test) = 32.72 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1722 0.402 h = 0.0001 0.005 y[1] (numeric) = 0.880521960976 -0.477517707894 y[1] (closed_form) = 0.880511863434 -0.477561479201 absolute error = 4.492e-05 relative error = 0.004485 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4838 Order of pole (three term test) = 32.73 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=204.9MB, alloc=44.3MB, time=2.46 x[1] = 0.1723 0.407 h = 0.0001 0.003 y[1] (numeric) = 0.882086429137 -0.4838217015 y[1] (closed_form) = 0.882077780402 -0.48385790919 absolute error = 3.723e-05 relative error = 0.0037 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3923 Order of pole (three term test) = 32.73 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1724 0.41 h = 0.001 0.001 y[1] (numeric) = 0.88298871375 -0.487621047556 y[1] (closed_form) = 0.882977465022 -0.487655705276 absolute error = 3.644e-05 relative error = 0.003612 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3092 Order of pole (three term test) = 32.73 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1734 0.411 h = 0.0001 0.004 y[1] (numeric) = 0.882076933981 -0.489221453515 y[1] (closed_form) = 0.88206467414 -0.489254915888 absolute error = 3.564e-05 relative error = 0.003533 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.859 Order of pole (three term test) = 32.73 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1735 0.415 h = 0.003 0.006 y[1] (numeric) = 0.883325607471 -0.494285302049 y[1] (closed_form) = 0.883319491329 -0.494320279805 absolute error = 3.551e-05 relative error = 0.003508 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.108 Order of pole (three term test) = 32.73 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1765 0.421 h = 0.0001 0.005 y[1] (numeric) = 0.88163805945 -0.50288986242 y[1] (closed_form) = 0.881627563645 -0.502935996512 absolute error = 4.731e-05 relative error = 0.004661 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4964 Order of pole (three term test) = 32.74 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1766 0.426 h = 0.0001 0.003 y[1] (numeric) = 0.883274195981 -0.509261219238 y[1] (closed_form) = 0.883265331957 -0.509299721369 absolute error = 3.951e-05 relative error = 0.003875 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4026 Order of pole (three term test) = 32.74 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1767 0.429 h = 0.001 0.001 y[1] (numeric) = 0.884219062198 -0.513101909882 y[1] (closed_form) = 0.884207597051 -0.513138785487 absolute error = 3.862e-05 relative error = 0.003777 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3174 Order of pole (three term test) = 32.74 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1777 0.43 h = 0.001 0.003 y[1] (numeric) = 0.88330857461 -0.51473029747 y[1] (closed_form) = 0.883296110573 -0.514765940059 absolute error = 3.776e-05 relative error = 0.003693 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.508 Order of pole (three term test) = 32.75 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1787 0.433 h = 0.0001 0.004 y[1] (numeric) = 0.883112463754 -0.518900655808 y[1] (closed_form) = 0.883102131799 -0.518938731421 absolute error = 3.945e-05 relative error = 0.003852 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.857 Order of pole (three term test) = 32.75 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1788 0.437 h = 0.003 0.006 y[1] (numeric) = 0.884429959722 -0.524031478224 y[1] (closed_form) = 0.884422348053 -0.524069075327 absolute error = 3.836e-05 relative error = 0.003731 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.142 Order of pole (three term test) = 32.75 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1818 0.443 h = 0.0001 0.005 y[1] (numeric) = 0.882795056469 -0.532781951984 y[1] (closed_form) = 0.882782718137 -0.532830767987 absolute error = 5.035e-05 relative error = 0.004883 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.512 Order of pole (three term test) = 32.76 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1819 0.448 h = 0.0001 0.003 y[1] (numeric) = 0.884512687082 -0.539235769886 y[1] (closed_form) = 0.884502196496 -0.539276874591 absolute error = 4.242e-05 relative error = 0.004095 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4153 Order of pole (three term test) = 32.76 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.182 0.451 h = 0.001 0.001 y[1] (numeric) = 0.885505928163 -0.543127006521 y[1] (closed_form) = 0.885492835615 -0.543166394506 absolute error = 4.151e-05 relative error = 0.003996 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3275 Order of pole (three term test) = 32.76 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.183 0.452 h = 0.001 0.003 y[1] (numeric) = 0.884595754953 -0.544788414991 y[1] (closed_form) = 0.884581678159 -0.544826525663 absolute error = 4.063e-05 relative error = 0.003911 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.556 Order of pole (three term test) = 32.76 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.184 0.455 h = 0.0001 0.004 y[1] (numeric) = 0.884433161054 -0.54902446274 y[1] (closed_form) = 0.884421190138 -0.549065098014 absolute error = 4.236e-05 relative error = 0.004069 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8844 Order of pole (three term test) = 32.76 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1841 0.459 h = 0.003 0.006 y[1] (numeric) = 0.885815405952 -0.554222852749 y[1] (closed_form) = 0.885806210886 -0.554263068847 absolute error = 4.125e-05 relative error = 0.003948 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.179 Order of pole (three term test) = 32.76 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1871 0.465 h = 0.0001 0.005 y[1] (numeric) = 0.884230361313 -0.56312284815 y[1] (closed_form) = 0.884216087812 -0.563174349726 absolute error = 5.344e-05 relative error = 0.005098 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5286 Order of pole (three term test) = 32.77 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1872 0.47 h = 0.0001 0.003 y[1] (numeric) = 0.886028763969 -0.569662470162 y[1] (closed_form) = 0.886016556819 -0.569706178015 absolute error = 4.538e-05 relative error = 0.004308 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4289 Order of pole (three term test) = 32.77 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1873 0.473 h = 0.001 0.001 y[1] (numeric) = 0.88706992525 -0.573606258532 y[1] (closed_form) = 0.887055114514 -0.573648158084 absolute error = 4.444e-05 relative error = 0.004207 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3383 Order of pole (three term test) = 32.78 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=248.4MB, alloc=44.3MB, time=2.97 x[1] = 0.1883 0.474 h = 0.001 0.003 y[1] (numeric) = 0.88615926398 -0.575301233088 y[1] (closed_form) = 0.88614348349 -0.575341810219 absolute error = 4.354e-05 relative error = 0.004121 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.607 Order of pole (three term test) = 32.78 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1893 0.477 h = 0.0001 0.004 y[1] (numeric) = 0.886029124985 -0.579604863639 y[1] (closed_form) = 0.886015424543 -0.579648058592 absolute error = 4.532e-05 relative error = 0.00428 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9136 Order of pole (three term test) = 32.78 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1894 0.481 h = 0.003 0.006 y[1] (numeric) = 0.887475536654 -0.584873513671 y[1] (closed_form) = 0.887464668988 -0.584916349237 absolute error = 4.419e-05 relative error = 0.004158 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.218 Order of pole (three term test) = 32.78 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1924 0.487 h = 0.0001 0.005 y[1] (numeric) = 0.885937552334 -0.593926718762 y[1] (closed_form) = 0.885921249514 -0.593980910344 absolute error = 5.659e-05 relative error = 0.005306 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5464 Order of pole (three term test) = 32.79 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1925 0.492 h = 0.0001 0.003 y[1] (numeric) = 0.887816021812 -0.600555545865 y[1] (closed_form) = 0.887802006707 -0.600601858231 absolute error = 4.839e-05 relative error = 0.004514 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4434 Order of pole (three term test) = 32.79 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1926 0.495 h = 0.001 0.001 y[1] (numeric) = 0.888904658221 -0.604553926852 y[1] (closed_form) = 0.88888803714 -0.604598337901 absolute error = 4.742e-05 relative error = 0.004411 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3497 Order of pole (three term test) = 32.79 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1936 0.496 h = 0.001 0.003 y[1] (numeric) = 0.8879926984 -0.606283027889 y[1] (closed_form) = 0.887975121925 -0.606326070581 absolute error = 4.649e-05 relative error = 0.004324 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.662 Order of pole (three term test) = 32.79 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1946 0.499 h = 0.0001 0.004 y[1] (numeric) = 0.887893951295 -0.610656173015 y[1] (closed_form) = 0.887878429373 -0.610701928427 absolute error = 4.832e-05 relative error = 0.004484 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9447 Order of pole (three term test) = 32.8 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1947 0.503 h = 0.003 0.006 y[1] (numeric) = 0.889403960444 -0.615997822495 y[1] (closed_form) = 0.889391329601 -0.616043278807 absolute error = 4.718e-05 relative error = 0.004361 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.26 Order of pole (three term test) = 32.8 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1977 0.509 h = 0.0001 0.005 y[1] (numeric) = 0.887910223873 -0.625208006154 y[1] (closed_form) = 0.887891796029 -0.62526489293 absolute error = 5.980e-05 relative error = 0.005506 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5652 Order of pole (three term test) = 32.81 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1978 0.514 h = 0.0001 0.003 y[1] (numeric) = 0.889868070649 -0.631929498675 y[1] (closed_form) = 0.889852154766 -0.631978417681 absolute error = 5.144e-05 relative error = 0.004713 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4588 Order of pole (three term test) = 32.81 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1979 0.517 h = 0.001 0.001 y[1] (numeric) = 0.891003746026 -0.63598454912 y[1] (closed_form) = 0.890985221034 -0.636031472321 absolute error = 5.045e-05 relative error = 0.004608 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3619 Order of pole (three term test) = 32.81 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1989 0.518 h = 0.0001 0.004 y[1] (numeric) = 0.890089668616 -0.63774835229 y[1] (closed_form) = 0.890070202471 -0.637793860349 absolute error = 4.950e-05 relative error = 0.00452 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.176 Order of pole (three term test) = 32.81 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.199 0.522 h = 0.003 0.006 y[1] (numeric) = 0.891651393535 -0.64315167063 y[1] (closed_form) = 0.891638365475 -0.643199579624 absolute error = 4.965e-05 relative error = 0.004516 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.298 Order of pole (three term test) = 32.81 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.202 0.528 h = 0.0001 0.005 y[1] (numeric) = 0.890195411775 -0.652499575537 y[1] (closed_form) = 0.890176271955 -0.652558986568 absolute error = 6.242e-05 relative error = 0.005655 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5825 Order of pole (three term test) = 32.82 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2021 0.533 h = 0.0001 0.003 y[1] (numeric) = 0.892222203945 -0.659302714015 y[1] (closed_form) = 0.892205770406 -0.65935407589 absolute error = 5.393e-05 relative error = 0.004861 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4729 Order of pole (three term test) = 32.82 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2022 0.536 h = 0.001 0.001 y[1] (numeric) = 0.893398735334 -0.663407681388 y[1] (closed_form) = 0.893379688255 -0.663456964961 absolute error = 5.284e-05 relative error = 0.004748 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3731 Order of pole (three term test) = 32.83 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2032 0.537 h = 0.001 0.003 y[1] (numeric) = 0.892482595393 -0.665201866335 y[1] (closed_form) = 0.892462618769 -0.665249693636 absolute error = 5.183e-05 relative error = 0.004656 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.773 Order of pole (three term test) = 32.83 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2042 0.54 h = 0.0001 0.004 y[1] (numeric) = 0.892440309022 -0.669709293521 y[1] (closed_form) = 0.892422341476 -0.669760015017 absolute error = 5.381e-05 relative error = 0.004823 % Correct digits = 4 memory used=292.0MB, alloc=44.3MB, time=3.50 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.008 Order of pole (three term test) = 32.83 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2043 0.544 h = 0.003 0.006 y[1] (numeric) = 0.894068132265 -0.675193492562 y[1] (closed_form) = 0.894053168722 -0.675244027868 absolute error = 5.270e-05 relative error = 0.004704 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.345 Order of pole (three term test) = 32.83 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2073 0.55 h = 0.0001 0.005 y[1] (numeric) = 0.892651166519 -0.684705641833 y[1] (closed_form) = 0.892629719389 -0.684767760831 absolute error = 6.572e-05 relative error = 0.005841 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6035 Order of pole (three term test) = 32.84 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2074 0.555 h = 0.0001 0.003 y[1] (numeric) = 0.894756133841 -0.691608055232 y[1] (closed_form) = 0.89473762289 -0.691662030823 absolute error = 5.706e-05 relative error = 0.005046 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4901 Order of pole (three term test) = 32.84 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2075 0.558 h = 0.001 0.001 y[1] (numeric) = 0.895978939777 -0.695773660183 y[1] (closed_form) = 0.895957810803 -0.69582546013 absolute error = 5.594e-05 relative error = 0.004931 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3866 Order of pole (three term test) = 32.85 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2085 0.559 h = 0.001 0.003 y[1] (numeric) = 0.895059140989 -0.697603669289 y[1] (closed_form) = 0.895037096532 -0.697653964558 absolute error = 5.491e-05 relative error = 0.004839 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.838 Order of pole (three term test) = 32.85 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2095 0.562 h = 0.0001 0.004 y[1] (numeric) = 0.895045216333 -0.702186367873 y[1] (closed_form) = 0.895025156261 -0.702239657243 absolute error = 5.694e-05 relative error = 0.005005 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.045 Order of pole (three term test) = 32.85 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2096 0.566 h = 0.003 0.006 y[1] (numeric) = 0.896735106066 -0.707751679194 y[1] (closed_form) = 0.896718112312 -0.707804844294 absolute error = 5.582e-05 relative error = 0.004886 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.394 Order of pole (three term test) = 32.85 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2126 0.572 h = 0.0001 0.005 y[1] (numeric) = 0.895354291905 -0.717432079172 y[1] (closed_form) = 0.895330437079 -0.71749691339 absolute error = 6.908e-05 relative error = 0.006021 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6258 Order of pole (three term test) = 32.86 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2127 0.577 h = 0.0001 0.003 y[1] (numeric) = 0.897536784317 -0.724437405376 y[1] (closed_form) = 0.897516098805 -0.724493998907 absolute error = 6.026e-05 relative error = 0.005224 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5082 Order of pole (three term test) = 32.87 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2128 0.58 h = 0.001 0.001 y[1] (numeric) = 0.898805450813 -0.728665832278 y[1] (closed_form) = 0.898782142108 -0.728720151221 absolute error = 5.911e-05 relative error = 0.005108 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.401 Order of pole (three term test) = 32.87 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2138 0.581 h = 0.001 0.003 y[1] (numeric) = 0.897881147031 -0.730532285374 y[1] (closed_form) = 0.897856936837 -0.730585050332 absolute error = 5.805e-05 relative error = 0.005015 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.906 Order of pole (three term test) = 32.87 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2148 0.584 h = 0.0001 0.004 y[1] (numeric) = 0.897894508975 -0.735192341464 y[1] (closed_form) = 0.897872258679 -0.735248202258 absolute error = 6.013e-05 relative error = 0.005181 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.084 Order of pole (three term test) = 32.87 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2149 0.588 h = 0.003 0.006 y[1] (numeric) = 0.899645937727 -0.74084169653 y[1] (closed_form) = 0.899626817492 -0.740897495633 absolute error = 5.898e-05 relative error = 0.005061 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.446 Order of pole (three term test) = 32.88 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2179 0.594 h = 0.0001 0.005 y[1] (numeric) = 0.898298387966 -0.7506944387 y[1] (closed_form) = 0.898272023325 -0.750761996066 absolute error = 7.252e-05 relative error = 0.006195 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6494 Order of pole (three term test) = 32.89 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.218 0.599 h = 0.0001 0.003 y[1] (numeric) = 0.900557766749 -0.757806380593 y[1] (closed_form) = 0.900534807925 -0.757865596974 absolute error = 6.351e-05 relative error = 0.005396 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5275 Order of pole (three term test) = 32.89 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2181 0.602 h = 0.001 0.001 y[1] (numeric) = 0.901871886075 -0.762099853158 y[1] (closed_form) = 0.901846298221 -0.762156694358 absolute error = 6.234e-05 relative error = 0.005279 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4162 Order of pole (three term test) = 32.89 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2191 0.603 h = 0.001 0.003 y[1] (numeric) = 0.900942220597 -0.764003385638 y[1] (closed_form) = 0.900915745202 -0.764058622628 absolute error = 6.125e-05 relative error = 0.005185 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.978 Order of pole (three term test) = 32.89 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2201 0.606 h = 0.0001 0.004 y[1] (numeric) = 0.900981788426 -0.768742926977 y[1] (closed_form) = 0.900957248613 -0.768801363406 absolute error = 6.338e-05 relative error = 0.005351 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.125 Order of pole (three term test) = 32.9 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=335.7MB, alloc=44.3MB, time=4.02 x[1] = 0.2202 0.61 h = 0.003 0.006 y[1] (numeric) = 0.902794237185 -0.774479309922 y[1] (closed_form) = 0.902772892616 -0.77453774794 absolute error = 6.221e-05 relative error = 0.00523 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.501 Order of pole (three term test) = 32.9 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2232 0.616 h = 0.0001 0.005 y[1] (numeric) = 0.901477039611 -0.784508572101 y[1] (closed_form) = 0.901448061256 -0.784578861198 absolute error = 7.603e-05 relative error = 0.006362 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6743 Order of pole (three term test) = 32.91 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2233 0.621 h = 0.0001 0.003 y[1] (numeric) = 0.903812676236 -0.791730899106 y[1] (closed_form) = 0.903787343699 -0.791792743913 absolute error = 6.683e-05 relative error = 0.005562 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5478 Order of pole (three term test) = 32.91 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2234 0.624 h = 0.001 0.001 y[1] (numeric) = 0.905171846215 -0.796091681302 y[1] (closed_form) = 0.905143878168 -0.796151048639 absolute error = 6.563e-05 relative error = 0.005444 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4323 Order of pole (three term test) = 32.92 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2244 0.625 h = 0.0001 0.004 y[1] (numeric) = 0.904235951249 -0.798032944215 y[1] (closed_form) = 0.904207109577 -0.798090656178 absolute error = 6.452e-05 relative error = 0.00535 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.6 Order of pole (three term test) = 32.92 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2245 0.629 h = 0.003 0.006 y[1] (numeric) = 0.906098064574 -0.803842658228 y[1] (closed_form) = 0.906076011816 -0.803903717819 absolute error = 6.492e-05 relative error = 0.00536 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.552 Order of pole (three term test) = 32.92 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2275 0.635 h = 0.0001 0.005 y[1] (numeric) = 0.904806812382 -0.814026961411 y[1] (closed_form) = 0.904776786845 -0.814099959617 absolute error = 7.893e-05 relative error = 0.006485 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.697 Order of pole (three term test) = 32.93 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2276 0.64 h = 0.0001 0.003 y[1] (numeric) = 0.907208970104 -0.821346476295 y[1] (closed_form) = 0.907182798594 -0.821410935966 absolute error = 6.957e-05 relative error = 0.005685 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5662 Order of pole (three term test) = 32.93 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2277 0.643 h = 0.001 0.001 y[1] (numeric) = 0.908607439104 -0.825766510515 y[1] (closed_form) = 0.908578624759 -0.825828403363 absolute error = 6.827e-05 relative error = 0.00556 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4469 Order of pole (three term test) = 32.94 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2287 0.644 h = 0.001 0.003 y[1] (numeric) = 0.907665938516 -0.827740872382 y[1] (closed_form) = 0.907636261887 -0.827801064884 absolute error = 6.711e-05 relative error = 0.005463 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.124 Order of pole (three term test) = 32.94 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2297 0.647 h = 0.0001 0.004 y[1] (numeric) = 0.907752378362 -0.832633844443 y[1] (closed_form) = 0.907724593695 -0.832697434568 absolute error = 6.940e-05 relative error = 0.005634 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.208 Order of pole (three term test) = 32.94 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2298 0.651 h = 0.003 0.006 y[1] (numeric) = 0.909678137954 -0.838539581319 y[1] (closed_form) = 0.909653674487 -0.838603291985 absolute error = 6.825e-05 relative error = 0.005516 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.613 Order of pole (three term test) = 32.95 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2328 0.657 h = 0.0001 0.005 y[1] (numeric) = 0.908411796733 -0.848908447956 y[1] (closed_form) = 0.908378959367 -0.848984196834 absolute error = 8.256e-05 relative error = 0.00664 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7245 Order of pole (three term test) = 32.96 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2329 0.662 h = 0.0001 0.003 y[1] (numeric) = 0.910889112719 -0.856345551732 y[1] (closed_form) = 0.910860376211 -0.856412653149 absolute error = 7.300e-05 relative error = 0.005839 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5887 Order of pole (three term test) = 32.96 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.233 0.665 h = 0.001 0.001 y[1] (numeric) = 0.912331924497 -0.860837223339 y[1] (closed_form) = 0.912300537508 -0.860901652366 absolute error = 7.167e-05 relative error = 0.005713 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4646 Order of pole (three term test) = 32.96 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.234 0.666 h = 0.001 0.003 y[1] (numeric) = 0.911382556455 -0.862850579758 y[1] (closed_form) = 0.91135032108 -0.862913255476 absolute error = 7.048e-05 relative error = 0.005616 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.209 Order of pole (three term test) = 32.97 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.235 0.669 h = 0.0001 0.004 y[1] (numeric) = 0.911492097756 -0.867829373633 y[1] (closed_form) = 0.911461730346 -0.867895556154 absolute error = 7.282e-05 relative error = 0.005786 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.256 Order of pole (three term test) = 32.97 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2351 0.673 h = 0.003 0.006 y[1] (numeric) = 0.91347746866 -0.873830983281 y[1] (closed_form) = 0.91345049185 -0.873897351859 absolute error = 7.164e-05 relative error = 0.005667 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.677 Order of pole (three term test) = 32.97 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2381 0.679 h = 0.0001 0.005 y[1] (numeric) = 0.912233042852 -0.884388845442 y[1] (closed_form) = 0.9121972844 -0.884467355365 absolute error = 8.627e-05 relative error = 0.00679 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7535 Order of pole (three term test) = 32.98 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=379.2MB, alloc=44.3MB, time=4.54 x[1] = 0.2382 0.684 h = 0.0001 0.003 y[1] (numeric) = 0.914784912101 -0.891947506609 y[1] (closed_form) = 0.914753505225 -0.892017257158 absolute error = 7.650e-05 relative error = 0.005987 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6123 Order of pole (three term test) = 32.99 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2383 0.687 h = 0.001 0.001 y[1] (numeric) = 0.91627167693 -0.896513199948 y[1] (closed_form) = 0.916237611342 -0.896580170703 absolute error = 7.514e-05 relative error = 0.005861 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4833 Order of pole (three term test) = 32.99 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2393 0.688 h = 0.001 0.003 y[1] (numeric) = 0.915313539047 -0.898566247444 y[1] (closed_form) = 0.915278638991 -0.89863141093 absolute error = 7.392e-05 relative error = 0.005763 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.297 Order of pole (three term test) = 33 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2403 0.691 h = 0.0001 0.004 y[1] (numeric) = 0.915445070601 -0.903633158626 y[1] (closed_form) = 0.915412014548 -0.90370194013 absolute error = 7.631e-05 relative error = 0.005933 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.307 Order of pole (three term test) = 33 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2404 0.695 h = 0.003 0.006 y[1] (numeric) = 0.917489558311 -0.909733840341 y[1] (closed_form) = 0.917459963762 -0.909802874293 absolute error = 7.511e-05 relative error = 0.005813 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.745 Order of pole (three term test) = 33 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2434 0.701 h = 0.0001 0.005 y[1] (numeric) = 0.916264018274 -0.920485221373 y[1] (closed_form) = 0.916225227503 -0.92056650329 absolute error = 9.006e-05 relative error = 0.006934 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.784 Order of pole (three term test) = 33.01 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2435 0.706 h = 0.0001 0.003 y[1] (numeric) = 0.918889841428 -0.928169481238 y[1] (closed_form) = 0.918855656978 -0.92824188889 absolute error = 8.007e-05 relative error = 0.006131 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6371 Order of pole (three term test) = 33.02 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2436 0.709 h = 0.001 0.001 y[1] (numeric) = 0.920420172358 -0.932811624653 y[1] (closed_form) = 0.920383320401 -0.932881143219 absolute error = 7.868e-05 relative error = 0.006004 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5029 Order of pole (three term test) = 33.02 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2446 0.71 h = 0.001 0.003 y[1] (numeric) = 0.919452348989 -0.934905075803 y[1] (closed_form) = 0.919414676523 -0.934972732121 absolute error = 7.744e-05 relative error = 0.005905 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.391 Order of pole (three term test) = 33.03 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2456 0.713 h = 0.0001 0.004 y[1] (numeric) = 0.919604749071 -0.940062445087 y[1] (closed_form) = 0.919568896643 -0.940133832718 absolute error = 7.988e-05 relative error = 0.006074 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.36 Order of pole (three term test) = 33.03 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2457 0.717 h = 0.003 0.006 y[1] (numeric) = 0.921707862929 -0.946265457118 y[1] (closed_form) = 0.921675544428 -0.946337164512 absolute error = 7.865e-05 relative error = 0.005954 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.816 Order of pole (three term test) = 33.03 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2487 0.723 h = 0.0001 0.005 y[1] (numeric) = 0.920498142498 -0.957214973004 y[1] (closed_form) = 0.920456206147 -0.957299038422 absolute error = 9.394e-05 relative error = 0.007074 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8161 Order of pole (three term test) = 33.05 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2488 0.728 h = 0.0001 0.003 y[1] (numeric) = 0.923197324624 -0.965028947385 y[1] (closed_form) = 0.923160253508 -0.965104020674 absolute error = 8.373e-05 relative error = 0.006269 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6632 Order of pole (three term test) = 33.05 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2489 0.731 h = 0.001 0.001 y[1] (numeric) = 0.924770836738 -0.969750014234 y[1] (closed_form) = 0.924731088777 -0.969822087208 absolute error = 8.231e-05 relative error = 0.006142 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5235 Order of pole (three term test) = 33.05 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2499 0.732 h = 0.0001 0.004 y[1] (numeric) = 0.9237923984 -0.971884597777 y[1] (closed_form) = 0.92375184395 -0.971954752482 absolute error = 8.103e-05 relative error = 0.006043 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.149 Order of pole (three term test) = 33.06 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.25 0.736 h = 0.003 0.006 y[1] (numeric) = 0.925943261406 -0.978173667007 y[1] (closed_form) = 0.92590990176 -0.97824818932 absolute error = 8.165e-05 relative error = 0.006062 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.88 Order of pole (three term test) = 33.06 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.253 0.742 h = 0.0001 0.005 y[1] (numeric) = 0.924747109711 -0.989297360861 y[1] (closed_form) = 0.924703764846 -0.989384343792 absolute error = 9.718e-05 relative error = 0.007176 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8452 Order of pole (three term test) = 33.07 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2531 0.747 h = 0.0001 0.003 y[1] (numeric) = 0.927510576155 -0.997225478913 y[1] (closed_form) = 0.927472321388 -0.997303362733 absolute error = 8.677e-05 relative error = 0.006371 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6869 Order of pole (three term test) = 33.08 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2532 0.75 h = 0.001 0.001 y[1] (numeric) = 0.929121931045 -1.002015988 y[1] (closed_form) = 0.92908098962 -1.00209077429 absolute error = 8.526e-05 relative error = 0.006239 % Correct digits = 4 memory used=422.8MB, alloc=44.3MB, time=5.06 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5423 Order of pole (three term test) = 33.08 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2542 0.751 h = 0.001 0.003 y[1] (numeric) = 0.928134102473 -1.00418671469 y[1] (closed_form) = 0.928092366004 -1.00425953348 absolute error = 8.393e-05 relative error = 0.006138 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.578 Order of pole (three term test) = 33.09 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2552 0.754 h = 0.0001 0.004 y[1] (numeric) = 0.928323453575 -1.00951857758 y[1] (closed_form) = 0.928283493823 -1.00959534446 absolute error = 8.654e-05 relative error = 0.00631 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.467 Order of pole (three term test) = 33.09 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2553 0.758 h = 0.0001 0.004 y[1] (numeric) = 0.930535673612 -1.0159201974 y[1] (closed_form) = 0.930499387485 -1.01599741102 absolute error = 8.531e-05 relative error = 0.006193 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.168 Order of pole (three term test) = 33.1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2554 0.762 h = 0.003 0.006 y[1] (numeric) = 0.932765633178 -1.02233925417 y[1] (closed_form) = 0.932729347051 -1.02241646779 absolute error = 8.531e-05 relative error = 0.006165 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.973 Order of pole (three term test) = 33.1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2584 0.768 h = 0.0001 0.005 y[1] (numeric) = 0.93158877087 -1.03370594485 y[1] (closed_form) = 0.931541992617 -1.03379577231 absolute error = 0.0001013 relative error = 0.007278 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8871 Order of pole (three term test) = 33.11 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2585 0.773 h = 0.0001 0.003 y[1] (numeric) = 0.934442202472 -1.04179319924 y[1] (closed_form) = 0.934400823313 -1.04187377251 absolute error = 9.058e-05 relative error = 0.006472 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.721 Order of pole (three term test) = 33.12 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2586 0.776 h = 0.001 0.001 y[1] (numeric) = 0.936106533152 -1.04668051807 y[1] (closed_form) = 0.936062450873 -1.04675785913 absolute error = 8.902e-05 relative error = 0.006339 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5692 Order of pole (three term test) = 33.12 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2596 0.777 h = 0.001 0.003 y[1] (numeric) = 0.935105691376 -1.0489017039 y[1] (closed_form) = 0.935060828504 -1.04897700878 absolute error = 8.766e-05 relative error = 0.006238 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.706 Order of pole (three term test) = 33.13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2606 0.78 h = 0.0001 0.004 y[1] (numeric) = 0.935319270497 -1.05434746376 y[1] (closed_form) = 0.935276160486 -1.05442685803 absolute error = 9.034e-05 relative error = 0.00641 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.54 Order of pole (three term test) = 33.13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2607 0.784 h = 0.003 0.006 y[1] (numeric) = 0.937602862166 -1.06087867791 y[1] (closed_form) = 0.937563518743 -1.06095859846 absolute error = 8.908e-05 relative error = 0.006292 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.056 Order of pole (three term test) = 33.14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2637 0.79 h = 0.0001 0.005 y[1] (numeric) = 0.93643251165 -1.07245824538 y[1] (closed_form) = 0.936382231897 -1.07255090036 absolute error = 0.0001054 relative error = 0.007404 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9244 Order of pole (three term test) = 33.15 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2638 0.795 h = 0.0001 0.003 y[1] (numeric) = 0.939357727091 -1.08068820291 y[1] (closed_form) = 0.939313118753 -1.08077147662 absolute error = 9.447e-05 relative error = 0.006597 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7514 Order of pole (three term test) = 33.16 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2639 0.798 h = 0.001 0.001 y[1] (numeric) = 0.941064205357 -1.08566225341 y[1] (closed_form) = 0.941016882945 -1.0857421775 absolute error = 9.288e-05 relative error = 0.006465 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5932 Order of pole (three term test) = 33.16 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2649 0.799 h = 0.001 0.003 y[1] (numeric) = 0.940049876656 -1.08792693063 y[1] (closed_form) = 0.940001787919 -1.08800475922 absolute error = 9.149e-05 relative error = 0.006363 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.82 Order of pole (three term test) = 33.17 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2659 0.802 h = 0.0001 0.004 y[1] (numeric) = 0.940279796302 -1.09347312511 y[1] (closed_form) = 0.940233436176 -1.09355516526 absolute error = 9.423e-05 relative error = 0.006534 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.605 Order of pole (three term test) = 33.17 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.266 0.806 h = 0.003 0.006 y[1] (numeric) = 0.942620227414 -1.10012046288 y[1] (closed_form) = 0.942577712663 -1.10020310076 absolute error = 9.293e-05 relative error = 0.006415 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.143 Order of pole (three term test) = 33.18 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.269 0.812 h = 0.0001 0.005 y[1] (numeric) = 0.94145315454 -1.11191791359 y[1] (closed_form) = 0.9413992513 -1.11201340973 absolute error = 0.0001097 relative error = 0.007526 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9635 Order of pole (three term test) = 33.19 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2691 0.817 h = 0.0001 0.003 y[1] (numeric) = 0.944449568121 -1.1202950087 y[1] (closed_form) = 0.944401613391 -1.12038099355 absolute error = 9.845e-05 relative error = 0.006719 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7832 Order of pole (three term test) = 33.2 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=466.5MB, alloc=44.3MB, time=5.57 x[1] = 0.2692 0.82 h = 0.001 0.001 y[1] (numeric) = 0.946197811958 -1.12535845663 y[1] (closed_form) = 0.946147131744 -1.12544097229 absolute error = 9.684e-05 relative error = 0.006586 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6184 Order of pole (three term test) = 33.2 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2702 0.821 h = 0.001 0.003 y[1] (numeric) = 0.945169005713 -1.1276674212 y[1] (closed_form) = 0.945117573581 -1.1277477809 absolute error = 9.541e-05 relative error = 0.006484 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.94 Order of pole (three term test) = 33.21 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2712 0.824 h = 0.0001 0.004 y[1] (numeric) = 0.945414077239 -1.13331663255 y[1] (closed_form) = 0.945364349274 -1.1334013283 absolute error = 9.822e-05 relative error = 0.006655 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.673 Order of pole (three term test) = 33.21 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2713 0.828 h = 0.003 0.006 y[1] (numeric) = 0.947810864573 -1.14008367046 y[1] (closed_form) = 0.947765062385 -1.14016903656 absolute error = 9.688e-05 relative error = 0.006534 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.234 Order of pole (three term test) = 33.22 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2743 0.834 h = 0.0001 0.005 y[1] (numeric) = 0.94664378587 -1.15210411095 y[1] (closed_form) = 0.946586134844 -1.15220246235 absolute error = 0.000114 relative error = 0.007645 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.005 Order of pole (three term test) = 33.23 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2744 0.839 h = 0.0001 0.003 y[1] (numeric) = 0.949710810038 -1.16063286176 y[1] (closed_form) = 0.949659389546 -1.16072156889 absolute error = 0.0001025 relative error = 0.006837 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8167 Order of pole (three term test) = 33.24 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2745 0.842 h = 0.001 0.001 y[1] (numeric) = 0.951500435624 -1.16578842338 y[1] (closed_form) = 0.951446277805 -1.16587353953 absolute error = 0.0001009 relative error = 0.006704 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6448 Order of pole (three term test) = 33.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2755 0.843 h = 0.001 0.003 y[1] (numeric) = 0.950456144288 -1.16814248808 y[1] (closed_form) = 0.950401249118 -1.16822538665 absolute error = 9.943e-05 relative error = 0.006602 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.066 Order of pole (three term test) = 33.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2765 0.846 h = 0.0001 0.004 y[1] (numeric) = 0.950715161932 -1.17389734906 y[1] (closed_form) = 0.950661946249 -1.17398471056 absolute error = 0.0001023 relative error = 0.006772 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.745 Order of pole (three term test) = 33.26 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2766 0.85 h = 0.003 0.006 y[1] (numeric) = 0.953167820044 -1.18078773132 y[1] (closed_form) = 0.953118612175 -1.18087583701 absolute error = 0.0001009 relative error = 0.00665 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.33 Order of pole (three term test) = 33.26 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2796 0.856 h = 0.0001 0.005 y[1] (numeric) = 0.951997400036 -1.1930363698 y[1] (closed_form) = 0.951935874548 -1.19313759099 absolute error = 0.0001185 relative error = 0.007761 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.048 Order of pole (three term test) = 33.28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2797 0.861 h = 0.0001 0.003 y[1] (numeric) = 0.955134444061 -1.20172138005 y[1] (closed_form) = 0.955079436221 -1.20181282105 absolute error = 0.0001067 relative error = 0.006951 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8517 Order of pole (three term test) = 33.29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2798 0.864 h = 0.001 0.001 y[1] (numeric) = 0.956965064959 -1.20697182328 y[1] (closed_form) = 0.956907307538 -1.20705954923 absolute error = 0.000105 relative error = 0.006819 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6725 Order of pole (three term test) = 33.29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2808 0.865 h = 0.0001 0.004 y[1] (numeric) = 0.955904263406 -1.20937181783 y[1] (closed_form) = 0.955845783381 -1.2094572634 absolute error = 0.0001035 relative error = 0.006717 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.046 Order of pole (three term test) = 33.29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2809 0.869 h = 0.003 0.006 y[1] (numeric) = 0.958402450537 -1.21636573983 y[1] (closed_form) = 0.958351752271 -1.21645693757 absolute error = 0.0001043 relative error = 0.006738 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.416 Order of pole (three term test) = 33.3 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2839 0.875 h = 0.0001 0.005 y[1] (numeric) = 0.9572292464 -1.22881514781 y[1] (closed_form) = 0.957165821667 -1.22891958133 absolute error = 0.0001222 relative error = 0.007844 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.087 Order of pole (three term test) = 33.32 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.284 0.88 h = 0.0001 0.003 y[1] (numeric) = 0.960428022345 -1.23763758991 y[1] (closed_form) = 0.960371364934 -1.23773212041 absolute error = 0.0001102 relative error = 0.007035 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8834 Order of pole (three term test) = 33.33 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2841 0.883 h = 0.001 0.001 y[1] (numeric) = 0.96229479467 -1.24297147883 y[1] (closed_form) = 0.962235375302 -1.24306218576 absolute error = 0.0001084 relative error = 0.006898 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6975 Order of pole (three term test) = 33.33 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2851 0.884 h = 0.001 0.003 y[1] (numeric) = 0.961219507755 -1.24541189935 y[1] (closed_form) = 0.961159377872 -1.2455002707 absolute error = 0.0001069 relative error = 0.006794 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.316 Order of pole (three term test) = 33.34 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=510.1MB, alloc=44.3MB, time=6.08 x[1] = 0.2861 0.887 h = 0.0001 0.004 y[1] (numeric) = 0.961502538155 -1.2513704023 y[1] (closed_form) = 0.961444042655 -1.25146347945 absolute error = 0.0001099 relative error = 0.006966 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.887 Order of pole (three term test) = 33.34 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2862 0.891 h = 0.003 0.006 y[1] (numeric) = 0.964059429666 -1.25849958556 y[1] (closed_form) = 0.964005099964 -1.2585935467 absolute error = 0.0001085 relative error = 0.006846 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.52 Order of pole (three term test) = 33.35 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2892 0.897 h = 0.0001 0.005 y[1] (numeric) = 0.962876594827 -1.27118720019 y[1] (closed_form) = 0.962809053573 -1.27129453317 absolute error = 0.0001268 relative error = 0.007952 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.134 Order of pole (three term test) = 33.37 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2893 0.902 h = 0.0001 0.003 y[1] (numeric) = 0.96614433569 -1.28017471001 y[1] (closed_form) = 0.966083858742 -1.2802719985 absolute error = 0.0001146 relative error = 0.007142 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9216 Order of pole (three term test) = 33.38 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2894 0.905 h = 0.001 0.001 y[1] (numeric) = 0.96805140895 -1.28560877718 y[1] (closed_form) = 0.967988157061 -1.28570211364 absolute error = 0.0001127 relative error = 0.007006 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7277 Order of pole (three term test) = 33.38 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2904 0.906 h = 0.001 0.003 y[1] (numeric) = 0.966957665608 -1.2880967298 y[1] (closed_form) = 0.966893718331 -1.28818766562 absolute error = 0.0001112 relative error = 0.006902 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.46 Order of pole (three term test) = 33.39 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2914 0.909 h = 0.0001 0.004 y[1] (numeric) = 0.967251121159 -1.29416871643 y[1] (closed_form) = 0.96718878272 -1.29426449201 absolute error = 0.0001143 relative error = 0.007073 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.969 Order of pole (three term test) = 33.39 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2915 0.913 h = 0.003 0.006 y[1] (numeric) = 0.969862519037 -1.30143206321 y[1] (closed_form) = 0.969804433233 -1.30152880038 absolute error = 0.0001128 relative error = 0.006952 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.63 Order of pole (three term test) = 33.4 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2945 0.919 h = 0.0001 0.005 y[1] (numeric) = 0.968666555238 -1.31436339321 y[1] (closed_form) = 0.968594763655 -1.31447364128 absolute error = 0.0001316 relative error = 0.008058 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.183 Order of pole (three term test) = 33.42 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2946 0.924 h = 0.0001 0.003 y[1] (numeric) = 0.972002654809 -1.32352083044 y[1] (closed_form) = 0.971938230081 -1.32362088965 absolute error = 0.000119 relative error = 0.007247 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9617 Order of pole (three term test) = 33.43 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2947 0.927 h = 0.001 0.001 y[1] (numeric) = 0.973949631162 -1.32905799814 y[1] (closed_form) = 0.973882418165 -1.32915397442 absolute error = 0.0001172 relative error = 0.007111 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7593 Order of pole (three term test) = 33.43 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2957 0.928 h = 0.001 0.003 y[1] (numeric) = 0.972836352494 -1.3315943621 y[1] (closed_form) = 0.97276845948 -1.33168787141 absolute error = 0.0001156 relative error = 0.007007 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.611 Order of pole (three term test) = 33.44 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2967 0.931 h = 0.0001 0.004 y[1] (numeric) = 0.973138950896 -1.33778266921 y[1] (closed_form) = 0.973072640778 -1.33788115481 absolute error = 0.0001187 relative error = 0.007177 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.055 Order of pole (three term test) = 33.45 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2968 0.935 h = 0.003 0.006 y[1] (numeric) = 0.975804351794 -1.34518410006 y[1] (closed_form) = 0.975742382865 -1.34528362629 absolute error = 0.0001172 relative error = 0.007055 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.744 Order of pole (three term test) = 33.45 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2998 0.941 h = 0.0001 0.005 y[1] (numeric) = 0.974591697953 -1.35836476219 y[1] (closed_form) = 0.974515519617 -1.35847794135 absolute error = 0.0001364 relative error = 0.00816 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.234 Order of pole (three term test) = 33.47 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2999 0.946 h = 0.0001 0.003 y[1] (numeric) = 0.977995541559 -1.36769707995 y[1] (closed_form) = 0.977927038363 -1.36779992295 absolute error = 0.0001236 relative error = 0.007349 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.004 Order of pole (three term test) = 33.48 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3 0.949 h = 0.001 0.001 y[1] (numeric) = 0.97998201731 -1.37334032678 y[1] (closed_form) = 0.979910712199 -1.37343895342 absolute error = 0.0001217 relative error = 0.007213 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7925 Order of pole (three term test) = 33.49 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.301 0.95 h = 0.001 0.003 y[1] (numeric) = 0.978848104224 -1.37592599882 y[1] (closed_form) = 0.978776134729 -1.37602209088 absolute error = 0.0001201 relative error = 0.00711 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.768 Order of pole (three term test) = 33.49 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.302 0.953 h = 0.0001 0.004 y[1] (numeric) = 0.979158540214 -1.38223351837 y[1] (closed_form) = 0.979088127236 -1.38233472589 absolute error = 0.0001233 relative error = 0.007278 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.145 Order of pole (three term test) = 33.5 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=553.4MB, alloc=44.3MB, time=6.60 x[1] = 0.3021 0.957 h = 0.003 0.006 y[1] (numeric) = 0.981877433205 -1.38977702939 y[1] (closed_form) = 0.981811451705 -1.38987935807 absolute error = 0.0001218 relative error = 0.007155 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.864 Order of pole (three term test) = 33.51 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3051 0.963 h = 0.0001 0.005 y[1] (numeric) = 0.980644462481 -1.4032127502 y[1] (closed_form) = 0.980563758286 -1.40332887676 absolute error = 0.0001414 relative error = 0.00826 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.288 Order of pole (three term test) = 33.53 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3052 0.968 h = 0.0001 0.003 y[1] (numeric) = 0.984115425551 -1.41272499716 y[1] (closed_form) = 0.984042710689 -1.41283063732 absolute error = 0.0001282 relative error = 0.007449 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.048 Order of pole (three term test) = 33.54 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3053 0.971 h = 0.001 0.001 y[1] (numeric) = 0.986140990274 -1.41847735927 y[1] (closed_form) = 0.986065459556 -1.41857864707 absolute error = 0.0001263 relative error = 0.007313 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8272 Order of pole (three term test) = 33.55 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3063 0.972 h = 0.0001 0.004 y[1] (numeric) = 0.984985322767 -1.42111325382 y[1] (closed_form) = 0.984909143589 -1.42121193813 absolute error = 0.0001247 relative error = 0.00721 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.977 Order of pole (three term test) = 33.55 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3064 0.976 h = 0.003 0.006 y[1] (numeric) = 0.987747806763 -1.42877589746 y[1] (closed_form) = 0.987679935267 -1.42888156777 absolute error = 0.0001256 relative error = 0.00723 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.973 Order of pole (three term test) = 33.56 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3094 0.982 h = 0.0001 0.005 y[1] (numeric) = 0.986497524418 -1.44243613717 y[1] (closed_form) = 0.986414482234 -1.44255573867 absolute error = 0.0001456 relative error = 0.008332 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.337 Order of pole (three term test) = 33.58 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3095 0.987 h = 0.0001 0.003 y[1] (numeric) = 0.99002797988 -1.45210658934 y[1] (closed_form) = 0.989953200509 -1.45221556896 absolute error = 0.0001322 relative error = 0.00752 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.087 Order of pole (three term test) = 33.6 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3096 0.99 h = 0.001 0.001 y[1] (numeric) = 0.992088206722 -1.45795489161 y[1] (closed_form) = 0.992010597616 -1.45805939987 absolute error = 0.0001302 relative error = 0.007381 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8585 Order of pole (three term test) = 33.6 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3106 0.991 h = 0.001 0.003 y[1] (numeric) = 0.990913513777 -1.46063503956 y[1] (closed_form) = 0.990835269323 -1.46073688373 absolute error = 0.0001284 relative error = 0.007276 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.082 Order of pole (three term test) = 33.61 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3116 0.994 h = 0.0001 0.004 y[1] (numeric) = 0.991236479778 -1.46717222039 y[1] (closed_form) = 0.991159743166 -1.46727944655 absolute error = 0.0001319 relative error = 0.007447 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.324 Order of pole (three term test) = 33.62 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3117 0.998 h = 0.003 0.006 y[1] (numeric) = 0.99405532686 -1.4749903887 y[1] (closed_form) = 0.993983195438 -1.47509888888 absolute error = 0.0001303 relative error = 0.007325 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.103 Order of pole (three term test) = 33.63 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3147 1.004 h = 0.0001 0.005 y[1] (numeric) = 0.992777865015 -1.48891668633 y[1] (closed_form) = 0.992690030953 -1.48903926804 absolute error = 0.0001508 relative error = 0.008427 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.396 Order of pole (three term test) = 33.65 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3148 1.009 h = 0.0001 0.003 y[1] (numeric) = 0.99637430931 -1.49877673152 y[1] (closed_form) = 0.996295063694 -1.49888853561 absolute error = 0.000137 relative error = 0.007614 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.135 Order of pole (three term test) = 33.66 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3149 1.012 h = 0.001 0.001 y[1] (numeric) = 0.998472878272 -1.50473996147 y[1] (closed_form) = 0.998390788467 -1.50484715324 absolute error = 0.000135 relative error = 0.007476 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8964 Order of pole (three term test) = 33.67 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3159 1.013 h = 0.001 0.003 y[1] (numeric) = 0.997274300107 -1.50747209496 y[1] (closed_form) = 0.99719159146 -1.50757655121 absolute error = 0.0001332 relative error = 0.007371 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.262 Order of pole (three term test) = 33.67 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3169 1.016 h = 0.0001 0.004 y[1] (numeric) = 0.997601268144 -1.51413709183 y[1] (closed_form) = 0.997520039489 -1.51424707712 absolute error = 0.0001367 relative error = 0.00754 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.426 Order of pole (three term test) = 33.68 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.317 1.02 h = 0.003 0.006 y[1] (numeric) = 1.00047214406 -1.5221092113 y[1] (closed_form) = 1.000395616 -1.52222055569 absolute error = 0.0001351 relative error = 0.007417 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.24 Order of pole (three term test) = 33.69 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.32 1.026 h = 0.0001 0.005 y[1] (numeric) = 0.999163672435 -1.53630761824 y[1] (closed_form) = 0.999070899337 -1.53643319725 absolute error = 0.0001561 relative error = 0.008519 % Correct digits = 4 memory used=597.1MB, alloc=52.3MB, time=7.14 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.458 Order of pole (three term test) = 33.72 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3201 1.031 h = 0.0001 0.003 y[1] (numeric) = 1.00282544573 -1.54636259062 y[1] (closed_form) = 1.00274159314 -1.54647723337 absolute error = 0.000142 relative error = 0.007706 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.185 Order of pole (three term test) = 33.73 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3202 1.034 h = 0.001 0.001 y[1] (numeric) = 1.00496192286 -1.55244395644 y[1] (closed_form) = 1.00487521141 -1.55255384315 absolute error = 0.00014 relative error = 0.007569 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9359 Order of pole (three term test) = 33.74 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3212 1.035 h = 0.001 0.003 y[1] (numeric) = 1.00373827584 -1.55522904159 y[1] (closed_form) = 1.0036509624 -1.55533611995 absolute error = 0.0001382 relative error = 0.007464 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.451 Order of pole (three term test) = 33.74 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3222 1.038 h = 0.0001 0.004 y[1] (numeric) = 1.00406784059 -1.56202496949 y[1] (closed_form) = 1.00398197868 -1.56213772679 absolute error = 0.0001417 relative error = 0.007632 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.533 Order of pole (three term test) = 33.75 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3223 1.042 h = 0.003 0.006 y[1] (numeric) = 1.006990195 -1.57015534432 y[1] (closed_form) = 1.00690913092 -1.57026954752 absolute error = 0.00014 relative error = 0.007508 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.383 Order of pole (three term test) = 33.76 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3253 1.048 h = 0.0001 0.005 y[1] (numeric) = 1.00564680571 -1.58463202879 y[1] (closed_form) = 1.00554894347 -1.58476062241 absolute error = 0.0001616 relative error = 0.00861 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.522 Order of pole (three term test) = 33.79 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3254 1.053 h = 0.0001 0.003 y[1] (numeric) = 1.00937323248 -1.59488736664 y[1] (closed_form) = 1.00928462943 -1.59500486246 absolute error = 0.0001472 relative error = 0.007796 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.238 Order of pole (three term test) = 33.8 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3255 1.056 h = 0.001 0.001 y[1] (numeric) = 1.01154717358 -1.60109013924 y[1] (closed_form) = 1.01145569679 -1.60120273244 absolute error = 0.0001451 relative error = 0.00766 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9774 Order of pole (three term test) = 33.81 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3265 1.057 h = 0.001 0.003 y[1] (numeric) = 1.01029725027 -1.60392916045 y[1] (closed_form) = 1.01020518875 -1.60403887106 absolute error = 0.0001432 relative error = 0.007555 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.648 Order of pole (three term test) = 33.82 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3275 1.06 h = 0.0001 0.004 y[1] (numeric) = 1.01062797706 -1.61085919465 y[1] (closed_form) = 1.01053733794 -1.61097473705 absolute error = 0.0001469 relative error = 0.007722 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.645 Order of pole (three term test) = 33.83 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3276 1.064 h = 0.003 0.006 y[1] (numeric) = 1.01360124619 -1.61915221322 y[1] (closed_form) = 1.01351550397 -1.61926929008 absolute error = 0.0001451 relative error = 0.007597 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.533 Order of pole (three term test) = 33.84 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3306 1.07 h = 0.0001 0.005 y[1] (numeric) = 1.01221895053 -1.63391346216 y[1] (closed_form) = 1.01211584601 -1.63404508788 absolute error = 0.0001672 relative error = 0.008699 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.59 Order of pole (three term test) = 33.86 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3307 1.075 h = 0.0001 0.003 y[1] (numeric) = 1.01600933803 -1.6443747102 y[1] (closed_form) = 1.01591583819 -1.64449507367 absolute error = 0.0001524 relative error = 0.007885 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.293 Order of pole (three term test) = 33.88 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3308 1.078 h = 0.001 0.001 y[1] (numeric) = 1.01822028764 -1.65070222455 y[1] (closed_form) = 1.01812389903 -1.65081753594 absolute error = 0.0001503 relative error = 0.007749 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.021 Order of pole (three term test) = 33.89 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3318 1.079 h = 0.0001 0.004 y[1] (numeric) = 1.01694285607 -1.6535961847 y[1] (closed_form) = 1.01684590037 -1.6537085378 absolute error = 0.0001484 relative error = 0.007644 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.141 Order of pole (three term test) = 33.89 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3319 1.083 h = 0.003 0.006 y[1] (numeric) = 1.01995759796 -1.66202545444 y[1] (closed_form) = 1.01986952744 -1.66214614828 absolute error = 0.0001494 relative error = 0.007662 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.668 Order of pole (three term test) = 33.9 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3349 1.089 h = 0.0001 0.005 y[1] (numeric) = 1.01854204871 -1.67703730317 y[1] (closed_form) = 1.0184361232 -1.67717269122 absolute error = 0.0001719 relative error = 0.008761 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.65 Order of pole (three term test) = 33.93 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.335 1.094 h = 0.0001 0.003 y[1] (numeric) = 1.02238946706 -1.68767956457 y[1] (closed_form) = 1.02229344721 -1.68780354227 absolute error = 0.0001568 relative error = 0.007947 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.342 Order of pole (three term test) = 33.95 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=640.8MB, alloc=52.3MB, time=7.65 x[1] = 0.3351 1.097 h = 0.001 0.001 y[1] (numeric) = 1.02463343955 -1.69411673978 y[1] (closed_form) = 1.02453451605 -1.69423553454 absolute error = 0.0001546 relative error = 0.007808 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.06 Order of pole (three term test) = 33.95 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3361 1.098 h = 0.001 0.003 y[1] (numeric) = 1.02333199496 -1.69705915495 y[1] (closed_form) = 1.02323251898 -1.69717492486 absolute error = 0.0001526 relative error = 0.007702 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.039 Order of pole (three term test) = 33.96 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3371 1.101 h = 0.0001 0.004 y[1] (numeric) = 1.02366264889 -1.70424741995 y[1] (closed_form) = 1.02356454108 -1.70436931443 absolute error = 0.0001565 relative error = 0.00787 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.868 Order of pole (three term test) = 33.97 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3372 1.105 h = 0.003 0.006 y[1] (numeric) = 1.0267311714 -1.71285446649 y[1] (closed_form) = 1.02663815097 -1.71297806397 absolute error = 0.0001547 relative error = 0.007746 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.831 Order of pole (three term test) = 33.99 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3402 1.111 h = 0.0001 0.005 y[1] (numeric) = 1.02526914567 -1.72816295085 y[1] (closed_form) = 1.02515768485 -1.72830140587 absolute error = 0.0001777 relative error = 0.008845 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.724 Order of pole (three term test) = 34.01 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3403 1.116 h = 0.0001 0.003 y[1] (numeric) = 1.02917925337 -1.73902174006 y[1] (closed_form) = 1.02907805686 -1.73914861482 absolute error = 0.0001623 relative error = 0.008031 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.402 Order of pole (three term test) = 34.03 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3404 1.119 h = 0.001 0.001 y[1] (numeric) = 1.0314593952 -1.74559004389 y[1] (closed_form) = 1.03135527973 -1.74571158064 absolute error = 0.00016 relative error = 0.007893 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.107 Order of pole (three term test) = 34.04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3414 1.12 h = 0.001 0.003 y[1] (numeric) = 1.03012809429 -1.74858932923 y[1] (closed_form) = 1.0300234448 -1.74870776265 absolute error = 0.000158 relative error = 0.007787 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.263 Order of pole (three term test) = 34.05 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3424 1.123 h = 0.0001 0.004 y[1] (numeric) = 1.03045567165 -1.7559211457 y[1] (closed_form) = 1.03035235907 -1.75604586526 absolute error = 0.000162 relative error = 0.007954 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.996 Order of pole (three term test) = 34.06 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3425 1.127 h = 0.003 0.006 y[1] (numeric) = 1.03357346606 -1.76470387905 y[1] (closed_form) = 1.0334753454 -1.76483039561 absolute error = 0.0001601 relative error = 0.007829 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.002 Order of pole (three term test) = 34.07 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3455 1.133 h = 0.0001 0.005 y[1] (numeric) = 1.03206072705 -1.78031563755 y[1] (closed_form) = 1.03194356873 -1.78045717746 absolute error = 0.0001837 relative error = 0.008928 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.801 Order of pole (three term test) = 34.1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3456 1.138 h = 0.0001 0.003 y[1] (numeric) = 1.03603277435 -1.79139681726 y[1] (closed_form) = 1.03592624637 -1.7915266041 absolute error = 0.0001679 relative error = 0.008114 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.464 Order of pole (three term test) = 34.12 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3457 1.141 h = 0.001 0.001 y[1] (numeric) = 1.03834859324 -1.79809977611 y[1] (closed_form) = 1.03823913092 -1.79822406677 absolute error = 0.0001656 relative error = 0.007976 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.156 Order of pole (three term test) = 34.13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3467 1.142 h = 0.001 0.003 y[1] (numeric) = 1.03698612957 -1.80115698858 y[1] (closed_form) = 1.03687615215 -1.80127809588 absolute error = 0.0001636 relative error = 0.007871 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.498 Order of pole (three term test) = 34.14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3477 1.145 h = 0.0001 0.004 y[1] (numeric) = 1.03730906978 -1.80863577564 y[1] (closed_form) = 1.03720039716 -1.80876333385 absolute error = 0.0001676 relative error = 0.008037 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.13 Order of pole (three term test) = 34.15 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3478 1.149 h = 0.003 0.006 y[1] (numeric) = 1.04047550929 -1.81759892719 y[1] (closed_form) = 1.04037213506 -1.81772837841 absolute error = 0.0001657 relative error = 0.00791 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.18 Order of pole (three term test) = 34.16 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3508 1.155 h = 0.0001 0.005 y[1] (numeric) = 1.03890772638 -1.83352072479 y[1] (closed_form) = 1.03878470505 -1.83366536757 absolute error = 0.0001899 relative error = 0.00901 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.881 Order of pole (three term test) = 34.19 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3509 1.16 h = 0.0001 0.003 y[1] (numeric) = 1.04294093989 -1.8448302735 y[1] (closed_form) = 1.04282892252 -1.84496298754 absolute error = 0.0001737 relative error = 0.008195 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.529 Order of pole (three term test) = 34.21 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.351 1.163 h = 0.001 0.001 y[1] (numeric) = 1.04529192843 -1.8516714835 y[1] (closed_form) = 1.04517696126 -1.85179853999 absolute error = 0.0001713 relative error = 0.008058 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.208 Order of pole (three term test) = 34.22 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=684.5MB, alloc=52.3MB, time=8.16 x[1] = 0.352 1.164 h = 0.001 0.003 y[1] (numeric) = 1.04389696781 -1.8547876992 y[1] (closed_form) = 1.04378150499 -1.85491149074 absolute error = 0.0001693 relative error = 0.007953 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.743 Order of pole (three term test) = 34.23 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.353 1.167 h = 0.0001 0.004 y[1] (numeric) = 1.04421367394 -1.86241694193 y[1] (closed_form) = 1.04409948289 -1.86254735237 absolute error = 0.0001733 relative error = 0.008118 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.269 Order of pole (three term test) = 34.24 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3531 1.171 h = 0.003 0.006 y[1] (numeric) = 1.04742811182 -1.87156533664 y[1] (closed_form) = 1.04731932762 -1.87169773821 absolute error = 0.0001714 relative error = 0.00799 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.366 Order of pole (three term test) = 34.26 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3561 1.177 h = 0.0001 0.005 y[1] (numeric) = 1.04580085697 -1.88780406681 y[1] (closed_form) = 1.04567180372 -1.88795183052 absolute error = 0.0001962 relative error = 0.00909 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.965 Order of pole (three term test) = 34.29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3562 1.182 h = 0.0001 0.003 y[1] (numeric) = 1.04989443795 -1.89934808143 y[1] (closed_form) = 1.04977677008 -1.89948373784 absolute error = 0.0001796 relative error = 0.008274 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.598 Order of pole (three term test) = 34.31 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3563 1.185 h = 0.001 0.001 y[1] (numeric) = 1.05228007251 -1.90633120993 y[1] (closed_form) = 1.05215943937 -1.90646104415 absolute error = 0.0001772 relative error = 0.008139 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.262 Order of pole (three term test) = 34.32 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3573 1.186 h = 0.0001 0.004 y[1] (numeric) = 1.0508512522 -1.90950752429 y[1] (closed_form) = 1.05073014338 -1.90963401036 absolute error = 0.0001751 relative error = 0.008034 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.591 Order of pole (three term test) = 34.33 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3574 1.19 h = 0.003 0.006 y[1] (numeric) = 1.05410474788 -1.91881098777 y[1] (closed_form) = 1.05399315217 -1.91894730802 absolute error = 0.0001762 relative error = 0.008047 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.534 Order of pole (three term test) = 34.35 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3604 1.196 h = 0.0001 0.005 y[1] (numeric) = 1.05242656816 -1.93532892481 y[1] (closed_form) = 1.05229415986 -1.93548076345 absolute error = 0.0002015 relative error = 0.009145 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.04 Order of pole (three term test) = 34.38 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3605 1.201 h = 0.0001 0.003 y[1] (numeric) = 1.05657434516 -1.94707902874 y[1] (closed_form) = 1.05645365478 -1.94721859944 absolute error = 0.0001845 relative error = 0.008329 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.659 Order of pole (three term test) = 34.4 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3606 1.204 h = 0.001 0.001 y[1] (numeric) = 1.05899112072 -1.95418690432 y[1] (closed_form) = 1.05886744974 -1.95432050861 absolute error = 0.0001821 relative error = 0.008191 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.31 Order of pole (three term test) = 34.41 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3616 1.205 h = 0.001 0.003 y[1] (numeric) = 1.05753277541 -1.95741626765 y[1] (closed_form) = 1.05740864538 -1.95754645062 absolute error = 0.0001799 relative error = 0.008085 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.231 Order of pole (three term test) = 34.42 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3626 1.208 h = 0.0001 0.004 y[1] (numeric) = 1.05783539332 -1.96533510075 y[1] (closed_form) = 1.0577124731 -1.96547222454 absolute error = 0.0001842 relative error = 0.008251 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.547 Order of pole (three term test) = 34.43 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3627 1.212 h = 0.003 0.006 y[1] (numeric) = 1.06113969645 -1.97484080823 y[1] (closed_form) = 1.06102239146 -1.9749801102 absolute error = 0.0001821 relative error = 0.008123 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.737 Order of pole (three term test) = 34.45 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3657 1.218 h = 0.0001 0.005 y[1] (numeric) = 1.05939361936 -1.99168890996 y[1] (closed_form) = 1.05925485574 -1.99184390522 absolute error = 0.000208 relative error = 0.009222 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.132 Order of pole (three term test) = 34.49 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3658 1.223 h = 0.0001 0.003 y[1] (numeric) = 1.06360027993 -2.00368515902 y[1] (closed_form) = 1.06347363071 -2.00382770235 absolute error = 0.0001907 relative error = 0.008405 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.733 Order of pole (three term test) = 34.51 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3659 1.226 h = 0.001 0.001 y[1] (numeric) = 1.06605072603 -2.01094197886 y[1] (closed_form) = 1.06592108073 -2.01107838487 absolute error = 0.0001882 relative error = 0.008268 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.369 Order of pole (three term test) = 34.52 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3669 1.227 h = 0.001 0.003 y[1] (numeric) = 1.06455591979 -2.0142335483 y[1] (closed_form) = 1.06442583647 -2.01436644671 absolute error = 0.000186 relative error = 0.008163 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.509 Order of pole (three term test) = 34.53 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3679 1.23 h = 0.0001 0.004 y[1] (numeric) = 1.0648475645 -2.02231320268 y[1] (closed_form) = 1.06471865509 -2.02245321958 absolute error = 0.0001903 relative error = 0.008327 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.705 Order of pole (three term test) = 34.55 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=728.2MB, alloc=52.3MB, time=8.67 x[1] = 0.368 1.234 h = 0.003 0.006 y[1] (numeric) = 1.06819795458 -2.03201850047 y[1] (closed_form) = 1.06807477468 -2.03216080005 absolute error = 0.0001882 relative error = 0.008198 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.949 Order of pole (three term test) = 34.56 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.371 1.24 h = 0.0001 0.005 y[1] (numeric) = 1.06637925478 -2.0492040411 y[1] (closed_form) = 1.06623395676 -2.04936221103 absolute error = 0.0002148 relative error = 0.009297 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.227 Order of pole (three term test) = 34.6 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3711 1.245 h = 0.0001 0.003 y[1] (numeric) = 1.07064391909 -2.06145288571 y[1] (closed_form) = 1.07051114037 -2.06159841688 absolute error = 0.000197 relative error = 0.008481 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.811 Order of pole (three term test) = 34.62 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3712 1.248 h = 0.001 0.001 y[1] (numeric) = 1.07312746053 -2.06886252985 y[1] (closed_form) = 1.07299167032 -2.06900174927 absolute error = 0.0001945 relative error = 0.008344 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.43 Order of pole (three term test) = 34.64 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3722 1.249 h = 0.001 0.003 y[1] (numeric) = 1.0715947442 -2.07221745749 y[1] (closed_form) = 1.07145853761 -2.07235308133 absolute error = 0.0001922 relative error = 0.008239 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.801 Order of pole (three term test) = 34.64 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3732 1.252 h = 0.0001 0.004 y[1] (numeric) = 1.07187366433 -2.08046168486 y[1] (closed_form) = 1.07173859465 -2.0806046084 absolute error = 0.0001966 relative error = 0.008402 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.871 Order of pole (three term test) = 34.66 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3733 1.256 h = 0.003 0.006 y[1] (numeric) = 1.07526940544 -2.0903717792 y[1] (closed_form) = 1.07514018163 -2.09051709228 absolute error = 0.0001945 relative error = 0.008272 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.17 Order of pole (three term test) = 34.68 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3763 1.262 h = 0.0001 0.005 y[1] (numeric) = 1.07337324577 -2.10790216986 y[1] (closed_form) = 1.07322123056 -2.10806353242 absolute error = 0.0002217 relative error = 0.009372 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.327 Order of pole (three term test) = 34.72 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3764 1.267 h = 0.0001 0.003 y[1] (numeric) = 1.07769500153 -2.12041018914 y[1] (closed_form) = 1.07755591917 -2.12055872328 absolute error = 0.0002035 relative error = 0.008555 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.892 Order of pole (three term test) = 34.74 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3765 1.27 h = 0.001 0.001 y[1] (numeric) = 1.08021104256 -2.12797661502 y[1] (closed_form) = 1.08006893339 -2.12811865939 absolute error = 0.0002009 relative error = 0.008419 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.494 Order of pole (three term test) = 34.76 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3775 1.271 h = 0.001 0.003 y[1] (numeric) = 1.0786389349 -2.13139607299 y[1] (closed_form) = 1.07849643165 -2.13153443207 absolute error = 0.0001986 relative error = 0.008315 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.105 Order of pole (three term test) = 34.77 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3785 1.274 h = 0.0001 0.004 y[1] (numeric) = 1.07890333494 -2.13980869713 y[1] (closed_form) = 1.07876193039 -2.1399545407 absolute error = 0.0002031 relative error = 0.008477 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.045 Order of pole (three term test) = 34.78 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3786 1.278 h = 0.003 0.006 y[1] (numeric) = 1.08234366406 -2.1499288982 y[1] (closed_form) = 1.08220822385 -2.15007724063 absolute error = 0.0002009 relative error = 0.008345 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.402 Order of pole (three term test) = 34.8 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3816 1.284 h = 0.0001 0.005 y[1] (numeric) = 1.08036509161 -2.16781168918 y[1] (closed_form) = 1.0802061726 -2.16797626222 absolute error = 0.0002288 relative error = 0.009445 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.431 Order of pole (three term test) = 34.85 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3817 1.289 h = 0.0001 0.003 y[1] (numeric) = 1.08474299212 -2.18058559374 y[1] (closed_form) = 1.08459742841 -2.18073714585 absolute error = 0.0002101 relative error = 0.008628 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.977 Order of pole (three term test) = 34.87 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3818 1.292 h = 0.001 0.001 y[1] (numeric) = 1.08729091523 -2.18831283784 y[1] (closed_form) = 1.08714230953 -2.18845771853 absolute error = 0.0002075 relative error = 0.008493 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.561 Order of pole (three term test) = 34.88 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3828 1.293 h = 0.0001 0.004 y[1] (numeric) = 1.085677902 -2.1917980185 y[1] (closed_form) = 1.0855289252 -2.1919391224 absolute error = 0.0002052 relative error = 0.008389 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.393 Order of pole (three term test) = 34.89 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3829 1.297 h = 0.003 0.006 y[1] (numeric) = 1.08915444829 -2.20209399513 y[1] (closed_form) = 1.08901566155 -2.20224658493 absolute error = 0.0002063 relative error = 0.008396 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.611 Order of pole (three term test) = 34.91 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3859 1.303 h = 0.0001 0.005 y[1] (numeric) = 1.08710520301 -2.22028733877 y[1] (closed_form) = 1.08694233636 -2.22045632506 absolute error = 0.0002347 relative error = 0.009493 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.525 Order of pole (three term test) = 34.96 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=772.0MB, alloc=52.3MB, time=9.18 x[1] = 0.386 1.308 h = 0.0001 0.003 y[1] (numeric) = 1.0915339237 -2.23329493189 y[1] (closed_form) = 1.09138478094 -2.23345072411 absolute error = 0.0002157 relative error = 0.008676 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.053 Order of pole (three term test) = 34.98 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3861 1.311 h = 0.001 0.001 y[1] (numeric) = 1.09411076046 -2.24116352754 y[1] (closed_form) = 1.09395856054 -2.24131248914 absolute error = 0.000213 relative error = 0.008539 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.621 Order of pole (three term test) = 35 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3871 1.312 h = 0.001 0.003 y[1] (numeric) = 1.0924621012 -2.24470676296 y[1] (closed_form) = 1.09230954941 -2.24485186728 absolute error = 0.0002105 relative error = 0.008433 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.71 Order of pole (three term test) = 35.01 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3881 1.315 h = 0.0001 0.004 y[1] (numeric) = 1.0926966623 -2.25344338932 y[1] (closed_form) = 1.09254513707 -2.25359633232 absolute error = 0.0002153 relative error = 0.008596 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.389 Order of pole (three term test) = 35.03 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3882 1.319 h = 0.003 0.006 y[1] (numeric) = 1.09622048624 -2.26396854035 y[1] (closed_form) = 1.09607515288 -2.26412419096 absolute error = 0.000213 relative error = 0.008466 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.862 Order of pole (three term test) = 35.05 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3912 1.325 h = 0.0001 0.005 y[1] (numeric) = 1.09407938407 -2.28252877432 y[1] (closed_form) = 1.09390925616 -2.28270100624 absolute error = 0.0002421 relative error = 0.009564 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.638 Order of pole (three term test) = 35.1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3913 1.33 h = 0.0001 0.003 y[1] (numeric) = 1.09856247322 -2.29581511161 y[1] (closed_form) = 1.09840650877 -2.29597395161 absolute error = 0.0002226 relative error = 0.008746 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.145 Order of pole (three term test) = 35.12 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3914 1.333 h = 0.001 0.001 y[1] (numeric) = 1.10117003131 -2.30385226074 y[1] (closed_form) = 1.10101099483 -2.30400408139 absolute error = 0.0002199 relative error = 0.00861 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.694 Order of pole (three term test) = 35.14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3924 1.334 h = 0.001 0.003 y[1] (numeric) = 1.09947757244 -2.30746351108 y[1] (closed_form) = 1.09931820839 -2.30761137957 absolute error = 0.0002174 relative error = 0.008505 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.056 Order of pole (three term test) = 35.15 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3934 1.337 h = 0.0001 0.004 y[1] (numeric) = 1.09969226593 -2.31637990638 y[1] (closed_form) = 1.09953388657 -2.31653580905 absolute error = 0.0002222 relative error = 0.008667 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.586 Order of pole (three term test) = 35.17 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3935 1.341 h = 0.003 0.006 y[1] (numeric) = 1.10325839877 -2.32713095993 y[1] (closed_form) = 1.10310633596 -2.32728968696 absolute error = 0.0002198 relative error = 0.008535 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.125 Order of pole (three term test) = 35.19 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3965 1.347 h = 0.0001 0.005 y[1] (numeric) = 1.10102013497 -2.34606604691 y[1] (closed_form) = 1.1008425478 -2.34624154186 absolute error = 0.0002497 relative error = 0.009634 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.756 Order of pole (three term test) = 35.24 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3966 1.352 h = 0.0001 0.003 y[1] (numeric) = 1.10555653789 -2.35963823146 y[1] (closed_form) = 1.10539356336 -2.35980013382 absolute error = 0.0002297 relative error = 0.008816 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.242 Order of pole (three term test) = 35.27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3967 1.355 h = 0.001 0.001 y[1] (numeric) = 1.10819413177 -2.36784820651 y[1] (closed_form) = 1.10802807055 -2.36800289688 absolute error = 0.0002269 relative error = 0.008681 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.77 Order of pole (three term test) = 35.29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3977 1.356 h = 0.001 0.003 y[1] (numeric) = 1.10645625945 -2.37152872352 y[1] (closed_form) = 1.10628989574 -2.37167936496 absolute error = 0.0002244 relative error = 0.008576 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.418 Order of pole (three term test) = 35.3 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3987 1.359 h = 0.0001 0.004 y[1] (numeric) = 1.10664910376 -2.38062900301 y[1] (closed_form) = 1.10648368143 -2.38078787804 absolute error = 0.0002294 relative error = 0.008736 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.792 Order of pole (three term test) = 35.32 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3988 1.363 h = 0.003 0.006 y[1] (numeric) = 1.11025666404 -2.39161169242 y[1] (closed_form) = 1.11009768517 -2.3917735113 absolute error = 0.0002268 relative error = 0.008603 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.4 Order of pole (three term test) = 35.34 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4018 1.369 h = 0.0001 0.005 y[1] (numeric) = 1.10791580213 -2.41092974334 y[1] (closed_form) = 1.10773055354 -2.41110851845 absolute error = 0.0002574 relative error = 0.009702 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.88 Order of pole (three term test) = 35.39 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4019 1.374 h = 0.0001 0.003 y[1] (numeric) = 1.11250442181 -2.42479502098 y[1] (closed_form) = 1.11233424485 -2.42496000006 absolute error = 0.000237 relative error = 0.008884 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.342 Order of pole (three term test) = 35.42 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=815.9MB, alloc=52.3MB, time=9.70 x[1] = 0.402 1.377 h = 0.001 0.001 y[1] (numeric) = 1.1151713393 -2.4331821802 y[1] (closed_form) = 1.11499806129 -2.43333975063 absolute error = 0.0002342 relative error = 0.00875 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.85 Order of pole (three term test) = 35.44 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.403 1.378 h = 0.001 0.003 y[1] (numeric) = 1.11338640283 -2.43693323661 y[1] (closed_form) = 1.1132128482 -2.43708665942 absolute error = 0.0002316 relative error = 0.008646 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.796 Order of pole (three term test) = 35.45 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.404 1.381 h = 0.0001 0.004 y[1] (numeric) = 1.11355536353 -2.44622159429 y[1] (closed_form) = 1.11338270549 -2.44638345408 absolute error = 0.0002367 relative error = 0.008805 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.007 Order of pole (three term test) = 35.48 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4041 1.385 h = 0.003 0.006 y[1] (numeric) = 1.11720343466 -2.45744176816 y[1] (closed_form) = 1.11703734925 -2.45760669415 absolute error = 0.0002341 relative error = 0.00867 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.688 Order of pole (three term test) = 35.5 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4071 1.391 h = 0.0001 0.005 y[1] (numeric) = 1.11475440208 -2.47715104465 y[1] (closed_form) = 1.11456128565 -2.47733311676 absolute error = 0.0002654 relative error = 0.00977 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.01 Order of pole (three term test) = 35.55 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4072 1.396 h = 0.0001 0.003 y[1] (numeric) = 1.11939409694 -2.49131680702 y[1] (closed_form) = 1.11921652123 -2.49148487688 absolute error = 0.0002445 relative error = 0.008952 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.447 Order of pole (three term test) = 35.59 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4073 1.399 h = 0.001 0.001 y[1] (numeric) = 1.12208959791 -2.49988559628 y[1] (closed_form) = 1.1219089071 -2.50004605674 absolute error = 0.0002417 relative error = 0.008819 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.933 Order of pole (three term test) = 35.61 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4083 1.4 h = 0.003 0.006 y[1] (numeric) = 1.12025590869 -2.503708486 y[1] (closed_form) = 1.12007496798 -2.5038646982 absolute error = 0.000239 relative error = 0.008715 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 19.5 Order of pole (three term test) = 35.62 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4113 1.406 h = 0.0001 0.005 y[1] (numeric) = 1.11771197031 -2.52366087348 y[1] (closed_form) = 1.11751054368 -2.52386232848 absolute error = 0.0002849 relative error = 0.01032 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.101 Order of pole (three term test) = 35.67 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4114 1.411 h = 0.0001 0.003 y[1] (numeric) = 1.12237831716 -2.53803895238 y[1] (closed_form) = 1.1221927652 -2.53822627379 absolute error = 0.0002637 relative error = 0.009501 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.522 Order of pole (three term test) = 35.71 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4115 1.414 h = 0.001 0.001 y[1] (numeric) = 1.12508832442 -2.54673600552 y[1] (closed_form) = 1.12489965306 -2.54691557669 absolute error = 0.0002605 relative error = 0.009355 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.991 Order of pole (three term test) = 35.73 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4125 1.415 h = 0.001 0.003 y[1] (numeric) = 1.1232182499 -2.5506077904 y[1] (closed_form) = 1.12302935014 -2.55078304361 absolute error = 0.0002577 relative error = 0.009245 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.47 Order of pole (three term test) = 35.74 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4135 1.418 h = 0.0001 0.004 y[1] (numeric) = 1.12333715391 -2.56022262086 y[1] (closed_form) = 1.1231490662 -2.56040666235 absolute error = 0.0002632 relative error = 0.009412 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.391 Order of pole (three term test) = 35.76 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4136 1.422 h = 0.003 0.006 y[1] (numeric) = 1.12704510498 -2.571858203 y[1] (closed_form) = 1.12686380985 -2.57204552728 absolute error = 0.0002607 relative error = 0.009284 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.201 Order of pole (three term test) = 35.79 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4166 1.428 h = 0.0001 0.005 y[1] (numeric) = 1.12439013531 -2.59224394591 y[1] (closed_form) = 1.1241804821 -2.59244872014 absolute error = 0.0002931 relative error = 0.01037 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.24 Order of pole (three term test) = 35.85 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4167 1.433 h = 0.0001 0.003 y[1] (numeric) = 1.12910532867 -2.60693529377 y[1] (closed_form) = 1.1289120369 -2.60712572381 absolute error = 0.0002713 relative error = 0.009551 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.635 Order of pole (three term test) = 35.88 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4168 1.436 h = 0.001 0.001 y[1] (numeric) = 1.13184248593 -2.61582166469 y[1] (closed_form) = 1.13164606145 -2.6160041366 absolute error = 0.0002681 relative error = 0.009406 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.081 Order of pole (three term test) = 35.9 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4178 1.437 h = 0.001 0.003 y[1] (numeric) = 1.12992068572 -2.61976747074 y[1] (closed_form) = 1.12972406111 -2.61994552068 absolute error = 0.0002653 relative error = 0.009297 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.896 Order of pole (three term test) = 35.92 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4188 1.44 h = 0.0001 0.004 y[1] (numeric) = 1.1300098488 -2.62958199802 y[1] (closed_form) = 1.12981398699 -2.62976905067 absolute error = 0.0002708 relative error = 0.009462 % Correct digits = 4 memory used=859.8MB, alloc=52.3MB, time=10.21 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.633 Order of pole (three term test) = 35.94 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4189 1.444 h = 0.003 0.006 y[1] (numeric) = 1.13375550197 -2.64147134921 y[1] (closed_form) = 1.13356656801 -2.64166181515 absolute error = 0.0002683 relative error = 0.009333 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.524 Order of pole (three term test) = 35.97 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4219 1.45 h = 0.0001 0.005 y[1] (numeric) = 1.13097645318 -2.66227113785 y[1] (closed_form) = 1.13075835504 -2.66247924705 absolute error = 0.0003015 relative error = 0.01042 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.386 Order of pole (three term test) = 36.03 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.422 1.455 h = 0.0001 0.003 y[1] (numeric) = 1.13573921653 -2.67728355247 y[1] (closed_form) = 1.13553797742 -2.67747710415 absolute error = 0.0002792 relative error = 0.0096 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.754 Order of pole (three term test) = 36.07 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4221 1.458 h = 0.001 0.001 y[1] (numeric) = 1.13850269927 -2.68636393102 y[1] (closed_form) = 1.13829831454 -2.68654931234 absolute error = 0.0002759 relative error = 0.009457 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.174 Order of pole (three term test) = 36.09 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4231 1.459 h = 0.001 0.003 y[1] (numeric) = 1.13652737694 -2.69038510902 y[1] (closed_form) = 1.13632282131 -2.69056596229 absolute error = 0.000273 relative error = 0.009349 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.34 Order of pole (three term test) = 36.1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4241 1.462 h = 0.0001 0.004 y[1] (numeric) = 1.13658455081 -2.70040382858 y[1] (closed_form) = 1.13638070697 -2.70059390328 absolute error = 0.0002787 relative error = 0.009513 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.887 Order of pole (three term test) = 36.13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4242 1.466 h = 0.003 0.006 y[1] (numeric) = 1.14036684099 -2.71255324301 y[1] (closed_form) = 1.14017006266 -2.71274686464 absolute error = 0.0002761 relative error = 0.009382 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.862 Order of pole (three term test) = 36.16 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4272 1.472 h = 0.0001 0.005 y[1] (numeric) = 1.13745759518 -2.73377591235 y[1] (closed_form) = 1.13723082914 -2.73398737181 absolute error = 0.0003101 relative error = 0.01047 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.538 Order of pole (three term test) = 36.22 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4273 1.477 h = 0.0001 0.003 y[1] (numeric) = 1.14226659881 -2.74911734899 y[1] (closed_form) = 1.14205720047 -2.7493140349 absolute error = 0.0002873 relative error = 0.00965 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.877 Order of pole (three term test) = 36.26 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4274 1.48 h = 0.001 0.001 y[1] (numeric) = 1.14505554925 -2.75839651961 y[1] (closed_form) = 1.14484299287 -2.75858481847 absolute error = 0.000284 relative error = 0.009508 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.272 Order of pole (three term test) = 36.29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4284 1.481 h = 0.0001 0.004 y[1] (numeric) = 1.14302486641 -2.76249444223 y[1] (closed_form) = 1.14281216931 -2.76267810486 absolute error = 0.000281 relative error = 0.0094 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 13.67 Order of pole (three term test) = 36.3 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4285 1.485 h = 0.003 0.006 y[1] (numeric) = 1.14683671657 -2.77486124524 y[1] (closed_form) = 1.14663549884 -2.77505975483 absolute error = 0.0002827 relative error = 0.009414 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.167 Order of pole (three term test) = 36.33 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4315 1.491 h = 0.0001 0.005 y[1] (numeric) = 1.14381556553 -2.79645676798 y[1] (closed_form) = 1.14358363931 -2.79667329387 absolute error = 0.0003173 relative error = 0.0105 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.675 Order of pole (three term test) = 36.4 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4316 1.496 h = 0.0001 0.003 y[1] (numeric) = 1.14866731529 -2.81208738062 y[1] (closed_form) = 1.14845320108 -2.81228893861 absolute error = 0.0002941 relative error = 0.00968 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.989 Order of pole (three term test) = 36.44 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4317 1.499 h = 0.001 0.001 y[1] (numeric) = 1.15147992147 -2.82154128095 y[1] (closed_form) = 1.15126263627 -2.82173426186 absolute error = 0.0002906 relative error = 0.009536 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.36 Order of pole (three term test) = 36.46 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4327 1.5 h = 0.001 0.003 y[1] (numeric) = 1.14940101793 -2.82570706887 y[1] (closed_form) = 1.1491836175 -2.82589531835 absolute error = 0.0002876 relative error = 0.009427 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.22 Order of pole (three term test) = 36.48 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4337 1.503 h = 0.0001 0.004 y[1] (numeric) = 1.14939503166 -2.83611844915 y[1] (closed_form) = 1.14917824594 -2.83631633938 absolute error = 0.0002935 relative error = 0.009591 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.389 Order of pole (three term test) = 36.51 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4338 1.507 h = 0.003 0.006 y[1] (numeric) = 1.1532457889 -2.84876856574 y[1] (closed_form) = 1.15303633289 -2.84897025867 absolute error = 0.0002908 relative error = 0.009461 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.534 Order of pole (three term test) = 36.54 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4368 1.513 h = 0.0001 0.005 y[1] (numeric) = 1.15008274243 -2.87080392076 y[1] (closed_form) = 1.14984172089 -2.87102382682 absolute error = 0.0003263 relative error = 0.01055 % Correct digits = 4 memory used=903.6MB, alloc=52.3MB, time=10.72 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.84 Order of pole (three term test) = 36.61 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4369 1.518 h = 0.0001 0.003 y[1] (numeric) = 1.15497820748 -2.88677880629 y[1] (closed_form) = 1.15475552798 -2.8869835233 absolute error = 0.0003025 relative error = 0.009728 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.123 Order of pole (three term test) = 36.65 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.437 1.521 h = 0.001 0.001 y[1] (numeric) = 1.15781465134 -2.89644067123 y[1] (closed_form) = 1.15758878936 -2.89663658588 absolute error = 0.000299 relative error = 0.009585 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.466 Order of pole (three term test) = 36.68 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.438 1.522 h = 0.001 0.003 y[1] (numeric) = 1.1556768677 -2.90068584003 y[1] (closed_form) = 1.15545092258 -2.90087691103 absolute error = 0.0002959 relative error = 0.009476 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.73 Order of pole (three term test) = 36.69 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.439 1.525 h = 0.0001 0.004 y[1] (numeric) = 1.15563216668 -2.91131478066 y[1] (closed_form) = 1.15540677989 -2.91151572389 absolute error = 0.000302 relative error = 0.00964 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.677 Order of pole (three term test) = 36.73 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4391 1.529 h = 0.003 0.006 y[1] (numeric) = 1.15951634459 -2.92424369233 y[1] (closed_form) = 1.15929843213 -2.9244485815 absolute error = 0.0002991 relative error = 0.009508 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.918 Order of pole (three term test) = 36.76 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4421 1.535 h = 0.0001 0.005 y[1] (numeric) = 1.15620482154 -2.94672818838 y[1] (closed_form) = 1.15595446789 -2.94695148843 absolute error = 0.0003355 relative error = 0.0106 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.013 Order of pole (three term test) = 36.83 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4422 1.54 h = 0.0001 0.003 y[1] (numeric) = 1.16114250823 -2.96305577183 y[1] (closed_form) = 1.16091103853 -2.96326365902 absolute error = 0.0003111 relative error = 0.009776 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.264 Order of pole (three term test) = 36.88 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4423 1.543 h = 0.001 0.001 y[1] (numeric) = 1.16400182964 -2.97293066794 y[1] (closed_form) = 1.16376716657 -2.97312952276 absolute error = 0.0003076 relative error = 0.009634 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.577 Order of pole (three term test) = 36.91 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4433 1.544 h = 0.001 0.003 y[1] (numeric) = 1.16180320118 -2.97725665452 y[1] (closed_form) = 1.16156848816 -2.97745055123 absolute error = 0.0003044 relative error = 0.009526 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.26 Order of pole (three term test) = 36.92 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4443 1.547 h = 0.0001 0.004 y[1] (numeric) = 1.16171728617 -2.98810799106 y[1] (closed_form) = 1.16148307306 -2.98831199611 absolute error = 0.0003106 relative error = 0.009688 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.977 Order of pole (three term test) = 36.95 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4444 1.551 h = 0.003 0.006 y[1] (numeric) = 1.16563364039 -3.00132249826 y[1] (closed_form) = 1.16540704872 -3.00153059601 absolute error = 0.0003076 relative error = 0.009555 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.319 Order of pole (three term test) = 36.99 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4474 1.557 h = 0.0001 0.005 y[1] (numeric) = 1.16216688718 -3.02426561423 y[1] (closed_form) = 1.16190695957 -3.02449232144 absolute error = 0.0003449 relative error = 0.01065 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.194 Order of pole (three term test) = 37.07 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4475 1.562 h = 0.0001 0.003 y[1] (numeric) = 1.16714523883 -3.04095449126 y[1] (closed_form) = 1.16690474929 -3.0411655592 absolute error = 0.00032 relative error = 0.009823 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.41 Order of pole (three term test) = 37.11 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4476 1.565 h = 0.001 0.001 y[1] (numeric) = 1.17002643842 -3.05104758759 y[1] (closed_form) = 1.16978274527 -3.05124938826 absolute error = 0.0003164 relative error = 0.009682 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.693 Order of pole (three term test) = 37.14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4486 1.566 h = 0.001 0.003 y[1] (numeric) = 1.16776495385 -3.0554558515 y[1] (closed_form) = 1.16752124506 -3.05565257735 absolute error = 0.0003132 relative error = 0.009575 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.81 Order of pole (three term test) = 37.16 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4496 1.569 h = 0.0001 0.004 y[1] (numeric) = 1.16763525495 -3.06653451127 y[1] (closed_form) = 1.16739198552 -3.0667415863 absolute error = 0.0003195 relative error = 0.009736 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.291 Order of pole (three term test) = 37.19 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4497 1.573 h = 0.003 0.006 y[1] (numeric) = 1.17158248917 -3.08004155217 y[1] (closed_form) = 1.17134699082 -3.0802528703 absolute error = 0.0003164 relative error = 0.009601 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.738 Order of pole (three term test) = 37.23 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4527 1.579 h = 0.0001 0.005 y[1] (numeric) = 1.1679535745 -3.10345293983 y[1] (closed_form) = 1.1676838259 -3.10368306673 absolute error = 0.0003546 relative error = 0.01069 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.382 Order of pole (three term test) = 37.31 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=947.3MB, alloc=52.3MB, time=11.23 x[1] = 0.4528 1.584 h = 0.0001 0.003 y[1] (numeric) = 1.1729709687 -3.12051188033 y[1] (closed_form) = 1.17272122481 -3.12072613893 absolute error = 0.0003291 relative error = 0.00987 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.564 Order of pole (three term test) = 37.36 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4529 1.587 h = 0.001 0.001 y[1] (numeric) = 1.17587300619 -3.13082845049 y[1] (closed_form) = 1.17562004916 -3.13103320197 absolute error = 0.0003254 relative error = 0.009731 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.814 Order of pole (three term test) = 37.39 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4539 1.588 h = 0.0001 0.004 y[1] (numeric) = 1.17354660635 -3.13532047414 y[1] (closed_form) = 1.17329366918 -3.13552003176 absolute error = 0.0003222 relative error = 0.009624 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 16.93 Order of pole (three term test) = 37.41 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.454 1.592 h = 0.003 0.006 y[1] (numeric) = 1.17751856571 -3.14907195521 y[1] (closed_form) = 1.17727790806 -3.14928856698 absolute error = 0.0003238 relative error = 0.00963 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.11 Order of pole (three term test) = 37.45 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.457 1.598 h = 0.0001 0.005 y[1] (numeric) = 1.17375011553 -3.17289632591 y[1] (closed_form) = 1.17347440703 -3.17313192968 absolute error = 0.0003627 relative error = 0.01072 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.552 Order of pole (three term test) = 37.53 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4571 1.603 h = 0.0001 0.003 y[1] (numeric) = 1.17880431852 -3.19028052556 y[1] (closed_form) = 1.17854910995 -3.19050005489 absolute error = 0.0003366 relative error = 0.009898 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.702 Order of pole (three term test) = 37.58 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4572 1.606 h = 0.001 0.001 y[1] (numeric) = 1.18172617653 -3.20079352841 y[1] (closed_form) = 1.18146774428 -3.20100334018 absolute error = 0.0003329 relative error = 0.009756 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.923 Order of pole (three term test) = 37.62 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4582 1.607 h = 0.001 0.003 y[1] (numeric) = 1.17934323562 -3.20535966188 y[1] (closed_form) = 1.17908485329 -3.205564175 absolute error = 0.0003295 relative error = 0.009648 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 13.9 Order of pole (three term test) = 37.63 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4592 1.61 h = 0.0001 0.004 y[1] (numeric) = 1.17912782439 -3.21687534998 y[1] (closed_form) = 1.17886976579 -3.21709067408 absolute error = 0.0003361 relative error = 0.009809 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.914 Order of pole (three term test) = 37.67 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4593 1.614 h = 0.003 0.006 y[1] (numeric) = 1.18313256821 -3.23094534879 y[1] (closed_form) = 1.18288256783 -3.23116520409 absolute error = 0.0003329 relative error = 0.009675 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.57 Order of pole (three term test) = 37.71 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4623 1.62 h = 0.0001 0.005 y[1] (numeric) = 1.1791886873 -3.25525650845 y[1] (closed_form) = 1.17890268418 -3.25549555628 absolute error = 0.0003727 relative error = 0.01077 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.757 Order of pole (three term test) = 37.8 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4624 1.625 h = 0.0001 0.003 y[1] (numeric) = 1.18427883897 -3.27302758768 y[1] (closed_form) = 1.1840139265 -3.27325032713 absolute error = 0.0003461 relative error = 0.009943 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.868 Order of pole (three term test) = 37.86 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4625 1.628 h = 0.001 0.001 y[1] (numeric) = 1.18721955025 -3.28377417674 y[1] (closed_form) = 1.18695140594 -3.28398694922 absolute error = 0.0003423 relative error = 0.009803 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.055 Order of pole (three term test) = 37.89 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4635 1.629 h = 0.001 0.003 y[1] (numeric) = 1.18476774903 -3.28842691581 y[1] (closed_form) = 1.18449969242 -3.28863426614 absolute error = 0.0003389 relative error = 0.009695 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 14.53 Order of pole (three term test) = 37.91 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4645 1.632 h = 0.0001 0.004 y[1] (numeric) = 1.18450085338 -3.30018457844 y[1] (closed_form) = 1.18423305343 -3.30040299468 absolute error = 0.0003456 relative error = 0.009855 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.27 Order of pole (three term test) = 37.95 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4646 1.636 h = 0.003 0.006 y[1] (numeric) = 1.18853255038 -3.31456776342 y[1] (closed_form) = 1.18827296573 -3.31479087223 absolute error = 0.0003423 relative error = 0.00972 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.05 Order of pole (three term test) = 37.99 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4676 1.642 h = 0.0001 0.005 y[1] (numeric) = 1.18440577084 -3.33937587627 y[1] (closed_form) = 1.18410921069 -3.33961837849 absolute error = 0.0003831 relative error = 0.01081 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.971 Order of pole (three term test) = 38.08 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4677 1.647 h = 0.0001 0.003 y[1] (numeric) = 1.18953004739 -3.35754312441 y[1] (closed_form) = 1.189255182 -3.35776908182 absolute error = 0.0003558 relative error = 0.009989 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.042 Order of pole (three term test) = 38.14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4678 1.65 h = 0.001 0.001 y[1] (numeric) = 1.19248844638 -3.36852888514 y[1] (closed_form) = 1.19221034185 -3.36874462085 absolute error = 0.000352 relative error = 0.00985 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.192 Order of pole (three term test) = 38.18 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=991.2MB, alloc=52.3MB, time=11.74 x[1] = 0.4688 1.651 h = 0.001 0.003 y[1] (numeric) = 1.18996558192 -3.37326977928 y[1] (closed_form) = 1.18968760417 -3.37347996691 absolute error = 0.0003485 relative error = 0.009742 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 15.18 Order of pole (three term test) = 38.19 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4698 1.654 h = 0.0001 0.004 y[1] (numeric) = 1.18964433805 -3.3852747148 y[1] (closed_form) = 1.18936654746 -3.38549622835 absolute error = 0.0003553 relative error = 0.009901 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.642 Order of pole (three term test) = 38.24 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4699 1.658 h = 0.003 0.006 y[1] (numeric) = 1.19370147197 -3.39997858383 y[1] (closed_form) = 1.19343205639 -3.40020495539 absolute error = 0.0003519 relative error = 0.009765 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.54 Order of pole (three term test) = 38.28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4729 1.664 h = 0.0001 0.005 y[1] (numeric) = 1.18938412663 -3.425293998 y[1] (closed_form) = 1.18907674138 -3.42553996408 absolute error = 0.0003937 relative error = 0.01086 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.195 Order of pole (three term test) = 38.38 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.473 1.669 h = 0.0001 0.003 y[1] (numeric) = 1.19454062739 -3.44386689301 y[1] (closed_form) = 1.19425555479 -3.44409607533 absolute error = 0.0003658 relative error = 0.01003 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.224 Order of pole (three term test) = 38.44 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4731 1.672 h = 0.001 0.001 y[1] (numeric) = 1.19751550082 -3.45509752401 y[1] (closed_form) = 1.19722718269 -3.4553162245 absolute error = 0.0003619 relative error = 0.009896 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.336 Order of pole (three term test) = 38.48 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4741 1.673 h = 0.001 0.003 y[1] (numeric) = 1.19491931722 -3.45992814633 y[1] (closed_form) = 1.1946311663 -3.4601411703 absolute error = 0.0003583 relative error = 0.009789 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 15.86 Order of pole (three term test) = 38.5 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4751 1.676 h = 0.0001 0.004 y[1] (numeric) = 1.19454077893 -3.47218575313 y[1] (closed_form) = 1.19425274308 -3.47241036825 absolute error = 0.0003653 relative error = 0.009947 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.031 Order of pole (three term test) = 38.54 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4752 1.68 h = 0.003 0.006 y[1] (numeric) = 1.1986217703 -3.48721795624 y[1] (closed_form) = 1.19834227188 -3.48744759897 absolute error = 0.0003617 relative error = 0.00981 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.06 Order of pole (three term test) = 38.59 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4782 1.686 h = 0.0001 0.005 y[1] (numeric) = 1.19410598677 -3.51305120673 y[1] (closed_form) = 1.19378750264 -3.51330064517 absolute error = 0.0004045 relative error = 0.0109 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.428 Order of pole (three term test) = 38.69 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4783 1.691 h = 0.0001 0.003 y[1] (numeric) = 1.19929273118 -3.532039419 y[1] (closed_form) = 1.19899719167 -3.5322718323 absolute error = 0.000376 relative error = 0.01008 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.414 Order of pole (three term test) = 38.75 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4784 1.694 h = 0.001 0.001 y[1] (numeric) = 1.20228281619 -3.54352073436 y[1] (closed_form) = 1.20198402571 -3.54374240016 absolute error = 0.000372 relative error = 0.009942 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.486 Order of pole (three term test) = 38.79 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4794 1.695 h = 0.0001 0.004 y[1] (numeric) = 1.19961100321 -3.54844268178 y[1] (closed_form) = 1.19931242176 -3.54865854006 absolute error = 0.0003684 relative error = 0.009836 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 20.98 Order of pole (three term test) = 38.81 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4795 1.699 h = 0.003 0.006 y[1] (numeric) = 1.20371081575 -3.56374915323 y[1] (closed_form) = 1.20342535345 -3.56398452428 absolute error = 0.00037 relative error = 0.009836 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.53 Order of pole (three term test) = 38.86 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4825 1.705 h = 0.0001 0.005 y[1] (numeric) = 1.19902410089 -3.59003921629 y[1] (closed_form) = 1.19869876279 -3.59029456863 absolute error = 0.0004136 relative error = 0.01093 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.639 Order of pole (three term test) = 38.97 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4826 1.71 h = 0.0001 0.003 y[1] (numeric) = 1.20424033638 -3.60939248683 y[1] (closed_form) = 1.20393849551 -3.60963059657 absolute error = 0.0003845 relative error = 0.0101 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.585 Order of pole (three term test) = 39.03 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4827 1.713 h = 0.001 0.001 y[1] (numeric) = 1.20724554702 -3.62109416885 y[1] (closed_form) = 1.20694044807 -3.62132129793 absolute error = 0.0003804 relative error = 0.009964 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.621 Order of pole (three term test) = 39.07 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4837 1.714 h = 0.001 0.003 y[1] (numeric) = 1.20450785645 -3.62609696233 y[1] (closed_form) = 1.20420300209 -3.62631816855 absolute error = 0.0003767 relative error = 0.009857 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 17.22 Order of pole (three term test) = 39.09 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4847 1.717 h = 0.0001 0.004 y[1] (numeric) = 1.20401773826 -3.638840219 y[1] (closed_form) = 1.20371286104 -3.63907352504 absolute error = 0.0003839 relative error = 0.01002 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.803 Order of pole (three term test) = 39.14 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1035.1MB, alloc=52.3MB, time=12.25 x[1] = 0.4848 1.721 h = 0.003 0.006 y[1] (numeric) = 1.20814282563 -3.65450403351 y[1] (closed_form) = 1.20784679745 -3.65474269224 absolute error = 0.0003803 relative error = 0.009879 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 13.09 Order of pole (three term test) = 39.2 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4878 1.727 h = 0.0001 0.005 y[1] (numeric) = 1.20324258786 -3.68133214337 y[1] (closed_form) = 1.20290562577 -3.68159098461 absolute error = 0.0004249 relative error = 0.01097 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.892 Order of pole (three term test) = 39.3 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4879 1.732 h = 0.0001 0.003 y[1] (numeric) = 1.20848527886 -3.70111927731 y[1] (closed_form) = 1.20817247307 -3.70136062993 absolute error = 0.0003951 relative error = 0.01015 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.792 Order of pole (three term test) = 39.37 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.488 1.735 h = 0.001 0.001 y[1] (numeric) = 1.21150328513 -3.71308279436 y[1] (closed_form) = 1.21118721771 -3.71331289001 absolute error = 0.000391 relative error = 0.01001 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.784 Order of pole (three term test) = 39.42 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.489 1.736 h = 0.001 0.003 y[1] (numeric) = 1.20868553647 -3.71817997756 y[1] (closed_form) = 1.20836975819 -3.71840401446 absolute error = 0.0003872 relative error = 0.009903 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 17.99 Order of pole (three term test) = 39.44 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.49 1.739 h = 0.0001 0.004 y[1] (numeric) = 1.20812928501 -3.73119195627 y[1] (closed_form) = 1.20781340401 -3.73142837373 absolute error = 0.0003946 relative error = 0.01006 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.24 Order of pole (three term test) = 39.49 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4901 1.743 h = 0.003 0.006 y[1] (numeric) = 1.2122734372 -3.74720687966 y[1] (closed_form) = 1.21196657558 -3.74744883195 absolute error = 0.0003908 relative error = 0.009922 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 13.68 Order of pole (three term test) = 39.55 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4931 1.749 h = 0.0001 0.005 y[1] (numeric) = 1.20715118561 -3.77458412505 y[1] (closed_form) = 1.20680230858 -3.77484646073 absolute error = 0.0004365 relative error = 0.01101 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.157 Order of pole (three term test) = 39.66 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4932 1.754 h = 0.0001 0.003 y[1] (numeric) = 1.21241810768 -3.79481536648 y[1] (closed_form) = 1.21209406112 -3.79505996518 absolute error = 0.000406 relative error = 0.01019 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.007 Order of pole (three term test) = 39.73 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4933 1.757 h = 0.001 0.001 y[1] (numeric) = 1.21544749543 -3.80704687686 y[1] (closed_form) = 1.21512018484 -3.80727993638 absolute error = 0.0004018 relative error = 0.01005 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.954 Order of pole (three term test) = 39.78 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4943 1.758 h = 0.001 0.003 y[1] (numeric) = 1.21254721527 -3.81224011655 y[1] (closed_form) = 1.21222023989 -3.81246697874 absolute error = 0.000398 relative error = 0.009948 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 18.8 Order of pole (three term test) = 39.8 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4953 1.761 h = 0.0001 0.004 y[1] (numeric) = 1.2119215423 -3.82552662003 y[1] (closed_form) = 1.21159438143 -3.82576614915 absolute error = 0.0004055 relative error = 0.0101 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.7 Order of pole (three term test) = 39.85 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4954 1.765 h = 0.003 0.006 y[1] (numeric) = 1.21608291376 -3.84190092036 y[1] (closed_form) = 1.21576494542 -3.84214617107 absolute error = 0.0004016 relative error = 0.009965 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 14.3 Order of pole (three term test) = 39.92 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4984 1.771 h = 0.0001 0.005 y[1] (numeric) = 1.21072992813 -3.86983858859 y[1] (closed_form) = 1.21036883897 -3.87010442305 absolute error = 0.0004484 relative error = 0.01106 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.434 Order of pole (three term test) = 40.03 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4985 1.776 h = 0.0001 0.003 y[1] (numeric) = 1.21601876429 -3.89052438974 y[1] (closed_form) = 1.21568319523 -3.89077223657 absolute error = 0.0004172 relative error = 0.01023 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.233 Order of pole (three term test) = 40.11 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4986 1.779 h = 0.001 0.001 y[1] (numeric) = 1.21905806211 -3.90303017657 y[1] (closed_form) = 1.21871922781 -3.903266196 absolute error = 0.0004129 relative error = 0.0101 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.132 Order of pole (three term test) = 40.16 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4996 1.78 h = 0.001 0.003 y[1] (numeric) = 1.21607271698 -3.90832116407 y[1] (closed_form) = 1.21573426557 -3.90855084484 absolute error = 0.000409 relative error = 0.009993 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 19.65 Order of pole (three term test) = 40.18 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5006 1.783 h = 0.0001 0.004 y[1] (numeric) = 1.2153742386 -3.92188810403 y[1] (closed_form) = 1.21503551587 -3.92213074382 absolute error = 0.0004167 relative error = 0.01015 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.19 Order of pole (three term test) = 40.24 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5007 1.787 h = 0.003 0.006 y[1] (numeric) = 1.21955090782 -3.93863021722 y[1] (closed_form) = 1.21922155364 -3.93887877012 absolute error = 0.0004126 relative error = 0.01001 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 14.94 Order of pole (three term test) = 40.3 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1078.8MB, alloc=52.3MB, time=12.76 x[1] = 0.5037 1.793 h = 0.0001 0.005 y[1] (numeric) = 1.21395823204 -3.9671397973 y[1] (closed_form) = 1.21358462718 -3.96740913364 absolute error = 0.0004606 relative error = 0.0111 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.724 Order of pole (three term test) = 40.42 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5038 1.798 h = 0.0001 0.003 y[1] (numeric) = 1.2192665693 -3.98829082274 y[1] (closed_form) = 1.21891918999 -3.98854191855 absolute error = 0.0004286 relative error = 0.01028 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.468 Order of pole (three term test) = 40.5 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5039 1.801 h = 0.001 0.001 y[1] (numeric) = 1.22231424628 -4.00107729652 y[1] (closed_form) = 1.22196360181 -4.00131627055 absolute error = 0.0004243 relative error = 0.01014 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.318 Order of pole (three term test) = 40.55 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5049 1.802 h = 0.0001 0.004 y[1] (numeric) = 1.21924124114 -4.00646774787 y[1] (closed_form) = 1.21889102889 -4.00670023912 absolute error = 0.0004204 relative error = 0.01004 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.98 Order of pole (three term test) = 40.58 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.505 1.806 h = 0.003 0.006 y[1] (numeric) = 1.22342953157 -4.0235170242 y[1] (closed_form) = 1.22309331316 -4.0237717694 absolute error = 0.0004218 relative error = 0.01003 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 15.52 Order of pole (three term test) = 40.65 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.508 1.812 h = 0.0001 0.005 y[1] (numeric) = 1.21763018426 -4.05253124823 y[1] (closed_form) = 1.21724872497 -4.05280696195 absolute error = 0.0004707 relative error = 0.01112 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.985 Order of pole (three term test) = 40.77 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5081 1.817 h = 0.0001 0.003 y[1] (numeric) = 1.22295901784 -4.07409123711 y[1] (closed_form) = 1.22260440126 -4.07434848219 absolute error = 0.0004381 relative error = 0.0103 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.68 Order of pole (three term test) = 40.86 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5082 1.82 h = 0.001 0.001 y[1] (numeric) = 1.22601608431 -4.08712447549 y[1] (closed_form) = 1.22565820008 -4.08736934034 absolute error = 0.0004336 relative error = 0.01016 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.485 Order of pole (three term test) = 40.91 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5092 1.821 h = 0.001 0.003 y[1] (numeric) = 1.22286671123 -4.09260302263 y[1] (closed_form) = 1.22250930128 -4.09284127773 absolute error = 0.0004295 relative error = 0.01006 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 21.33 Order of pole (three term test) = 40.94 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5102 1.824 h = 0.0001 0.004 y[1] (numeric) = 1.22202692469 -4.10670887193 y[1] (closed_form) = 1.22166907891 -4.10696064633 absolute error = 0.0004375 relative error = 0.01021 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.14 Order of pole (three term test) = 41 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5103 1.828 h = 0.003 0.006 y[1] (numeric) = 1.2262312999 -4.12415831626 y[1] (closed_form) = 1.22588316034 -4.12441637105 absolute error = 0.0004334 relative error = 0.01007 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 16.22 Order of pole (three term test) = 41.07 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5133 1.834 h = 0.0001 0.005 y[1] (numeric) = 1.22017508876 -4.15376649177 y[1] (closed_form) = 1.21978053143 -4.15404571338 absolute error = 0.0004834 relative error = 0.01116 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.299 Order of pole (three term test) = 41.2 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5134 1.839 h = 0.0001 0.003 y[1] (numeric) = 1.22551879872 -4.17581216083 y[1] (closed_form) = 1.22515181999 -4.17607265663 absolute error = 0.00045 relative error = 0.01034 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.935 Order of pole (three term test) = 41.29 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5135 1.842 h = 0.001 0.001 y[1] (numeric) = 1.22858131003 -4.18913838239 y[1] (closed_form) = 1.22821106618 -4.18938619176 absolute error = 0.0004455 relative error = 0.01021 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.687 Order of pole (three term test) = 41.34 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5145 1.843 h = 0.001 0.003 y[1] (numeric) = 1.22533929997 -4.19471968567 y[1] (closed_form) = 1.22496958294 -4.1949607358 absolute error = 0.0004414 relative error = 0.0101 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.29 Order of pole (three term test) = 41.37 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5155 1.846 h = 0.0001 0.004 y[1] (numeric) = 1.22441654763 -4.2091235468 y[1] (closed_form) = 1.22404629971 -4.20937842537 absolute error = 0.0004495 relative error = 0.01025 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.69 Order of pole (three term test) = 41.43 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5156 1.85 h = 0.003 0.006 y[1] (numeric) = 1.22863038585 -4.22696592102 y[1] (closed_form) = 1.2282700286 -4.22722728579 absolute error = 0.0004452 relative error = 0.01011 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 16.95 Order of pole (three term test) = 41.51 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5186 1.856 h = 0.0001 0.005 y[1] (numeric) = 1.22230764457 -4.25718013465 y[1] (closed_form) = 1.22189966655 -4.25746286335 absolute error = 0.0004964 relative error = 0.01121 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.627 Order of pole (three term test) = 41.64 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5187 1.861 h = 0.0001 0.003 y[1] (numeric) = 1.22766352578 -4.27972278125 y[1] (closed_form) = 1.22728387921 -4.27998652488 absolute error = 0.0004623 relative error = 0.01038 % Correct digits = 4 memory used=1122.6MB, alloc=52.3MB, time=13.27 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.203 Order of pole (three term test) = 41.74 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5188 1.864 h = 0.001 0.001 y[1] (numeric) = 1.23072977028 -4.29334877596 y[1] (closed_form) = 1.2303468626 -4.2935995204 absolute error = 0.0004577 relative error = 0.01025 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.898 Order of pole (three term test) = 41.8 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5198 1.865 h = 0.001 0.003 y[1] (numeric) = 1.22739234349 -4.29903462394 y[1] (closed_form) = 1.22701001696 -4.29927845668 absolute error = 0.0004535 relative error = 0.01014 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.29 Order of pole (three term test) = 41.82 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5208 1.868 h = 0.0001 0.004 y[1] (numeric) = 1.2263828454 -4.31374284873 y[1] (closed_form) = 1.22599988947 -4.31400082526 absolute error = 0.0004617 relative error = 0.0103 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 13.26 Order of pole (three term test) = 41.89 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5209 1.872 h = 0.003 0.006 y[1] (numeric) = 1.23060390667 -4.33198727033 y[1] (closed_form) = 1.23023102884 -4.33225194412 absolute error = 0.0004573 relative error = 0.01015 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 17.71 Order of pole (three term test) = 41.97 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5239 1.878 h = 0.0001 0.005 y[1] (numeric) = 1.22400470608 -4.36281982286 y[1] (closed_form) = 1.2235829778 -4.36310605631 absolute error = 0.0005097 relative error = 0.01125 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.97 Order of pole (three term test) = 42.11 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.524 1.883 h = 0.0001 0.003 y[1] (numeric) = 1.22936994305 -4.38587097379 y[1] (closed_form) = 1.22897731642 -4.38613796088 absolute error = 0.0004748 relative error = 0.01042 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.482 Order of pole (three term test) = 42.21 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5241 1.886 h = 0.001 0.001 y[1] (numeric) = 1.2324381409 -4.39980366914 y[1] (closed_form) = 1.2320422587 -4.4000573376 absolute error = 0.0004702 relative error = 0.01029 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.118 Order of pole (three term test) = 42.27 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5251 1.887 h = 0.001 0.003 y[1] (numeric) = 1.22900244972 -4.40559587578 y[1] (closed_form) = 1.2286072049 -4.40584247706 absolute error = 0.0004659 relative error = 0.01019 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.34 Order of pole (three term test) = 42.3 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5261 1.89 h = 0.0001 0.004 y[1] (numeric) = 1.22790231541 -4.42061493462 y[1] (closed_form) = 1.22750633908 -4.42087600133 absolute error = 0.0004743 relative error = 0.01034 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 13.86 Order of pole (three term test) = 42.37 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5262 1.894 h = 0.003 0.006 y[1] (numeric) = 1.23212826928 -4.43927070608 y[1] (closed_form) = 1.23174256153 -4.43953868652 absolute error = 0.0004697 relative error = 0.01019 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 18.51 Order of pole (three term test) = 42.45 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5292 1.9 h = 0.0001 0.005 y[1] (numeric) = 1.22524240995 -4.47073411571 y[1] (closed_form) = 1.22480659477 -4.47102385 absolute error = 0.0005233 relative error = 0.01129 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.329 Order of pole (three term test) = 42.6 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5293 1.905 h = 0.0001 0.003 y[1] (numeric) = 1.2306140729 -4.49430553179 y[1] (closed_form) = 1.23020814731 -4.49457575642 absolute error = 0.0004876 relative error = 0.01046 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.773 Order of pole (three term test) = 42.7 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5294 1.908 h = 0.001 0.001 y[1] (numeric) = 1.23368237359 -4.50855199558 y[1] (closed_form) = 1.23327319961 -4.50880857531 absolute error = 0.000483 relative error = 0.01033 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.349 Order of pole (three term test) = 42.77 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5304 1.909 h = 0.0001 0.004 y[1] (numeric) = 1.23014550078 -4.51445240041 y[1] (closed_form) = 1.22973702232 -4.51470175441 absolute error = 0.0004786 relative error = 0.01023 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 32.18 Order of pole (three term test) = 42.8 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5305 1.913 h = 0.003 0.006 y[1] (numeric) = 1.23437432227 -4.53345161255 y[1] (closed_form) = 1.23398074192 -4.53372627866 absolute error = 0.0004799 relative error = 0.01021 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 19.22 Order of pole (three term test) = 42.88 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5335 1.919 h = 0.0001 0.005 y[1] (numeric) = 1.2272410591 -4.56547182085 y[1] (closed_form) = 1.22679626929 -4.56576842196 absolute error = 0.0005346 relative error = 0.01131 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.652 Order of pole (three term test) = 43.04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5336 1.924 h = 0.0001 0.003 y[1] (numeric) = 1.23262220938 -4.58950063684 y[1] (closed_form) = 1.23220799878 -4.58977749044 absolute error = 0.0004982 relative error = 0.01048 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.036 Order of pole (three term test) = 43.15 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5337 1.927 h = 0.001 0.001 y[1] (numeric) = 1.23569291585 -4.60402298104 y[1] (closed_form) = 1.23527546039 -4.60428590319 absolute error = 0.0004934 relative error = 0.01035 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.556 Order of pole (three term test) = 43.21 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5347 1.928 h = 0.001 0.003 y[1] (numeric) = 1.23206787791 -4.61001926585 memory used=1166.4MB, alloc=52.3MB, time=13.78 y[1] (closed_form) = 1.23165116768 -4.61027482257 absolute error = 0.0004888 relative error = 0.01024 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.42 Order of pole (three term test) = 43.24 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5357 1.931 h = 0.0001 0.004 y[1] (numeric) = 1.23079223407 -4.62563554446 y[1] (closed_form) = 1.23037459642 -4.62590618363 absolute error = 0.0004977 relative error = 0.0104 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 15.04 Order of pole (three term test) = 43.32 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5358 1.935 h = 0.003 0.006 y[1] (numeric) = 1.23502593646 -4.64508216165 y[1] (closed_form) = 1.23461893275 -4.64536012986 absolute error = 0.0004929 relative error = 0.01025 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 20.09 Order of pole (three term test) = 43.41 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5388 1.941 h = 0.0001 0.005 y[1] (numeric) = 1.22758644586 -4.67775724013 y[1] (closed_form) = 1.22712692322 -4.67805733442 absolute error = 0.0005488 relative error = 0.01135 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.041 Order of pole (three term test) = 43.57 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5389 1.946 h = 0.0001 0.003 y[1] (numeric) = 1.23296839898 -4.70232888264 y[1] (closed_form) = 1.23254027765 -4.70260896237 absolute error = 0.0005116 relative error = 0.01052 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.352 Order of pole (three term test) = 43.68 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.539 1.949 h = 0.001 0.001 y[1] (numeric) = 1.23603565666 -4.71717855392 y[1] (closed_form) = 1.23560430078 -4.7174443628 absolute error = 0.0005067 relative error = 0.01039 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.806 Order of pole (three term test) = 43.75 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.54 1.95 h = 0.001 0.003 y[1] (numeric) = 1.23230384007 -4.72328656527 y[1] (closed_form) = 1.23187329133 -4.72354484426 absolute error = 0.0005021 relative error = 0.01029 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.61 Order of pole (three term test) = 43.79 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.541 1.953 h = 0.0001 0.004 y[1] (numeric) = 1.23092587219 -4.73923291222 y[1] (closed_form) = 1.23049428305 -4.73950661407 absolute error = 0.0005111 relative error = 0.01044 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 15.72 Order of pole (three term test) = 43.86 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5411 1.957 h = 0.003 0.006 y[1] (numeric) = 1.23515738997 -4.75911857805 y[1] (closed_form) = 1.2347366342 -4.75939984163 absolute error = 0.0005061 relative error = 0.01029 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 20.99 Order of pole (three term test) = 43.96 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5441 1.963 h = 0.0001 0.005 y[1] (numeric) = 1.22740065968 -4.792461689 y[1] (closed_form) = 1.22692604642 -4.79276526756 absolute error = 0.0005634 relative error = 0.01139 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.448 Order of pole (three term test) = 44.13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5442 1.968 h = 0.0001 0.003 y[1] (numeric) = 1.23278013887 -4.81758861598 y[1] (closed_form) = 1.23233776798 -4.81787191114 absolute error = 0.0005253 relative error = 0.01056 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.683 Order of pole (three term test) = 44.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5443 1.971 h = 0.001 0.001 y[1] (numeric) = 1.23584188297 -4.83277309997 y[1] (closed_form) = 1.23539628971 -4.83304177761 absolute error = 0.0005203 relative error = 0.01043 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.067 Order of pole (three term test) = 44.32 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5453 1.972 h = 0.001 0.003 y[1] (numeric) = 1.23200016182 -4.83899475231 y[1] (closed_form) = 1.23155543971 -4.83925573237 absolute error = 0.0005156 relative error = 0.01033 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.85 Order of pole (three term test) = 44.35 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5463 1.975 h = 0.0001 0.004 y[1] (numeric) = 1.23051552267 -4.85527811654 y[1] (closed_form) = 1.23006964313 -4.85555486665 absolute error = 0.0005248 relative error = 0.01048 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 16.43 Order of pole (three term test) = 44.43 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5464 1.979 h = 0.003 0.006 y[1] (numeric) = 1.2347421474 -4.8756128842 y[1] (closed_form) = 1.23430730383 -4.87589743471 absolute error = 0.0005197 relative error = 0.01033 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 21.94 Order of pole (three term test) = 44.53 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5494 1.985 h = 0.0001 0.005 y[1] (numeric) = 1.22665686476 -4.90963742051 y[1] (closed_form) = 1.22616679537 -4.90994447251 absolute error = 0.0005783 relative error = 0.01143 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.873 Order of pole (three term test) = 44.71 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5495 1.99 h = 0.0001 0.003 y[1] (numeric) = 1.23203046259 -4.93533234248 y[1] (closed_form) = 1.23157349609 -4.9356188405 absolute error = 0.0005394 relative error = 0.0106 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.029 Order of pole (three term test) = 44.84 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5496 1.993 h = 0.001 0.001 y[1] (numeric) = 1.23508454774 -4.95085927618 y[1] (closed_form) = 1.23462437298 -4.95113080263 absolute error = 0.0005343 relative error = 0.01047 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.34 Order of pole (three term test) = 44.91 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5506 1.994 h = 0.001 0.003 y[1] (numeric) = 1.23112971951 -4.95719651015 y[1] (closed_form) = 1.2306704821 -4.957460168 absolute error = 0.0005295 relative error = 0.01037 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.15 Order of pole (three term test) = 44.95 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1210.2MB, alloc=52.3MB, time=14.30 x[1] = 0.5516 1.997 h = 0.0001 0.004 y[1] (numeric) = 1.22953393463 -4.97382396938 y[1] (closed_form) = 1.22907341857 -4.97410375139 absolute error = 0.0005388 relative error = 0.01052 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 17.16 Order of pole (three term test) = 45.03 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5517 2.001 h = 0.003 0.006 y[1] (numeric) = 1.2337528509 -4.99461809568 y[1] (closed_form) = 1.23330357661 -4.99490592288 absolute error = 0.0005336 relative error = 0.01037 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.93 Order of pole (three term test) = 45.14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5547 2.007 h = 0.0001 0.005 y[1] (numeric) = 1.22532739452 -5.02933768427 y[1] (closed_form) = 1.22482149565 -5.02964819687 absolute error = 0.0005936 relative error = 0.01147 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.32 Order of pole (three term test) = 45.32 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5548 2.012 h = 0.0001 0.003 y[1] (numeric) = 1.23069156843 -5.05561356934 y[1] (closed_form) = 1.23021965284 -5.05590325574 absolute error = 0.0005537 relative error = 0.01064 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.39 Order of pole (three term test) = 45.45 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5549 2.015 h = 0.001 0.001 y[1] (numeric) = 1.23373576591 -5.07149074412 y[1] (closed_form) = 1.2332606582 -5.07176509728 absolute error = 0.0005486 relative error = 0.01051 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.625 Order of pole (three term test) = 45.53 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5559 2.016 h = 0.0001 0.004 y[1] (numeric) = 1.22966454953 -5.07794552667 y[1] (closed_form) = 1.22919044766 -5.07821183687 absolute error = 0.0005438 relative error = 0.01041 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 39.87 Order of pole (three term test) = 45.57 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.556 2.02 h = 0.003 0.006 y[1] (numeric) = 1.23387573328 -5.09912309808 y[1] (closed_form) = 1.2334174564 -5.09941813352 absolute error = 0.000545 relative error = 0.01039 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.81 Order of pole (three term test) = 45.68 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.559 2.026 h = 0.0001 0.005 y[1] (numeric) = 1.2251564234 -5.13445630429 y[1] (closed_form) = 1.22464029519 -5.13477419831 absolute error = 0.0006062 relative error = 0.01148 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.72 Order of pole (three term test) = 45.87 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5591 2.031 h = 0.0001 0.003 y[1] (numeric) = 1.23051667764 -5.16124302027 y[1] (closed_form) = 1.23003530354 -5.16153984169 absolute error = 0.0005655 relative error = 0.01066 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.715 Order of pole (three term test) = 46 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5592 2.034 h = 0.001 0.001 y[1] (numeric) = 1.23355481499 -5.17742818557 y[1] (closed_form) = 1.23307025992 -5.17770935605 absolute error = 0.0005602 relative error = 0.01053 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.882 Order of pole (three term test) = 46.09 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5602 2.035 h = 0.001 0.003 y[1] (numeric) = 1.22938215943 -5.1839871864 y[1] (closed_form) = 1.22889866887 -5.18426016021 absolute error = 0.0005552 relative error = 0.01042 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 32.73 Order of pole (three term test) = 46.13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5612 2.038 h = 0.0001 0.004 y[1] (numeric) = 1.22757150223 -5.20127566989 y[1] (closed_form) = 1.22708650016 -5.20156544723 absolute error = 0.000565 relative error = 0.01057 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 18.63 Order of pole (three term test) = 46.22 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5613 2.042 h = 0.003 0.006 y[1] (numeric) = 1.23177396985 -5.22295274475 y[1] (closed_form) = 1.2313006043 -5.22325103711 absolute error = 0.0005595 relative error = 0.01043 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.88 Order of pole (three term test) = 46.33 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5643 2.048 h = 0.0001 0.005 y[1] (numeric) = 1.22269217976 -5.25900714226 y[1] (closed_form) = 1.22215950566 -5.25932847194 absolute error = 0.0006221 relative error = 0.01152 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.2 Order of pole (three term test) = 46.53 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5644 2.053 h = 0.0001 0.003 y[1] (numeric) = 1.22803620447 -5.28639970129 y[1] (closed_form) = 1.22753920309 -5.28669968304 absolute error = 0.0005805 relative error = 0.0107 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.107 Order of pole (three term test) = 46.67 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5645 2.056 h = 0.001 0.001 y[1] (numeric) = 1.23106017268 -5.30295005579 y[1] (closed_form) = 1.2305600104 -5.30323401039 absolute error = 0.0005751 relative error = 0.01056 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.192 Order of pole (three term test) = 46.76 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5655 2.057 h = 0.001 0.003 y[1] (numeric) = 1.22676483216 -5.3096303771 y[1] (closed_form) = 1.22626580722 -5.30990595421 absolute error = 0.0005701 relative error = 0.01046 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 34.2 Order of pole (three term test) = 46.8 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5665 2.06 h = 0.0001 0.004 y[1] (numeric) = 1.22482958253 -5.32728399279 y[1] (closed_form) = 1.22432891213 -5.32757674814 absolute error = 0.00058 relative error = 0.01061 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 19.47 Order of pole (three term test) = 46.9 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5666 2.064 h = 0.003 0.006 y[1] (numeric) = 1.22901579411 -5.34945096745 y[1] (closed_form) = 1.22852697551 -5.349752501 absolute error = 0.0005743 relative error = 0.01046 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26 Order of pole (three term test) = 47.02 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1254.0MB, alloc=52.3MB, time=14.80 x[1] = 0.5696 2.07 h = 0.0001 0.005 y[1] (numeric) = 1.2195589747 -5.38624087625 y[1] (closed_form) = 1.2190093579 -5.38656562254 absolute error = 0.0006384 relative error = 0.01156 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.7 Order of pole (three term test) = 47.22 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5697 2.075 h = 0.0001 0.003 y[1] (numeric) = 1.2248828179 -5.41425301353 y[1] (closed_form) = 1.2243698137 -5.41455613515 absolute error = 0.0005959 relative error = 0.01073 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.517 Order of pole (three term test) = 47.38 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5698 2.078 h = 0.001 0.001 y[1] (numeric) = 1.22789013583 -5.43117680815 y[1] (closed_form) = 1.22737399309 -5.43146351838 absolute error = 0.0005904 relative error = 0.0106 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.515 Order of pole (three term test) = 47.47 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5708 2.079 h = 0.001 0.003 y[1] (numeric) = 1.22346859404 -5.43798049393 y[1] (closed_form) = 1.22295366395 -5.43825864227 absolute error = 0.0005853 relative error = 0.0105 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 35.74 Order of pole (three term test) = 47.51 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5718 2.082 h = 0.0001 0.004 y[1] (numeric) = 1.22140375251 -5.45600683916 y[1] (closed_form) = 1.22088703825 -5.4563025479 absolute error = 0.0005953 relative error = 0.01065 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 20.35 Order of pole (three term test) = 47.61 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5719 2.086 h = 0.003 0.006 y[1] (numeric) = 1.22557044691 -5.47867479634 y[1] (closed_form) = 1.22506580309 -5.47897955323 absolute error = 0.0005895 relative error = 0.0105 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.17 Order of pole (three term test) = 47.73 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5749 2.092 h = 0.0001 0.005 y[1] (numeric) = 1.21572570654 -5.51621478429 y[1] (closed_form) = 1.21515874173 -5.51654292574 absolute error = 0.0006551 relative error = 0.0116 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.23 Order of pole (three term test) = 47.95 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.575 2.097 h = 0.0001 0.003 y[1] (numeric) = 1.22102526258 -5.54486051281 y[1] (closed_form) = 1.22049587197 -5.54516675154 absolute error = 0.0006116 relative error = 0.01077 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.945 Order of pole (three term test) = 48.11 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5751 2.1 h = 0.001 0.001 y[1] (numeric) = 1.2240133544 -5.56216616486 y[1] (closed_form) = 1.22348085001 -5.56245559974 absolute error = 0.0006061 relative error = 0.01064 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.854 Order of pole (three term test) = 48.2 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5761 2.101 h = 0.001 0.003 y[1] (numeric) = 1.21946200872 -5.56909528587 y[1] (closed_form) = 1.21893079484 -5.56937597084 absolute error = 0.0006008 relative error = 0.01054 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 37.35 Order of pole (three term test) = 48.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5771 2.104 h = 0.0001 0.004 y[1] (numeric) = 1.21726242982 -5.58750209772 y[1] (closed_form) = 1.21672928815 -5.58780073282 absolute error = 0.0006111 relative error = 0.01069 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 21.26 Order of pole (three term test) = 48.35 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5772 2.108 h = 0.003 0.006 y[1] (numeric) = 1.22140622016 -5.61068234401 y[1] (closed_form) = 1.22088537096 -5.61099030415 absolute error = 0.0006051 relative error = 0.01054 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.4 Order of pole (three term test) = 48.48 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5802 2.114 h = 0.0001 0.005 y[1] (numeric) = 1.21116031539 -5.64898723046 y[1] (closed_form) = 1.21057558857 -5.64931874314 absolute error = 0.0006722 relative error = 0.01163 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.78 Order of pole (three term test) = 48.71 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5803 2.119 h = 0.0001 0.003 y[1] (numeric) = 1.21643131976 -5.67828084642 y[1] (closed_form) = 1.21588515098 -5.67859017708 absolute error = 0.0006277 relative error = 0.01081 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.39 Order of pole (three term test) = 48.87 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5804 2.122 h = 0.001 0.001 y[1] (numeric) = 1.21939751183 -5.69597694281 y[1] (closed_form) = 1.21884825652 -5.69626906878 absolute error = 0.0006221 relative error = 0.01068 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.207 Order of pole (three term test) = 48.98 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5814 2.123 h = 0.0001 0.004 y[1] (numeric) = 1.2147126712 -5.70303359674 y[1] (closed_form) = 1.21416478689 -5.70331678109 absolute error = 0.0006167 relative error = 0.01058 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 49.38 Order of pole (three term test) = 49.02 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5815 2.127 h = 0.003 0.006 y[1] (numeric) = 1.2188359491 -5.72664139379 y[1] (closed_form) = 1.21830483063 -5.72695711344 absolute error = 0.0006179 relative error = 0.01055 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.5 Order of pole (three term test) = 49.15 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5845 2.133 h = 0.0001 0.005 y[1] (numeric) = 1.20824321125 -5.76562174114 y[1] (closed_form) = 1.20764684948 -5.76596117366 absolute error = 0.0006862 relative error = 0.01165 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 13.27 Order of pole (three term test) = 49.39 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5846 2.138 h = 0.0001 0.003 y[1] (numeric) = 1.21349405397 -5.7954851176 y[1] (closed_form) = 1.21293711196 -5.79580211472 absolute error = 0.0006408 relative error = 0.01082 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.8 Order of pole (three term test) = 49.56 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1298.0MB, alloc=52.3MB, time=15.32 x[1] = 0.5847 2.141 h = 0.001 0.001 y[1] (numeric) = 1.21644397079 -5.81352460966 y[1] (closed_form) = 1.21588396289 -5.81382404982 absolute error = 0.000635 relative error = 0.01069 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.525 Order of pole (three term test) = 49.67 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5857 2.142 h = 0.001 0.003 y[1] (numeric) = 1.21164275102 -5.82069439178 y[1] (closed_form) = 1.21108418321 -5.82098472131 absolute error = 0.0006295 relative error = 0.01059 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 40.54 Order of pole (three term test) = 49.71 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5867 2.145 h = 0.0001 0.004 y[1] (numeric) = 1.20918300138 -5.83983200073 y[1] (closed_form) = 1.2086222298 -5.84014102819 absolute error = 0.0006403 relative error = 0.01074 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.08 Order of pole (three term test) = 49.83 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5868 2.149 h = 0.003 0.006 y[1] (numeric) = 1.21328114125 -5.86399674962 y[1] (closed_form) = 1.21273308795 -5.86431563369 absolute error = 0.0006341 relative error = 0.01059 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.82 Order of pole (three term test) = 49.97 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5898 2.155 h = 0.0001 0.005 y[1] (numeric) = 1.20226181084 -5.90377042094 y[1] (closed_form) = 1.20164689252 -5.9041131783 absolute error = 0.000704 relative error = 0.01168 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 13.87 Order of pole (three term test) = 50.21 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5899 2.16 h = 0.0001 0.003 y[1] (numeric) = 1.20747590423 -5.93430911497 y[1] (closed_form) = 1.20690143226 -5.93462915536 absolute error = 0.0006576 relative error = 0.01086 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.28 Order of pole (three term test) = 50.39 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.59 2.163 h = 0.001 0.001 y[1] (numeric) = 1.21039878203 -5.95275552712 y[1] (closed_form) = 1.20982127625 -5.9530575936 absolute error = 0.0006517 relative error = 0.01073 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.908 Order of pole (three term test) = 50.5 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.591 2.164 h = 0.001 0.003 y[1] (numeric) = 1.20545698202 -5.960056864 y[1] (closed_form) = 1.20488100188 -5.96034962105 absolute error = 0.0006461 relative error = 0.01063 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 42.36 Order of pole (three term test) = 50.55 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.592 2.167 h = 0.0001 0.004 y[1] (numeric) = 1.2028470291 -5.97959793349 y[1] (closed_form) = 1.20226868675 -5.97990980079 absolute error = 0.0006571 relative error = 0.01077 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.12 Order of pole (three term test) = 50.67 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5921 2.171 h = 0.003 0.006 y[1] (numeric) = 1.20691198764 -6.0043086383 y[1] (closed_form) = 1.2063465956 -6.00463065993 absolute error = 0.0006507 relative error = 0.01062 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 32.21 Order of pole (three term test) = 50.82 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5951 2.177 h = 0.0001 0.005 y[1] (numeric) = 1.19545176478 -6.04489119743 y[1] (closed_form) = 1.19481784995 -6.04523724803 absolute error = 0.0007222 relative error = 0.01172 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 14.5 Order of pole (three term test) = 51.07 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5952 2.182 h = 0.0001 0.003 y[1] (numeric) = 1.2006243639 -6.07612034833 y[1] (closed_form) = 1.20003194574 -6.07644339948 absolute error = 0.0006748 relative error = 0.01089 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.79 Order of pole (three term test) = 51.26 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5953 2.185 h = 0.001 0.001 y[1] (numeric) = 1.20351723325 -6.09498277239 y[1] (closed_form) = 1.20292181618 -6.09528742375 absolute error = 0.0006688 relative error = 0.01077 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.309 Order of pole (three term test) = 51.38 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5963 2.186 h = 0.001 0.003 y[1] (numeric) = 1.19843089713 -6.10241784034 y[1] (closed_form) = 1.19783709412 -6.10271297961 absolute error = 0.0006631 relative error = 0.01066 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 44.27 Order of pole (three term test) = 51.43 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5973 2.189 h = 0.0001 0.004 y[1] (numeric) = 1.19566499367 -6.12237067089 y[1] (closed_form) = 1.19506866447 -6.12268534092 absolute error = 0.0006743 relative error = 0.01081 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.2 Order of pole (three term test) = 51.55 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5974 2.193 h = 0.003 0.006 y[1] (numeric) = 1.1996928612 -6.14763954584 y[1] (closed_form) = 1.19910971788 -6.14796467553 absolute error = 0.0006677 relative error = 0.01066 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 33.66 Order of pole (three term test) = 51.71 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6004 2.199 h = 0.0001 0.005 y[1] (numeric) = 1.18777705636 -6.18904682255 y[1] (closed_form) = 1.18712369562 -6.18939613189 absolute error = 0.0007409 relative error = 0.01176 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 15.15 Order of pole (three term test) = 51.97 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6005 2.204 h = 0.0001 0.003 y[1] (numeric) = 1.19290323632 -6.22098187476 y[1] (closed_form) = 1.19229244686 -6.22130790134 absolute error = 0.0006924 relative error = 0.01093 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.32 Order of pole (three term test) = 52.17 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6006 2.207 h = 0.001 0.001 y[1] (numeric) = 1.19576301709 -6.24026958518 y[1] (closed_form) = 1.19514926655 -6.24057677704 absolute error = 0.0006863 relative error = 0.0108 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.728 Order of pole (three term test) = 52.29 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1341.7MB, alloc=52.3MB, time=15.83 x[1] = 0.6016 2.208 h = 0.001 0.003 y[1] (numeric) = 1.19052809189 -6.24784058781 y[1] (closed_form) = 1.18991604677 -6.24813806094 absolute error = 0.0006805 relative error = 0.0107 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 46.26 Order of pole (three term test) = 52.34 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6026 2.211 h = 0.0001 0.004 y[1] (numeric) = 1.1876003235 -6.26821363133 y[1] (closed_form) = 1.18698558251 -6.26853106401 absolute error = 0.0006919 relative error = 0.01084 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.34 Order of pole (three term test) = 52.47 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6027 2.215 h = 0.003 0.006 y[1] (numeric) = 1.19158704328 -6.29405313642 y[1] (closed_form) = 1.19098572731 -6.29438134197 absolute error = 0.0006851 relative error = 0.01069 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 35.17 Order of pole (three term test) = 52.64 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6057 2.221 h = 0.0001 0.005 y[1] (numeric) = 1.17920056685 -6.33630123027 y[1] (closed_form) = 1.17852730118 -6.33665376077 absolute error = 0.00076 relative error = 0.01179 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 15.83 Order of pole (three term test) = 52.91 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6058 2.226 h = 0.0001 0.003 y[1] (numeric) = 1.18427521697 -6.36895793921 y[1] (closed_form) = 1.18364562203 -6.36928690298 absolute error = 0.0007104 relative error = 0.01097 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.87 Order of pole (three term test) = 53.12 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6059 2.229 h = 0.001 0.001 y[1] (numeric) = 1.18709871477 -6.38868039667 y[1] (closed_form) = 1.18646619961 -6.38899008148 absolute error = 0.0007043 relative error = 0.01084 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.17 Order of pole (three term test) = 53.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6069 2.23 h = 0.0001 0.004 y[1] (numeric) = 1.18171104807 -6.39638956488 y[1] (closed_form) = 1.18108033275 -6.3966893203 absolute error = 0.0006983 relative error = 0.01074 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 61.17 Order of pole (three term test) = 53.3 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.607 2.234 h = 0.003 0.006 y[1] (numeric) = 1.18566191649 -6.42270523437 y[1] (closed_form) = 1.18504891116 -6.42304177836 absolute error = 0.0006993 relative error = 0.01071 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 36.54 Order of pole (three term test) = 53.47 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.61 2.24 h = 0.0001 0.005 y[1] (numeric) = 1.17286818688 -6.46569603531 y[1] (closed_form) = 1.17218171164 -6.46605704607 absolute error = 0.0007756 relative error = 0.0118 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 16.44 Order of pole (three term test) = 53.75 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6101 2.245 h = 0.0001 0.003 y[1] (numeric) = 1.17790310073 -6.49898748095 y[1] (closed_form) = 1.17726125952 -6.49932466656 absolute error = 0.000725 relative error = 0.01098 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 13.37 Order of pole (three term test) = 53.97 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6102 2.248 h = 0.001 0.001 y[1] (numeric) = 1.18069805501 -6.51909236096 y[1] (closed_form) = 1.18005332584 -6.51940987713 absolute error = 0.0007187 relative error = 0.01085 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.56 Order of pole (three term test) = 54.1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6112 2.249 h = 0.001 0.003 y[1] (numeric) = 1.17517719317 -6.52692415352 y[1] (closed_form) = 1.17453434504 -6.5272315545 absolute error = 0.0007126 relative error = 0.01074 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 50.22 Order of pole (three term test) = 54.16 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6122 2.252 h = 0.0001 0.004 y[1] (numeric) = 1.17193714908 -6.54810424167 y[1] (closed_form) = 1.17129127887 -6.54843242497 absolute error = 0.0007245 relative error = 0.01089 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.59 Order of pole (three term test) = 54.3 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6123 2.256 h = 0.003 0.006 y[1] (numeric) = 1.17584314115 -6.57504019236 y[1] (closed_form) = 1.17521115454 -6.57537974991 absolute error = 0.0007174 relative error = 0.01074 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 38.18 Order of pole (three term test) = 54.48 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6153 2.262 h = 0.0001 0.005 y[1] (numeric) = 1.16254975993 -6.61890269051 y[1] (closed_form) = 1.16184249879 -6.61926684974 absolute error = 0.0007955 relative error = 0.01184 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 17.18 Order of pole (three term test) = 54.77 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6154 2.267 h = 0.0001 0.003 y[1] (numeric) = 1.16752331569 -6.65294602481 y[1] (closed_form) = 1.16686183576 -6.65328607368 absolute error = 0.0007438 relative error = 0.01101 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 13.97 Order of pole (three term test) = 55 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6155 2.27 h = 0.001 0.001 y[1] (numeric) = 1.17027584432 -6.67350380517 y[1] (closed_form) = 1.16961152317 -6.67382372254 absolute error = 0.0007373 relative error = 0.01088 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.03 Order of pole (three term test) = 55.14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6165 2.271 h = 0.001 0.003 y[1] (numeric) = 1.16459426867 -6.68147803978 y[1] (closed_form) = 1.16393192883 -6.68178762356 absolute error = 0.0007311 relative error = 0.01078 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 52.47 Order of pole (three term test) = 55.2 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6175 2.274 h = 0.0001 0.004 y[1] (numeric) = 1.16117458171 -6.70310345546 y[1] (closed_form) = 1.1605090329 -6.70343427509 absolute error = 0.0007432 relative error = 0.01092 % Correct digits = 4 memory used=1385.6MB, alloc=52.3MB, time=16.34 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.87 Order of pole (three term test) = 55.34 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6176 2.278 h = 0.003 0.006 y[1] (numeric) = 1.16502712395 -6.73064713641 y[1] (closed_form) = 1.1643757084 -6.73098966701 absolute error = 0.000736 relative error = 0.01077 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 39.9 Order of pole (three term test) = 55.53 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6206 2.284 h = 0.0001 0.005 y[1] (numeric) = 1.15121780084 -6.77539822943 y[1] (closed_form) = 1.15048926609 -6.77576549028 absolute error = 0.0008159 relative error = 0.01187 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 17.96 Order of pole (three term test) = 55.84 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6207 2.289 h = 0.0001 0.003 y[1] (numeric) = 1.15612432657 -6.81021013346 y[1] (closed_form) = 1.1554427467 -6.81055299839 absolute error = 0.000763 relative error = 0.01104 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 14.6 Order of pole (three term test) = 56.08 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6208 2.292 h = 0.001 0.001 y[1] (numeric) = 1.15883089005 -6.83123082886 y[1] (closed_form) = 1.15814651909 -6.83155309041 absolute error = 0.0007564 relative error = 0.01092 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.53 Order of pole (three term test) = 56.22 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6218 2.293 h = 0.001 0.003 y[1] (numeric) = 1.15298415048 -6.83934981612 y[1] (closed_form) = 1.15230186443 -6.83966152141 absolute error = 0.0007501 relative error = 0.01081 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 54.84 Order of pole (three term test) = 56.28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6228 2.296 h = 0.0001 0.004 y[1] (numeric) = 1.14937821813 -6.86142962131 y[1] (closed_form) = 1.14869252979 -6.86176302494 absolute error = 0.0007624 relative error = 0.01096 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.22 Order of pole (three term test) = 56.44 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6229 2.3 h = 0.003 0.006 y[1] (numeric) = 1.15317264332 -6.8895944888 y[1] (closed_form) = 1.15250134162 -6.88993994873 absolute error = 0.000755 relative error = 0.01081 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 41.69 Order of pole (three term test) = 56.63 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6259 2.306 h = 0.0001 0.005 y[1] (numeric) = 1.13883064559 -6.93525135915 y[1] (closed_form) = 1.13808033908 -6.93562167121 absolute error = 0.0008367 relative error = 0.0119 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 18.76 Order of pole (three term test) = 56.95 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.626 2.311 h = 0.0001 0.003 y[1] (numeric) = 1.14366425952 -6.97084884873 y[1] (closed_form) = 1.14296210867 -6.97119447915 absolute error = 0.0007826 relative error = 0.01108 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 15.26 Order of pole (three term test) = 57.2 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6261 2.314 h = 0.001 0.001 y[1] (numeric) = 1.14632118944 -6.9923426742 y[1] (closed_form) = 1.14561630117 -6.99266721931 absolute error = 0.000776 relative error = 0.01095 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.05 Order of pole (three term test) = 57.35 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6271 2.315 h = 0.001 0.003 y[1] (numeric) = 1.14030472681 -7.00060875217 y[1] (closed_form) = 1.13960203045 -7.00092251404 absolute error = 0.0007696 relative error = 0.01085 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 57.3 Order of pole (three term test) = 57.41 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6281 2.318 h = 0.0001 0.004 y[1] (numeric) = 1.13650575563 -7.0231521726 y[1] (closed_form) = 1.13579945705 -7.02348810438 absolute error = 0.0007821 relative error = 0.01099 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 32.62 Order of pole (three term test) = 57.57 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6282 2.322 h = 0.003 0.006 y[1] (numeric) = 1.14023722519 -7.05195195257 y[1] (closed_form) = 1.13954557037 -7.05230029483 absolute error = 0.0007744 relative error = 0.01084 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 43.57 Order of pole (three term test) = 57.78 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6312 2.328 h = 0.0001 0.005 y[1] (numeric) = 1.12534536601 -7.09853207144 y[1] (closed_form) = 1.12457277896 -7.09890538062 absolute error = 0.0008581 relative error = 0.01194 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 19.61 Order of pole (three term test) = 58.12 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6313 2.333 h = 0.0001 0.003 y[1] (numeric) = 1.13009996993 -7.13493250356 y[1] (closed_form) = 1.12937676704 -7.13528084536 absolute error = 0.0008027 relative error = 0.01111 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 15.95 Order of pole (three term test) = 58.38 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6314 2.336 h = 0.001 0.001 y[1] (numeric) = 1.1327034649 -7.15690987828 y[1] (closed_form) = 1.13197758192 -7.15723664258 absolute error = 0.000796 relative error = 0.01099 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.59 Order of pole (three term test) = 58.54 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6324 2.337 h = 0.0001 0.004 y[1] (numeric) = 1.12651260838 -7.16532541251 y[1] (closed_form) = 1.12578902782 -7.16564116218 absolute error = 0.0007895 relative error = 0.01088 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 75.77 Order of pole (three term test) = 58.6 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6325 2.341 h = 0.003 0.006 y[1] (numeric) = 1.13018989714 -7.19465491992 y[1] (closed_form) = 1.129484961 -7.1950122058 absolute error = 0.0007903 relative error = 0.01085 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 45.26 Order of pole (three term test) = 58.81 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6355 2.347 h = 0.0001 0.005 y[1] (numeric) = 1.11482190368 -7.24205079141 y[1] (closed_form) = 1.11403434332 -7.24243316066 absolute error = 0.0008755 relative error = 0.01195 % Correct digits = 4 memory used=1429.4MB, alloc=52.3MB, time=16.86 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 20.37 Order of pole (three term test) = 59.16 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6356 2.352 h = 0.0001 0.003 y[1] (numeric) = 1.11951329732 -7.27915757815 y[1] (closed_form) = 1.11877619782 -7.27951471908 absolute error = 0.0008191 relative error = 0.01112 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 16.56 Order of pole (three term test) = 59.43 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6357 2.355 h = 0.001 0.001 y[1] (numeric) = 1.12207358141 -7.30156037872 y[1] (closed_form) = 1.1213338482 -7.30189550938 absolute error = 0.0008121 relative error = 0.01099 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 13.08 Order of pole (three term test) = 59.6 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6367 2.356 h = 0.001 0.003 y[1] (numeric) = 1.11573060408 -7.31010863038 y[1] (closed_form) = 1.11499326849 -7.31043254227 absolute error = 0.0008053 relative error = 0.01089 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 62.2 Order of pole (three term test) = 59.66 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6377 2.359 h = 0.0001 0.004 y[1] (numeric) = 1.1115594658 -7.33354235671 y[1] (closed_form) = 1.11081814357 -7.33388934337 absolute error = 0.0008185 relative error = 0.01103 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 35.41 Order of pole (three term test) = 59.83 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6378 2.363 h = 0.003 0.006 y[1] (numeric) = 1.11516826402 -7.36356193212 y[1] (closed_form) = 1.11444207854 -7.36392200948 absolute error = 0.0008106 relative error = 0.01088 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 47.29 Order of pole (three term test) = 60.06 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6408 2.369 h = 0.0001 0.005 y[1] (numeric) = 1.09921739521 -7.41191456207 y[1] (closed_form) = 1.09840657779 -7.41229982384 absolute error = 0.0008977 relative error = 0.01198 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 21.28 Order of pole (three term test) = 60.42 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6409 2.374 h = 0.0001 0.003 y[1] (numeric) = 1.10381804853 -7.44985759805 y[1] (closed_form) = 1.1030589737 -7.45021734578 absolute error = 0.00084 relative error = 0.01115 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 17.31 Order of pole (three term test) = 60.7 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.641 2.377 h = 0.001 0.001 y[1] (numeric) = 1.10631758597 -7.47276394132 y[1] (closed_form) = 1.10555594184 -7.4731011669 absolute error = 0.000833 relative error = 0.01103 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 13.67 Order of pole (three term test) = 60.88 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.642 2.378 h = 0.001 0.003 y[1] (numeric) = 1.09979124587 -7.48146618296 y[1] (closed_form) = 1.09903211664 -7.48179194994 absolute error = 0.0008261 relative error = 0.01092 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 65 Order of pole (three term test) = 60.94 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.643 2.381 h = 0.0001 0.004 y[1] (numeric) = 1.0954066494 -7.50539093395 y[1] (closed_form) = 1.09464331368 -7.50574027433 absolute error = 0.0008395 relative error = 0.01107 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 37 Order of pole (three term test) = 61.12 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6431 2.385 h = 0.003 0.006 y[1] (numeric) = 1.09893782935 -7.53608628888 y[1] (closed_form) = 1.09818989853 -7.53644910067 absolute error = 0.0008313 relative error = 0.01091 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 49.42 Order of pole (three term test) = 61.36 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6461 2.391 h = 0.0001 0.005 y[1] (numeric) = 1.08238553616 -7.58541400234 y[1] (closed_form) = 1.08155092118 -7.58580209132 absolute error = 0.0009204 relative error = 0.01201 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.24 Order of pole (three term test) = 61.73 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6462 2.396 h = 0.0001 0.003 y[1] (numeric) = 1.08688869771 -7.62421165959 y[1] (closed_form) = 1.0861071366 -7.62457394926 absolute error = 0.0008614 relative error = 0.01119 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 18.09 Order of pole (three term test) = 62.03 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6463 2.399 h = 0.001 0.001 y[1] (numeric) = 1.08932328592 -7.64763257202 y[1] (closed_form) = 1.08853922401 -7.6479718168 absolute error = 0.0008543 relative error = 0.01106 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 14.28 Order of pole (three term test) = 62.21 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6473 2.4 h = 0.001 0.003 y[1] (numeric) = 1.08260857804 -7.65649124914 y[1] (closed_form) = 1.08182715212 -7.65681879084 absolute error = 0.0008473 relative error = 0.01096 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 67.92 Order of pole (three term test) = 62.28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6483 2.403 h = 0.0001 0.004 y[1] (numeric) = 1.07800294466 -7.68091691006 y[1] (closed_form) = 1.07721708498 -7.68126853354 absolute error = 0.0008609 relative error = 0.0111 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 38.67 Order of pole (three term test) = 62.47 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6484 2.407 h = 0.003 0.006 y[1] (numeric) = 1.08145095759 -7.71230286276 y[1] (closed_form) = 1.08068077484 -7.7126683481 absolute error = 0.0008525 relative error = 0.01095 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 51.64 Order of pole (three term test) = 62.72 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6514 2.413 h = 0.0001 0.005 y[1] (numeric) = 1.06427818935 -7.76262428907 y[1] (closed_form) = 1.06341922481 -7.76301513568 absolute error = 0.0009437 relative error = 0.01204 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.24 Order of pole (three term test) = 63.11 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1473.2MB, alloc=52.3MB, time=17.37 x[1] = 0.6515 2.418 h = 0.0001 0.003 y[1] (numeric) = 1.06867686393 -7.80229530656 y[1] (closed_form) = 1.06787229474 -7.8026600692 absolute error = 0.0008834 relative error = 0.01122 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 18.9 Order of pole (three term test) = 63.42 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6516 2.421 h = 0.001 0.001 y[1] (numeric) = 1.07104215072 -7.82624203406 y[1] (closed_form) = 1.07023515347 -7.82658321797 absolute error = 0.0008762 relative error = 0.01109 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 14.93 Order of pole (three term test) = 63.61 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6526 2.422 h = 0.001 0.003 y[1] (numeric) = 1.06413394766 -7.83525961954 y[1] (closed_form) = 1.06332971143 -7.83558885117 absolute error = 0.000869 relative error = 0.01099 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 70.98 Order of pole (three term test) = 63.68 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6536 2.425 h = 0.0001 0.004 y[1] (numeric) = 1.05929948106 -7.86019625248 y[1] (closed_form) = 1.05849057617 -7.86055008425 absolute error = 0.0008829 relative error = 0.01113 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 40.41 Order of pole (three term test) = 63.88 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6537 2.429 h = 0.003 0.006 y[1] (numeric) = 1.06265857924 -7.89228791666 y[1] (closed_form) = 1.06186562721 -7.8926560107 absolute error = 0.0008742 relative error = 0.01098 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 53.97 Order of pole (three term test) = 64.13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6567 2.435 h = 0.0001 0.005 y[1] (numeric) = 1.04484577064 -7.94362199351 y[1] (closed_form) = 1.04396189281 -7.94401552376 absolute error = 0.0009675 relative error = 0.01208 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.29 Order of pole (three term test) = 64.54 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6568 2.44 h = 0.0001 0.003 y[1] (numeric) = 1.04913271172 -7.98418548401 y[1] (closed_form) = 1.0483046016 -7.98455264641 absolute error = 0.0009059 relative error = 0.01125 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 19.75 Order of pole (three term test) = 64.87 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6569 2.443 h = 0.001 0.001 y[1] (numeric) = 1.05142419069 -8.00866949606 y[1] (closed_form) = 1.05059372964 -8.0090125346 absolute error = 0.0008985 relative error = 0.01112 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 15.6 Order of pole (three term test) = 65.07 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6579 2.444 h = 0.0001 0.004 y[1] (numeric) = 1.04431723977 -8.01784849012 y[1] (closed_form) = 1.04348966882 -8.01817932236 absolute error = 0.0008912 relative error = 0.01102 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 93.85 Order of pole (three term test) = 65.14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.658 2.448 h = 0.003 0.006 y[1] (numeric) = 1.0476003463 -8.05052887284 y[1] (closed_form) = 1.04679232857 -8.05090653969 absolute error = 0.0008919 relative error = 0.01099 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 56.06 Order of pole (three term test) = 65.41 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.661 2.454 h = 0.0001 0.005 y[1] (numeric) = 1.02923291764 -8.10275795988 y[1] (closed_form) = 1.02833209144 -8.10316114608 absolute error = 0.0009869 relative error = 0.01208 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.23 Order of pole (three term test) = 65.83 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6611 2.459 h = 0.0001 0.003 y[1] (numeric) = 1.03342862984 -8.14410671022 y[1] (closed_form) = 1.03258477453 -8.14448326815 absolute error = 0.0009241 relative error = 0.01126 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 20.52 Order of pole (three term test) = 66.17 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6612 2.462 h = 0.001 0.001 y[1] (numeric) = 1.03565943793 -8.16906351235 y[1] (closed_form) = 1.03481329503 -8.16941546694 absolute error = 0.0009164 relative error = 0.01113 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 16.2 Order of pole (three term test) = 66.37 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6622 2.463 h = 0.001 0.003 y[1] (numeric) = 1.02837907118 -8.17838591944 y[1] (closed_form) = 1.0275359297 -8.17872544358 absolute error = 0.0009089 relative error = 0.01103 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 77.04 Order of pole (three term test) = 66.45 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6632 2.466 h = 0.0001 0.004 y[1] (numeric) = 1.02310365733 -8.20430370562 y[1] (closed_form) = 1.02225539543 -8.20466882452 absolute error = 0.0009235 relative error = 0.01117 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 43.86 Order of pole (three term test) = 66.67 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6633 2.47 h = 0.003 0.006 y[1] (numeric) = 1.02629014651 -8.23775102556 y[1] (closed_form) = 1.02545836652 -8.23813117582 absolute error = 0.0009145 relative error = 0.01102 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 58.58 Order of pole (three term test) = 66.94 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6663 2.476 h = 0.0001 0.005 y[1] (numeric) = 1.00724508982 -8.29102908457 y[1] (closed_form) = 1.00631826824 -8.29143481144 absolute error = 0.001012 relative error = 0.01211 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.36 Order of pole (three term test) = 67.39 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6664 2.481 h = 0.0001 0.003 y[1] (numeric) = 1.0113151273 -8.33330698514 y[1] (closed_form) = 1.01044670831 -8.33368580148 absolute error = 0.0009474 relative error = 0.01129 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 21.44 Order of pole (three term test) = 67.74 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6665 2.484 h = 0.001 0.001 y[1] (numeric) = 1.01346345852 -8.35882308151 y[1] (closed_form) = 1.01259283753 -8.35917672762 absolute error = 0.0009397 relative error = 0.01116 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 16.93 Order of pole (three term test) = 67.95 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1517.0MB, alloc=52.3MB, time=17.88 x[1] = 0.6675 2.485 h = 0.001 0.003 y[1] (numeric) = 1.00597425679 -8.36831168812 y[1] (closed_form) = 1.0051067741 -8.36865264055 absolute error = 0.0009321 relative error = 0.01106 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 80.51 Order of pole (three term test) = 68.03 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6685 2.488 h = 0.0001 0.004 y[1] (numeric) = 1.00044657845 -8.39477033514 y[1] (closed_form) = 0.999573717413 -8.39513743025 absolute error = 0.0009469 relative error = 0.0112 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 45.83 Order of pole (three term test) = 68.26 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6686 2.492 h = 0.003 0.006 y[1] (numeric) = 1.00352674782 -8.428968362 y[1] (closed_form) = 1.00267065615 -8.42935091876 absolute error = 0.0009377 relative error = 0.01105 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 61.21 Order of pole (three term test) = 68.55 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6716 2.498 h = 0.0001 0.005 y[1] (numeric) = 0.983782954644 -8.48331524203 y[1] (closed_form) = 0.98282953896 -8.48372342215 absolute error = 0.001037 relative error = 0.01214 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.55 Order of pole (three term test) = 69.01 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6717 2.503 h = 0.0001 0.003 y[1] (numeric) = 0.987719313076 -8.5265425175 y[1] (closed_form) = 0.986825764577 -8.52692350617 absolute error = 0.0009714 relative error = 0.01132 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.4 Order of pole (three term test) = 69.38 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6718 2.506 h = 0.001 0.001 y[1] (numeric) = 0.989780196084 -8.55263004249 y[1] (closed_form) = 0.988884536047 -8.55298528207 absolute error = 0.0009635 relative error = 0.01119 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 17.69 Order of pole (three term test) = 69.6 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6728 2.507 h = 0.001 0.003 y[1] (numeric) = 0.982076531977 -8.56228742809 y[1] (closed_form) = 0.981184151483 -8.5626297057 absolute error = 0.0009558 relative error = 0.01109 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 84.13 Order of pole (three term test) = 69.69 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6738 2.51 h = 0.0001 0.004 y[1] (numeric) = 0.976287898322 -8.5892977099 y[1] (closed_form) = 0.975389873023 -8.58966668875 absolute error = 0.0009709 relative error = 0.01123 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 47.89 Order of pole (three term test) = 69.92 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6739 2.514 h = 0.003 0.006 y[1] (numeric) = 0.979255176617 -8.62426275369 y[1] (closed_form) = 0.978374212168 -8.62464763544 absolute error = 0.0009614 relative error = 0.01108 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 63.97 Order of pole (three term test) = 70.22 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6769 2.52 h = 0.0001 0.005 y[1] (numeric) = 0.958790970654 -8.6796986281 y[1] (closed_form) = 0.957810349427 -8.68010916896 absolute error = 0.001063 relative error = 0.01217 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.79 Order of pole (three term test) = 70.7 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.677 2.525 h = 0.0001 0.003 y[1] (numeric) = 0.96258536334 -8.72389590479 y[1] (closed_form) = 0.961666107535 -8.72427897485 absolute error = 0.0009959 relative error = 0.01135 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.41 Order of pole (three term test) = 71.09 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6771 2.528 h = 0.001 0.001 y[1] (numeric) = 0.964553653676 -8.75056723295 y[1] (closed_form) = 0.963632381832 -8.75092396282 absolute error = 0.0009879 relative error = 0.01122 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 18.49 Order of pole (three term test) = 71.33 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6781 2.529 h = 0.001 0.003 y[1] (numeric) = 0.956629762636 -8.76039600392 y[1] (closed_form) = 0.955711916107 -8.76073949839 absolute error = 0.00098 relative error = 0.01112 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 87.92 Order of pole (three term test) = 71.41 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6791 2.532 h = 0.0001 0.004 y[1] (numeric) = 0.950571235219 -8.78796888511 y[1] (closed_form) = 0.949647468624 -8.78833965025 absolute error = 0.0009954 relative error = 0.01126 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 50.05 Order of pole (three term test) = 71.65 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6792 2.536 h = 0.003 0.006 y[1] (numeric) = 0.953418820823 -8.82371757921 y[1] (closed_form) = 0.952512410633 -8.82410469974 absolute error = 0.0009856 relative error = 0.01111 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 66.85 Order of pole (three term test) = 71.97 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6822 2.542 h = 0.0001 0.005 y[1] (numeric) = 0.932211943348 -8.88026294988 y[1] (closed_form) = 0.93120349219 -8.88067575371 absolute error = 0.00109 relative error = 0.0122 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.08 Order of pole (three term test) = 72.47 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6823 2.547 h = 0.0001 0.003 y[1] (numeric) = 0.93585579265 -8.92545126326 y[1] (closed_form) = 0.934910239536 -8.92583631872 absolute error = 0.001021 relative error = 0.01138 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.46 Order of pole (three term test) = 72.88 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6824 2.55 h = 0.001 0.001 y[1] (numeric) = 0.937726167475 -8.95271901369 y[1] (closed_form) = 0.936778699046 -8.95307712538 absolute error = 0.001013 relative error = 0.01125 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 19.32 Order of pole (three term test) = 73.12 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6834 2.551 h = 0.0001 0.004 y[1] (numeric) = 0.929576144576 -8.9627218032 y[1] (closed_form) = 0.928632251882 -8.96306640083 absolute error = 0.001005 relative error = 0.01115 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 116.2 Order of pole (three term test) = 73.21 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1560.9MB, alloc=52.3MB, time=18.39 x[1] = 0.6835 2.555 h = 0.003 0.006 y[1] (numeric) = 0.932321888101 -8.99912415319 y[1] (closed_form) = 0.931398412691 -8.99952149681 absolute error = 0.001005 relative error = 0.01111 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 69.44 Order of pole (three term test) = 73.54 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6865 2.561 h = 0.0001 0.005 y[1] (numeric) = 0.910471018693 -9.05665043108 y[1] (closed_form) = 0.909443408167 -9.05707349842 absolute error = 0.001111 relative error = 0.01221 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.25 Order of pole (three term test) = 74.06 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6866 2.566 h = 0.0001 0.003 y[1] (numeric) = 0.913990341845 -9.1027108963 y[1] (closed_form) = 0.913026973435 -9.10310595914 absolute error = 0.001041 relative error = 0.01138 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.41 Order of pole (three term test) = 74.48 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6867 2.569 h = 0.001 0.001 y[1] (numeric) = 0.915779345497 -9.13050357831 y[1] (closed_form) = 0.914814145401 -9.13087116637 absolute error = 0.001033 relative error = 0.01126 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 20.07 Order of pole (three term test) = 74.74 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6877 2.57 h = 0.001 0.003 y[1] (numeric) = 0.907431953796 -9.14066107814 y[1] (closed_form) = 0.90647045933 -9.14101490614 absolute error = 0.001025 relative error = 0.01115 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 95.43 Order of pole (three term test) = 74.83 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6887 2.573 h = 0.0001 0.004 y[1] (numeric) = 0.900853570299 -9.16931415166 y[1] (closed_form) = 0.899885626353 -9.169696343 absolute error = 0.001041 relative error = 0.01129 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 54.33 Order of pole (three term test) = 75.09 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6888 2.577 h = 0.003 0.006 y[1] (numeric) = 0.903469332905 -9.20656806742 y[1] (closed_form) = 0.902519311972 -9.20696748331 absolute error = 0.001031 relative error = 0.01114 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 72.56 Order of pole (three term test) = 75.44 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6918 2.583 h = 0.0001 0.005 y[1] (numeric) = 0.880833025798 -9.26524316149 y[1] (closed_form) = 0.879776386801 -9.265668303 absolute error = 0.001139 relative error = 0.01224 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 32.65 Order of pole (three term test) = 75.98 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6919 2.588 h = 0.0001 0.003 y[1] (numeric) = 0.884185302283 -9.31233503129 y[1] (closed_form) = 0.883194504078 -9.31273189425 absolute error = 0.001067 relative error = 0.01141 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.55 Order of pole (three term test) = 76.42 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.692 2.591 h = 0.001 0.001 y[1] (numeric) = 0.885866150043 -9.34074835191 y[1] (closed_form) = 0.884873630942 -9.34111711254 absolute error = 0.001059 relative error = 0.01128 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 20.97 Order of pole (three term test) = 76.68 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.693 2.592 h = 0.001 0.003 y[1] (numeric) = 0.877281285909 -9.35108491509 y[1] (closed_form) = 0.876292631801 -9.35143962695 absolute error = 0.00105 relative error = 0.01118 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 99.72 Order of pole (three term test) = 76.78 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.694 2.595 h = 0.0001 0.004 y[1] (numeric) = 0.870406148854 -9.38033315108 y[1] (closed_form) = 0.869410743514 -9.38071682798 absolute error = 0.001067 relative error = 0.01132 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 56.77 Order of pole (three term test) = 77.05 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6941 2.599 h = 0.003 0.006 y[1] (numeric) = 0.872881637236 -9.41842023205 y[1] (closed_form) = 0.871904462409 -9.4188216196 absolute error = 0.001056 relative error = 0.01117 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 75.82 Order of pole (three term test) = 77.41 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6971 2.605 h = 0.0001 0.005 y[1] (numeric) = 0.84943588795 -9.47826561444 y[1] (closed_form) = 0.848349557503 -9.47869271636 absolute error = 0.001167 relative error = 0.01227 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 34.12 Order of pole (three term test) = 77.98 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6972 2.61 h = 0.0001 0.003 y[1] (numeric) = 0.85261166349 -9.52641114088 y[1] (closed_form) = 0.851592809124 -9.52680969266 absolute error = 0.001094 relative error = 0.01144 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.75 Order of pole (three term test) = 78.44 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6973 2.613 h = 0.001 0.001 y[1] (numeric) = 0.854178495205 -9.55545844639 y[1] (closed_form) = 0.8531580365 -9.55582825509 absolute error = 0.001085 relative error = 0.01131 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 21.91 Order of pole (three term test) = 78.72 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6983 2.614 h = 0.001 0.003 y[1] (numeric) = 0.845349833933 -9.56597678345 y[1] (closed_form) = 0.844333404623 -9.56633224916 absolute error = 0.001077 relative error = 0.01121 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 104.2 Order of pole (three term test) = 78.82 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6993 2.617 h = 0.0001 0.004 y[1] (numeric) = 0.838167987579 -9.59583191345 y[1] (closed_form) = 0.837144495455 -9.59621695753 absolute error = 0.001094 relative error = 0.01135 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 59.32 Order of pole (three term test) = 79.1 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6994 2.621 h = 0.003 0.006 y[1] (numeric) = 0.840495447788 -9.63477010173 y[1] (closed_form) = 0.839490497858 -9.63517335489 absolute error = 0.001083 relative error = 0.0112 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 79.23 Order of pole (three term test) = 79.48 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1604.7MB, alloc=52.3MB, time=18.90 x[1] = 0.7024 2.627 h = 0.0001 0.005 y[1] (numeric) = 0.816215609867 -9.69580758934 y[1] (closed_form) = 0.815098910997 -9.69623653189 absolute error = 0.001196 relative error = 0.01229 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 35.66 Order of pole (three term test) = 80.07 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7025 2.632 h = 0.0001 0.003 y[1] (numeric) = 0.819205103981 -9.74502946371 y[1] (closed_form) = 0.818157553902 -9.74542958726 absolute error = 0.001121 relative error = 0.01147 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29 Order of pole (three term test) = 80.55 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7026 2.635 h = 0.001 0.001 y[1] (numeric) = 0.820651859658 -9.77472436285 y[1] (closed_form) = 0.819602827772 -9.77509508909 absolute error = 0.001113 relative error = 0.01134 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.9 Order of pole (three term test) = 80.84 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7036 2.636 h = 0.001 0.003 y[1] (numeric) = 0.811572922998 -9.78542721034 y[1] (closed_form) = 0.81052809009 -9.78578329377 absolute error = 0.001104 relative error = 0.01124 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 108.9 Order of pole (three term test) = 80.94 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7046 2.639 h = 0.0001 0.004 y[1] (numeric) = 0.804074130234 -9.81590117106 y[1] (closed_form) = 0.803021912809 -9.81628745801 absolute error = 0.001121 relative error = 0.01138 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 61.99 Order of pole (three term test) = 81.24 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7047 2.643 h = 0.003 0.006 y[1] (numeric) = 0.806245542336 -9.85570876226 y[1] (closed_form) = 0.805212182994 -9.85611376934 absolute error = 0.00111 relative error = 0.01122 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 82.8 Order of pole (three term test) = 81.63 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7077 2.649 h = 0.0001 0.005 y[1] (numeric) = 0.781106311025 -9.91796052098 y[1] (closed_form) = 0.779958552483 -9.91839117813 absolute error = 0.001226 relative error = 0.01232 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 37.26 Order of pole (three term test) = 82.25 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7078 2.654 h = 0.0001 0.003 y[1] (numeric) = 0.783899407277 -9.96828188186 y[1] (closed_form) = 0.782822508485 -9.96868345413 absolute error = 0.001149 relative error = 0.01149 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.3 Order of pole (three term test) = 82.75 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7079 2.657 h = 0.001 0.001 y[1] (numeric) = 0.785219821149 -9.99863825063 y[1] (closed_form) = 0.78414156926 -9.99900975761 absolute error = 0.00114 relative error = 0.01137 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.93 Order of pole (three term test) = 83.05 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7089 2.658 h = 0.0001 0.004 y[1] (numeric) = 0.775883973713 -10.0095283709 y[1] (closed_form) = 0.774810095716 -10.0098849295 absolute error = 0.001132 relative error = 0.01127 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 144 Order of pole (three term test) = 83.16 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.709 2.662 h = 0.003 0.006 y[1] (numeric) = 0.777923019376 -10.0500610619 y[1] (closed_form) = 0.776870355004 -10.0504769596 absolute error = 0.001132 relative error = 0.01123 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 86.01 Order of pole (three term test) = 83.57 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.712 2.668 h = 0.0001 0.005 y[1] (numeric) = 0.752038102847 -10.113386704 y[1] (closed_form) = 0.750868710795 -10.1138282384 absolute error = 0.00125 relative error = 0.01233 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 38.71 Order of pole (three term test) = 84.21 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7121 2.673 h = 0.0001 0.003 y[1] (numeric) = 0.754667262138 -10.1646758524 y[1] (closed_form) = 0.753570230729 -10.1650880546 absolute error = 0.001172 relative error = 0.0115 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.48 Order of pole (three term test) = 84.73 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7122 2.676 h = 0.001 0.001 y[1] (numeric) = 0.755881855546 -10.1956145218 y[1] (closed_form) = 0.754783578758 -10.1959960709 absolute error = 0.001163 relative error = 0.01137 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.86 Order of pole (three term test) = 85.04 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7132 2.677 h = 0.001 0.003 y[1] (numeric) = 0.746321707799 -10.2066712425 y[1] (closed_form) = 0.745227956111 -10.2070375735 absolute error = 0.001153 relative error = 0.01127 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 118.2 Order of pole (three term test) = 85.15 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7142 2.68 h = 0.0001 0.004 y[1] (numeric) = 0.738212627346 -10.2383332652 y[1] (closed_form) = 0.73711087238 -10.2387309994 absolute error = 0.001171 relative error = 0.01141 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 67.29 Order of pole (three term test) = 85.48 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7143 2.684 h = 0.003 0.006 y[1] (numeric) = 0.740082268595 -10.279810642 y[1] (closed_form) = 0.738999977246 -10.280228078 absolute error = 0.00116 relative error = 0.01125 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 89.87 Order of pole (three term test) = 85.91 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7173 2.69 h = 0.0001 0.005 y[1] (numeric) = 0.713289336881 -10.3443930647 y[1] (closed_form) = 0.712087558243 -10.3448360705 absolute error = 0.001281 relative error = 0.01235 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 40.45 Order of pole (three term test) = 86.57 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7174 2.695 h = 0.0001 0.003 y[1] (numeric) = 0.715702633949 -10.3968261041 y[1] (closed_form) = 0.714575000378 -10.3972395177 absolute error = 0.001201 relative error = 0.01152 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 32.89 Order of pole (three term test) = 87.11 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1648.6MB, alloc=52.3MB, time=19.42 x[1] = 0.7175 2.698 h = 0.001 0.001 y[1] (numeric) = 0.716778830787 -10.4284528719 y[1] (closed_form) = 0.715650092454 -10.428834938 absolute error = 0.001192 relative error = 0.0114 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.97 Order of pole (three term test) = 87.44 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7185 2.699 h = 0.001 0.003 y[1] (numeric) = 0.706949028118 -10.4397021564 y[1] (closed_form) = 0.705825000048 -10.440068688 absolute error = 0.001182 relative error = 0.0113 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 123.5 Order of pole (three term test) = 87.56 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7195 2.702 h = 0.0001 0.004 y[1] (numeric) = 0.698492244677 -10.4720184523 y[1] (closed_form) = 0.697359861189 -10.4724170473 absolute error = 0.0012 relative error = 0.01144 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 70.32 Order of pole (three term test) = 87.9 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7196 2.706 h = 0.003 0.006 y[1] (numeric) = 0.700181586714 -10.5144196889 y[1] (closed_form) = 0.699068995064 -10.5148385347 absolute error = 0.001189 relative error = 0.01128 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 93.92 Order of pole (three term test) = 88.34 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7226 2.712 h = 0.0001 0.005 y[1] (numeric) = 0.672453362543 -10.5802820883 y[1] (closed_form) = 0.671218463553 -10.5807264205 absolute error = 0.001312 relative error = 0.01238 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 42.27 Order of pole (three term test) = 89.03 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7227 2.717 h = 0.0001 0.003 y[1] (numeric) = 0.674639669351 -10.633883487 y[1] (closed_form) = 0.67348074056 -10.6342979708 absolute error = 0.001231 relative error = 0.01155 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 34.37 Order of pole (three term test) = 89.6 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7228 2.72 h = 0.001 0.001 y[1] (numeric) = 0.67557058436 -10.6662130235 y[1] (closed_form) = 0.674410698229 -10.6665954508 absolute error = 0.001221 relative error = 0.01143 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.14 Order of pole (three term test) = 89.95 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7238 2.721 h = 0.001 0.003 y[1] (numeric) = 0.665464021604 -10.6776577082 y[1] (closed_form) = 0.66430903667 -10.6780242786 absolute error = 0.001212 relative error = 0.01133 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 129.1 Order of pole (three term test) = 90.07 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7248 2.724 h = 0.0001 0.004 y[1] (numeric) = 0.656648142803 -10.7106410387 y[1] (closed_form) = 0.655484439024 -10.7110403455 absolute error = 0.00123 relative error = 0.01146 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 73.48 Order of pole (three term test) = 90.42 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7249 2.728 h = 0.003 0.006 y[1] (numeric) = 0.658148067118 -10.7539858608 y[1] (closed_form) = 0.657004487699 -10.7544059811 absolute error = 0.001218 relative error = 0.01131 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 98.14 Order of pole (three term test) = 90.89 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7279 2.734 h = 0.0001 0.005 y[1] (numeric) = 0.629456548281 -10.8211517983 y[1] (closed_form) = 0.628187779765 -10.8215973049 absolute error = 0.001345 relative error = 0.01241 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 44.17 Order of pole (three term test) = 91.61 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.728 2.739 h = 0.0001 0.003 y[1] (numeric) = 0.63140436082 -10.8759465043 y[1] (closed_form) = 0.630213429232 -10.8763619103 absolute error = 0.001261 relative error = 0.01158 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 35.92 Order of pole (three term test) = 92.2 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7281 2.742 h = 0.001 0.001 y[1] (numeric) = 0.632182878605 -10.9089937663 y[1] (closed_form) = 0.630991144139 -10.9093763921 absolute error = 0.001252 relative error = 0.01145 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.36 Order of pole (three term test) = 92.56 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7291 2.743 h = 0.001 0.003 y[1] (numeric) = 0.621792278846 -10.9206367121 y[1] (closed_form) = 0.620605642445 -10.9210031525 absolute error = 0.001242 relative error = 0.01135 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 134.9 Order of pole (three term test) = 92.69 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7301 2.746 h = 0.0001 0.004 y[1] (numeric) = 0.612605593028 -10.954300059 y[1] (closed_form) = 0.611409862744 -10.9546999217 absolute error = 0.001261 relative error = 0.01149 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 76.78 Order of pole (three term test) = 93.06 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7302 2.75 h = 0.003 0.006 y[1] (numeric) = 0.613906674691 -10.9986085784 y[1] (closed_form) = 0.612731405609 -10.9990298313 absolute error = 0.001248 relative error = 0.01133 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 102.6 Order of pole (three term test) = 93.54 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7332 2.756 h = 0.0001 0.005 y[1] (numeric) = 0.584223115784 -11.067101985 y[1] (closed_form) = 0.58291971285 -11.0675485066 absolute error = 0.001378 relative error = 0.01243 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 46.15 Order of pole (three term test) = 94.3 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7333 2.761 h = 0.0001 0.003 y[1] (numeric) = 0.585920543008 -11.1231154347 y[1] (closed_form) = 0.584696886241 -11.123531608 absolute error = 0.001292 relative error = 0.0116 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 37.53 Order of pole (three term test) = 94.92 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7334 2.764 h = 0.001 0.001 y[1] (numeric) = 0.586539311307 -11.1568956708 y[1] (closed_form) = 0.585315013402 -11.157278325 absolute error = 0.001283 relative error = 0.01148 % Correct digits = 4 memory used=1692.4MB, alloc=52.3MB, time=19.93 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.64 Order of pole (three term test) = 95.3 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7344 2.765 h = 0.0001 0.004 y[1] (numeric) = 0.575857221893 -11.1687397628 y[1] (closed_form) = 0.574638225019 -11.1691058968 absolute error = 0.001273 relative error = 0.01138 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 178.3 Order of pole (three term test) = 95.43 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7345 2.769 h = 0.003 0.006 y[1] (numeric) = 0.576990018412 -11.2138519378 y[1] (closed_form) = 0.575792936344 -11.214284761 absolute error = 0.001273 relative error = 0.01134 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 106.5 Order of pole (three term test) = 95.93 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7375 2.775 h = 0.0001 0.005 y[1] (numeric) = 0.546445152402 -11.2835197317 y[1] (closed_form) = 0.545117348583 -11.2839777436 absolute error = 0.001405 relative error = 0.01243 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 47.94 Order of pole (three term test) = 96.71 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7376 2.78 h = 0.0001 0.003 y[1] (numeric) = 0.54793216963 -11.3406061664 y[1] (closed_form) = 0.546685787259 -11.3410335971 absolute error = 0.001318 relative error = 0.0116 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 38.99 Order of pole (three term test) = 97.36 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7377 2.783 h = 0.001 0.001 y[1] (numeric) = 0.54841634134 -11.3750317861 y[1] (closed_form) = 0.547169454017 -11.3754250472 absolute error = 0.001307 relative error = 0.01148 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.79 Order of pole (three term test) = 97.75 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7387 2.784 h = 0.001 0.003 y[1] (numeric) = 0.537479685545 -11.3870549426 y[1] (closed_form) = 0.536238274884 -11.3874313879 absolute error = 0.001297 relative error = 0.01138 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 146.4 Order of pole (three term test) = 97.88 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7397 2.787 h = 0.0001 0.004 y[1] (numeric) = 0.527579190739 -11.422023723 y[1] (closed_form) = 0.526327964843 -11.4224349069 absolute error = 0.001317 relative error = 0.01152 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 83.35 Order of pole (three term test) = 98.28 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7398 2.791 h = 0.003 0.006 y[1] (numeric) = 0.528496164333 -11.4681829859 y[1] (closed_form) = 0.527266045276 -11.4686166682 absolute error = 0.001304 relative error = 0.01136 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 111.3 Order of pole (three term test) = 98.81 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7428 2.797 h = 0.0001 0.005 y[1] (numeric) = 0.496904023053 -11.5392241417 y[1] (closed_form) = 0.495540116518 -11.539682861 absolute error = 0.001439 relative error = 0.01246 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 50.1 Order of pole (three term test) = 99.62 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7429 2.802 h = 0.0001 0.003 y[1] (numeric) = 0.498117776441 -11.5975781347 y[1] (closed_form) = 0.496837282235 -11.5980060337 absolute error = 0.00135 relative error = 0.01163 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 40.74 Order of pole (three term test) = 100.3 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.743 2.805 h = 0.001 0.001 y[1] (numeric) = 0.498428053681 -11.6327659914 y[1] (closed_form) = 0.497147230279 -11.6331589529 absolute error = 0.00134 relative error = 0.01151 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 32.17 Order of pole (three term test) = 100.7 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.744 2.806 h = 0.001 0.003 y[1] (numeric) = 0.487185593871 -11.6449958191 y[1] (closed_form) = 0.485910461826 -11.6453716182 absolute error = 0.001329 relative error = 0.01141 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 153 Order of pole (three term test) = 100.8 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.745 2.809 h = 0.0001 0.004 y[1] (numeric) = 0.476879112577 -11.6806831525 y[1] (closed_form) = 0.475593755354 -11.6810944143 absolute error = 0.00135 relative error = 0.01154 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 87.1 Order of pole (three term test) = 101.3 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7451 2.813 h = 0.003 0.006 y[1] (numeric) = 0.47756876308 -11.7278659674 y[1] (closed_form) = 0.476304862183 -11.728300347 absolute error = 0.001336 relative error = 0.01139 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 116.3 Order of pole (three term test) = 101.8 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7481 2.819 h = 0.0001 0.005 y[1] (numeric) = 0.444898374897 -11.8003055065 y[1] (closed_form) = 0.443497553957 -11.8007647515 absolute error = 0.001474 relative error = 0.01248 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 52.35 Order of pole (three term test) = 102.7 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7482 2.824 h = 0.0001 0.003 y[1] (numeric) = 0.445825808637 -11.8599539457 y[1] (closed_form) = 0.444510436126 -11.8603821368 absolute error = 0.001383 relative error = 0.01166 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 42.57 Order of pole (three term test) = 103.4 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7483 2.827 h = 0.001 0.001 y[1] (numeric) = 0.445954126437 -11.8959201548 y[1] (closed_form) = 0.444638608485 -11.8963126244 absolute error = 0.001373 relative error = 0.01153 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 33.62 Order of pole (three term test) = 103.8 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7493 2.828 h = 0.001 0.003 y[1] (numeric) = 0.434397884706 -11.9083596076 y[1] (closed_form) = 0.433088279404 -11.9087345617 absolute error = 0.001362 relative error = 0.01143 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 159.9 Order of pole (three term test) = 103.9 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1736.1MB, alloc=52.3MB, time=20.44 x[1] = 0.7503 2.831 h = 0.0001 0.004 y[1] (numeric) = 0.423672395047 -11.944779361 y[1] (closed_form) = 0.422352141689 -11.9451905158 absolute error = 0.001383 relative error = 0.01157 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 91.01 Order of pole (three term test) = 104.4 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7504 2.835 h = 0.003 0.006 y[1] (numeric) = 0.424124033017 -11.9930074004 y[1] (closed_form) = 0.422825589864 -11.9934423079 absolute error = 0.001369 relative error = 0.01141 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 121.6 Order of pole (three term test) = 105 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7534 2.841 h = 0.0001 0.005 y[1] (numeric) = 0.390343608571 -12.0668707304 y[1] (closed_form) = 0.388905044588 -12.0673303111 absolute error = 0.00151 relative error = 0.01251 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 54.71 Order of pole (three term test) = 105.8 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7535 2.846 h = 0.0001 0.003 y[1] (numeric) = 0.39097123443 -12.1278410273 y[1] (closed_form) = 0.389620201173 -12.1282693261 absolute error = 0.001417 relative error = 0.01168 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 44.49 Order of pole (three term test) = 106.6 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7536 2.849 h = 0.001 0.001 y[1] (numeric) = 0.390909263335 -12.1646020165 y[1] (closed_form) = 0.389558276657 -12.1649937935 absolute error = 0.001407 relative error = 0.01156 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 35.13 Order of pole (three term test) = 107 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7546 2.85 h = 0.001 0.003 y[1] (numeric) = 0.379031069828 -12.1772540706 y[1] (closed_form) = 0.377686223874 -12.1776279725 absolute error = 0.001396 relative error = 0.01146 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 167.1 Order of pole (three term test) = 107.2 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7556 2.853 h = 0.0001 0.004 y[1] (numeric) = 0.367873188077 -12.2144203473 y[1] (closed_form) = 0.366517257894 -12.2148312019 absolute error = 0.001417 relative error = 0.01159 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 95.11 Order of pole (three term test) = 107.6 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7557 2.857 h = 0.003 0.006 y[1] (numeric) = 0.368075771793 -12.2637157049 y[1] (closed_form) = 0.366742010097 -12.2641509628 absolute error = 0.001403 relative error = 0.01143 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 127 Order of pole (three term test) = 108.2 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7587 2.863 h = 0.0001 0.005 y[1] (numeric) = 0.333152683582 -12.3390286235 y[1] (closed_form) = 0.331675530629 -12.3394883412 absolute error = 0.001547 relative error = 0.01253 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 57.17 Order of pole (three term test) = 109.2 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7588 2.868 h = 0.0001 0.003 y[1] (numeric) = 0.333466568354 -12.4013487222 y[1] (closed_form) = 0.332079075629 -12.4017769362 absolute error = 0.001452 relative error = 0.0117 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 46.49 Order of pole (three term test) = 109.9 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7589 2.871 h = 0.001 0.001 y[1] (numeric) = 0.333205706797 -12.4389212371 y[1] (closed_form) = 0.331818461209 -12.4393121125 absolute error = 0.001441 relative error = 0.01158 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 36.71 Order of pole (three term test) = 110.4 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7599 2.872 h = 0.001 0.003 y[1] (numeric) = 0.320997195292 -12.4517888908 y[1] (closed_form) = 0.31961632547 -12.4521615246 absolute error = 0.00143 relative error = 0.01148 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 174.6 Order of pole (three term test) = 110.5 0 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = neg ( sin ( x ) ) - cos ( x ) ; Iterations = 754 Total Elapsed Time = 20 Seconds Expected Time Remaining = 0 Seconds Optimized Time Remaining = 0 Seconds Expected Total Time = 20 Seconds > quit memory used=1765.0MB, alloc=52.3MB, time=20.76