|\^/| Maple 2016 (X86 64 LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2016 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. #BEGIN OUTFILE1 # before write maple top matter # before write_ats library and user def block #BEGIN ATS LIBRARY BLOCK # Begin Function number 2 > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s\n",str); > fi;# end if 1; > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc # End Function number 2 # Begin Function number 3 > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s",str); > fi;# end if 1; > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc # End Function number 3 # Begin Function number 4 > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > print(label,str); > fi;# end if 1; > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc # End Function number 4 # Begin Function number 5 > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc # End Function number 5 # Begin Function number 6 > omniout_complex := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > if vallen = 4 then > printf("%-30s = %-20.4g %-20g %s \n",prelabel,Re(value), Im(value), postlabel); > else > printf("%-30s = %-20.12g %-20.12g %s \n",prelabel,Re(value),Im(value), postlabel); > fi;# end if 0; > fi;# end if -1; > end; omniout_complex := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-20.4g %-20g %s \n", prelabel, Re(value), Im(value), postlabel) else printf("%-30s = %-20.12g %-20.12g %s \n", prelabel, Re(value), Im(value), postlabel) end if end if end proc # End Function number 6 # Begin Function number 7 > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number -1 > if vallen = 5 then # if number 0 > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi;# end if 0; > fi;# end if -1; > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc # End Function number 7 # Begin Function number 8 > logitem_time := proc(fd,secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > fprintf(fd,""); > if (secs_in >= 0) then # if number -1 > years_int := int_trunc(secs_in / glob_sec_in_year); > sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year); > days_int := int_trunc(sec_temp / glob_sec_in_day) ; > sec_temp := sec_temp mod int_trunc(glob_sec_in_day) ; > hours_int := int_trunc(sec_temp / glob_sec_in_hour); > sec_temp := sec_temp mod int_trunc(glob_sec_in_hour); > minutes_int := int_trunc(sec_temp / glob_sec_in_minute); > sec_int := sec_temp mod int_trunc(glob_sec_in_minute); > if (years_int > 0) then # if number 0 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 1 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 2 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 3 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 3 > else > fprintf(fd," 0.0 Seconds"); > fi;# end if 2 > fprintf(fd,"\n"); > end; logitem_time := proc(fd, secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; fprintf(fd, ""); if 0 <= secs_in then years_int := int_trunc(secs_in/glob_sec_in_year); sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year); days_int := int_trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod int_trunc(glob_sec_in_day); hours_int := int_trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod int_trunc(glob_sec_in_hour); minutes_int := int_trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod int_trunc(glob_sec_in_minute); if 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, " 0.0 Seconds") end if; fprintf(fd, "\n") end proc # End Function number 8 # Begin Function number 9 > omniout_timestr := proc(secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > if (secs_in >= 0) then # if number 2 > years_int := int_trunc(secs_in / glob_sec_in_year); > sec_temp := (int_trunc(secs_in) mod int_trunc(glob_sec_in_year)); > days_int := int_trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod int_trunc(glob_sec_in_day)) ; > hours_int := int_trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod int_trunc(glob_sec_in_hour)); > minutes_int := int_trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod int_trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 3 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 4 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 5 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 6 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 6 > else > printf(" 0.0 Seconds\n"); > fi;# end if 5 > end; omniout_timestr := proc(secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; if 0 <= secs_in then years_int := int_trunc(secs_in/glob_sec_in_year); sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year); days_int := int_trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod int_trunc(glob_sec_in_day); hours_int := int_trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod int_trunc(glob_sec_in_hour); minutes_int := int_trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod int_trunc(glob_sec_in_minute); if 0 < years_int then printf( " = %d Years %d Days %d Hours %d Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" 0.0 Seconds\n") end if end proc # End Function number 9 # Begin Function number 10 > zero_ats_ar := proc(arr_a) > global ATS_MAX_TERMS; > local iii; > iii := 1; > while (iii <= ATS_MAX_TERMS) do # do number 1 > arr_a [iii] := glob__0; > iii := iii + 1; > od;# end do number 1 > end; zero_ats_ar := proc(arr_a) local iii; global ATS_MAX_TERMS; iii := 1; while iii <= ATS_MAX_TERMS do arr_a[iii] := glob__0; iii := iii + 1 end do end proc # End Function number 10 # Begin Function number 11 > ats := proc(mmm_ats,arr_a,arr_b,jjj_ats) > global ATS_MAX_TERMS; > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := glob__0; > if (jjj_ats <= mmm_ats) then # if number 5 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > if ((lll_ats <= ATS_MAX_TERMS and (iii_ats <= ATS_MAX_TERMS) )) then # if number 6 > ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]); > fi;# end if 6; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 5; > ret_ats; > end; ats := proc(mmm_ats, arr_a, arr_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; global ATS_MAX_TERMS; ret_ats := glob__0; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; if lll_ats <= ATS_MAX_TERMS and iii_ats <= ATS_MAX_TERMS then ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]) end if; iii_ats := iii_ats + 1 end do end if; ret_ats end proc # End Function number 11 # Begin Function number 12 > att := proc(mmm_att,arr_aa,arr_bb,jjj_att) > global ATS_MAX_TERMS; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := glob__0; > if (jjj_att < mmm_att) then # if number 5 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while ((iii_att < mmm_att) and (iii_att <= ATS_MAX_TERMS) ) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if ((lll_att <= ATS_MAX_TERMS and (iii_att <= ATS_MAX_TERMS) )) then # if number 6 > ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att); > fi;# end if 6; > iii_att := iii_att + 1; > od;# end do number 1; > ret_att := ret_att / c(mmm_att) ; > fi;# end if 5; > ret_att; > end; att := proc(mmm_att, arr_aa, arr_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global ATS_MAX_TERMS; ret_att := glob__0; if jjj_att < mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att < mmm_att and iii_att <= ATS_MAX_TERMS do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= ATS_MAX_TERMS and iii_att <= ATS_MAX_TERMS then ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])*c(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/c(mmm_att) end if; ret_att end proc # End Function number 12 # Begin Function number 13 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc # End Function number 13 # Begin Function number 14 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc # End Function number 14 # Begin Function number 15 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc # End Function number 15 # Begin Function number 16 > logitem_good_digits := proc(file,rel_error) > global glob_small_float,glob_prec; > local good_digits; > fprintf(file,""); > fprintf(file,"%d",glob_min_good_digits); > fprintf(file,""); > end; logitem_good_digits := proc(file, rel_error) local good_digits; global glob_small_float, glob_prec; fprintf(file, ""); fprintf(file, "%d", glob_min_good_digits); fprintf(file, "") end proc # End Function number 16 # Begin Function number 17 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc # End Function number 17 # Begin Function number 18 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc # End Function number 18 # Begin Function number 19 > logitem_complex := proc(file,x) > fprintf(file,""); > fprintf(file,"%g + %g I",Re(x),Im(x)); > fprintf(file,""); > end; logitem_complex := proc(file, x) fprintf(file, ""); fprintf(file, "%g + %g I", Re(x), Im(x)); fprintf(file, "") end proc # End Function number 19 # Begin Function number 20 > logitem_h_reason := proc(file) > global glob_h_reason; > fprintf(file,""); > if (glob_h_reason = 1) then # if number 5 > fprintf(file,"Max H"); > elif > (glob_h_reason = 2) then # if number 6 > fprintf(file,"Display Interval"); > elif > (glob_h_reason = 3) then # if number 7 > fprintf(file,"Optimal"); > elif > (glob_h_reason = 4) then # if number 8 > fprintf(file,"Pole Accuracy"); > elif > (glob_h_reason = 5) then # if number 9 > fprintf(file,"Min H (Pole)"); > elif > (glob_h_reason = 6) then # if number 10 > fprintf(file,"Pole"); > elif > (glob_h_reason = 7) then # if number 11 > fprintf(file,"Opt Iter"); > else > fprintf(file,"Impossible"); > fi;# end if 11 > fprintf(file,""); > end; logitem_h_reason := proc(file) global glob_h_reason; fprintf(file, ""); if glob_h_reason = 1 then fprintf(file, "Max H") elif glob_h_reason = 2 then fprintf(file, "Display Interval") elif glob_h_reason = 3 then fprintf(file, "Optimal") elif glob_h_reason = 4 then fprintf(file, "Pole Accuracy") elif glob_h_reason = 5 then fprintf(file, "Min H (Pole)") elif glob_h_reason = 6 then fprintf(file, "Pole") elif glob_h_reason = 7 then fprintf(file, "Opt Iter") else fprintf(file, "Impossible") end if; fprintf(file, "") end proc # End Function number 20 # Begin Function number 21 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc # End Function number 21 # Begin Function number 22 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, "\n") end proc # End Function number 22 # Begin Function number 23 > chk_data := proc() > global glob_max_iter,ALWAYS, ATS_MAX_TERMS; > local errflag; > errflag := false; > if (glob_max_iter < 2) then # if number 11 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 11; > if (errflag) then # if number 11 > quit; > fi;# end if 11 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, ATS_MAX_TERMS; errflag := false; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc # End Function number 23 # Begin Function number 24 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := c(clock_sec2); > sub1 := c(t_end2-t_start2); > sub2 := c(t2-t_start2); > if (sub1 = glob__0) then # if number 11 > sec_left := glob__0; > else > if (sub2 > glob__0) then # if number 12 > rrr := (sub1/sub2); > sec_left := rrr * c(ms2) - c(ms2); > else > sec_left := glob__0; > fi;# end if 12 > fi;# end if 11; > sec_left; > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := c(clock_sec2); sub1 := c(t_end2 - t_start2); sub2 := c(t2 - t_start2); if sub1 = glob__0 then sec_left := glob__0 else if glob__0 < sub2 then rrr := sub1/sub2; sec_left := rrr*c(ms2) - c(ms2) else sec_left := glob__0 end if end if; sec_left end proc # End Function number 24 # Begin Function number 25 > comp_percent := proc(t_end2,t_start2, t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub2 > glob_small_float) then # if number 11 > rrr := (glob__100*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 11; > rrr; > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < sub2 then rrr := glob__100*sub2/sub1 else rrr := 0. end if; rrr end proc # End Function number 25 # Begin Function number 26 > comp_rad_from_ratio := proc(term1,term2,last_no) > #TOP TWO TERM RADIUS ANALYSIS > global glob_h,glob_larger_float; > local ret; > if (float_abs(term2) > glob__0) then # if number 11 > ret := float_abs(term1 * glob_h / term2); > else > ret := glob_larger_float; > fi;# end if 11; > ret; > #BOTTOM TWO TERM RADIUS ANALYSIS > end; comp_rad_from_ratio := proc(term1, term2, last_no) local ret; global glob_h, glob_larger_float; if glob__0 < float_abs(term2) then ret := float_abs(term1*glob_h/term2) else ret := glob_larger_float end if; ret end proc # End Function number 26 # Begin Function number 27 > comp_ord_from_ratio := proc(term1,term2,last_no) > #TOP TWO TERM ORDER ANALYSIS > global glob_h,glob_larger_float; > local ret; > if (float_abs(term2) > glob__0) then # if number 11 > ret := glob__1 + float_abs(term2) * c(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(c(last_no)); > else > ret := glob_larger_float; > fi;# end if 11; > ret; > #BOTTOM TWO TERM ORDER ANALYSIS > end; comp_ord_from_ratio := proc(term1, term2, last_no) local ret; global glob_h, glob_larger_float; if glob__0 < float_abs(term2) then ret := glob__1 + float_abs(term2)* c(last_no)*ln(float_abs(term1*glob_h/term2))/ln(c(last_no)) else ret := glob_larger_float end if; ret end proc # End Function number 27 # Begin Function number 28 > c := proc(in_val) > #To Force Conversion when needed > local ret; > ret := evalc(in_val); > ret; > #End Conversion > end; c := proc(in_val) local ret; ret := evalc(in_val); ret end proc # End Function number 28 # Begin Function number 29 > comp_rad_from_three_terms := proc(term1,term2,term3,last_no) > #TOP THREE TERM RADIUS ANALYSIS > global glob_h,glob_larger_float; > local ret,temp; > temp := float_abs(term2*term2*c(last_no)+glob__m2*term2*term2-term1*term3*c(last_no)+term1*term3); > if (float_abs(temp) > glob__0) then # if number 11 > ret := float_abs((term2*glob_h*term1)/(temp)); > else > ret := glob_larger_float; > fi;# end if 11; > ret; > #BOTTOM THREE TERM RADIUS ANALYSIS > end; comp_rad_from_three_terms := proc(term1, term2, term3, last_no) local ret, temp; global glob_h, glob_larger_float; temp := float_abs(term2*term2*c(last_no) + glob__m2*term2*term2 - term1*term3*c(last_no) + term1*term3); if glob__0 < float_abs(temp) then ret := float_abs(term2*glob_h*term1/temp) else ret := glob_larger_float end if; ret end proc # End Function number 29 # Begin Function number 30 > comp_ord_from_three_terms := proc(term1,term2,term3,last_no) > #TOP THREE TERM ORDER ANALYSIS > local ret; > ret := float_abs((glob__4*term1*term3*c(last_no)-glob__3*term1*term3-glob__4*term2*term2*c(last_no)+glob__4*term2*term2+term2*term2*c(last_no*last_no)-term1*term3*c(last_no*last_no))/(term2*term2*c(last_no)-glob__2*term2*term2-term1*term3*c(last_no)+term1*term3)); > ret; > #TOP THREE TERM ORDER ANALYSIS > end; comp_ord_from_three_terms := proc(term1, term2, term3, last_no) local ret; ret := float_abs((glob__4*term1*term3*c(last_no) - glob__3*term1*term3 - glob__4*term2*term2*c(last_no) + glob__4*term2*term2 + term2*term2*c(last_no*last_no) - term1*term3*c(last_no*last_no)) /(term2*term2*c(last_no) - glob__2*term2*term2 - term1*term3*c(last_no) + term1*term3)); ret end proc # End Function number 30 # Begin Function number 31 > comp_rad_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no) > #TOP SIX TERM RADIUS ANALYSIS > global glob_h,glob_larger_float,glob_six_term_ord_save; > local ret,rm0,rm1,rm2,rm3,rm4,nr1,nr2,dr1,dr2,ds2,rad_c,ord_no,ds1,rcs; > if ((term5 <> glob__0) and (term4 <> glob__0) and (term3 <> glob__0) and (term2 <> glob__0) and (term1 <> glob__0)) then # if number 11 > rm0 := term6/term5; > rm1 := term5/term4; > rm2 := term4/term3; > rm3 := term3/term2; > rm4 := term2/term1; > nr1 := c(last_no-1)*rm0 - glob__2*c(last_no-2)*rm1 + c(last_no-3)*rm2; > nr2 := c(last_no-2)*rm1 - glob__2*c(last_no-3)*rm2 + c(last_no-4)*rm3; > dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3; > dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4; > ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3; > ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4; > if ((float_abs(nr1 * dr2 - nr2 * dr1) = glob__0) or (float_abs(dr1) = glob__0)) then # if number 12 > rad_c := glob_larger_float; > ord_no := glob_larger_float; > else > if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0) then # if number 13 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) -c(last_no)/glob__2; > if (float_abs(rcs) <> glob__0) then # if number 14 > if (rcs > glob__0) then # if number 15 > rad_c := float_abs( sqrt(rcs) * float_abs(glob_h)); > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 15 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 14 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 13 > fi;# end if 12 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 11; > glob_six_term_ord_save := ord_no; > rad_c; > #BOTTOM SIX TERM RADIUS ANALYSIS > end; comp_rad_from_six_terms := proc( term1, term2, term3, term4, term5, term6, last_no) local ret, rm0, rm1, rm2, rm3, rm4, nr1, nr2, dr1, dr2, ds2, rad_c, ord_no, ds1, rcs; global glob_h, glob_larger_float, glob_six_term_ord_save; if term5 <> glob__0 and term4 <> glob__0 and term3 <> glob__0 and term2 <> glob__0 and term1 <> glob__0 then rm0 := term6/term5; rm1 := term5/term4; rm2 := term4/term3; rm3 := term3/term2; rm4 := term2/term1; nr1 := c(last_no - 1)*rm0 - glob__2*c(last_no - 2)*rm1 + c(last_no - 3)*rm2; nr2 := c(last_no - 2)*rm1 - glob__2*c(last_no - 3)*rm2 + c(last_no - 4)*rm3; dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3; dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4; ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3; ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4; if float_abs(nr1*dr2 - nr2*dr1) = glob__0 or float_abs(dr1) = glob__0 then rad_c := glob_larger_float; ord_no := glob_larger_float else if glob__0 < float_abs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) - c(last_no)/glob__2; if float_abs(rcs) <> glob__0 then if glob__0 < rcs then rad_c := float_abs(sqrt(rcs)*float_abs(glob_h)) else rad_c := glob_larger_float; ord_no := glob_larger_float end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if; glob_six_term_ord_save := ord_no; rad_c end proc # End Function number 31 # Begin Function number 32 > comp_ord_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no) > global glob_six_term_ord_save; > #TOP SIX TERM ORDER ANALYSIS > #TOP SAVED FROM SIX TERM RADIUS ANALYSIS > glob_six_term_ord_save; > #BOTTOM SIX TERM ORDER ANALYSIS > end; comp_ord_from_six_terms := proc( term1, term2, term3, term4, term5, term6, last_no) global glob_six_term_ord_save; glob_six_term_ord_save end proc # End Function number 32 # Begin Function number 33 > factorial_2 := proc(nnn) > ret := nnn!; > ret;; > end; Warning, `ret` is implicitly declared local to procedure `factorial_2` factorial_2 := proc(nnn) local ret; ret := nnn!; ret end proc # End Function number 33 # Begin Function number 34 > factorial_1 := proc(nnn) > global ATS_MAX_TERMS,array_fact_1; > local ret; > if (nnn <= ATS_MAX_TERMS) then # if number 11 > if (array_fact_1[nnn] = 0) then # if number 12 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 12; > else > ret := factorial_2(nnn); > fi;# end if 11; > ret; > end; factorial_1 := proc(nnn) local ret; global ATS_MAX_TERMS, array_fact_1; if nnn <= ATS_MAX_TERMS then if array_fact_1[nnn] = 0 then ret := factorial_2(nnn); array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := factorial_2(nnn) end if; ret end proc # End Function number 34 # Begin Function number 35 > factorial_3 := proc(mmm,nnn) > global ATS_MAX_TERMS,array_fact_2; > local ret; > if ((nnn <= ATS_MAX_TERMS) and (mmm <= ATS_MAX_TERMS)) then # if number 11 > if (array_fact_2[mmm,nnn] = 0) then # if number 12 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 12; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 11; > ret; > end; factorial_3 := proc(mmm, nnn) local ret; global ATS_MAX_TERMS, array_fact_2; if nnn <= ATS_MAX_TERMS and mmm <= ATS_MAX_TERMS then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := factorial_2(mmm)/factorial_2(nnn) end if; ret end proc # End Function number 35 # Begin Function number 36 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc # End Function number 36 # Begin Function number 37 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc # End Function number 37 # Begin Function number 38 > float_abs := proc(x) > abs(x); > end; float_abs := proc(x) abs(x) end proc # End Function number 38 # Begin Function number 39 > expt := proc(x,y) > x^y; > end; expt := proc(x, y) x^y end proc # End Function number 39 # Begin Function number 40 > neg := proc(x) > -x; > end; neg := proc(x) -x end proc # End Function number 40 # Begin Function number 41 > int_trunc := proc(x) > trunc(x); > end; int_trunc := proc(x) trunc(x) end proc # End Function number 41 # Begin Function number 42 > estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer) > local desired_abs_gbl_error,range,estimated_steps,step_error; > global glob_desired_digits_correct,ALWAYS,ATS_MAX_TERMS; > omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,""); > desired_abs_gbl_error := expt(glob__10,c( -glob_desired_digits_correct)) * c(float_abs(c(estimated_answer))); > omniout_float(ALWAYS,"estimated_h",32,estimated_h,32,""); > omniout_float(ALWAYS,"estimated_answer",32,estimated_answer,32,""); > omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,""); > range := (x_end - x_start); > omniout_float(ALWAYS,"range",32,range,32,""); > estimated_steps := range / estimated_h; > omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,""); > step_error := (c(float_abs(desired_abs_gbl_error) /sqrt(c( estimated_steps))/c(ATS_MAX_TERMS))); > omniout_float(ALWAYS,"step_error",32,step_error,32,""); > (step_error);; > end; estimated_needed_step_error := proc( x_start, x_end, estimated_h, estimated_answer) local desired_abs_gbl_error, range, estimated_steps, step_error; global glob_desired_digits_correct, ALWAYS, ATS_MAX_TERMS; omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""); desired_abs_gbl_error := expt(glob__10, c(-glob_desired_digits_correct))* c(float_abs(c(estimated_answer))); omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, ""); omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, "") ; omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""); range := x_end - x_start; omniout_float(ALWAYS, "range", 32, range, 32, ""); estimated_steps := range/estimated_h; omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, ""); step_error := c(float_abs(desired_abs_gbl_error)/( sqrt(c(estimated_steps))*c(ATS_MAX_TERMS))); omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""); step_error end proc # End Function number 42 #END ATS LIBRARY BLOCK #BEGIN USER FUNCTION BLOCK #BEGIN BLOCK 3 #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > return(c(1.0)/c(x)/c(x)); > end; exact_soln_y := proc(x) return c(1.0)/(c(x)*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, > array_const_2D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_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_const_2D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_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, > array_const_2D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_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_const_2D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_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, > array_const_2D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_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_const_2D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_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, > array_const_2D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_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_const_2D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_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, > array_const_2D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_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_const_2D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_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, > array_const_2D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_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_const_2D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_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, > array_const_2D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_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_const_2D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_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, > array_const_2D0, #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > # before write maple main top matter > # before generate constants assign > # before generate globals assign > #END OUTFILE1 > #BEGIN OUTFILE2 > #END OUTFILE2 > #BEGIN ATOMHDR1 > #emit pre neg ID_CONST $eq_no = 1 > array_tmp1[1] := neg(array_const_2D0[1]); > #emit pre div CONST - LINEAR $eq_no = 1 i = 1 > array_tmp2[1] := array_tmp1[1] / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 1 > array_tmp3[1] := array_tmp2[1] / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 1 > array_tmp4[1] := array_tmp3[1] / array_x[1]; > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp5[1] := array_const_0D0[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 div CONST - LINEAR $eq_no = 1 i = 2 > array_tmp2[2] := neg(array_tmp2[1])* array_x[2] / array_x[1]; > #emit pre div CONST - LINEAR $eq_no = 1 i = 3 > #emit pre div CONST - LINEAR $eq_no = 1 i = 4 > #emit pre div CONST - LINEAR $eq_no = 1 i = 5 > #emit pre div FULL - LINEAR $eq_no = 1 i = 2 > array_tmp3[2] := (array_tmp2[2] - array_tmp3[1] * array_x[2]) / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 2 > array_tmp4[2] := (array_tmp3[2] - array_tmp4[1] * array_x[2]) / array_x[1]; > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp5[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 > array_tmp2[3] := neg(array_tmp2[2])* array_x[2] / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 3 > array_tmp3[3] := (array_tmp2[3] - array_tmp3[2] * array_x[2]) / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 3 > array_tmp4[3] := (array_tmp3[3] - array_tmp4[2] * array_x[2]) / array_x[1]; > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp5[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 > array_tmp2[4] := neg(array_tmp2[3])* array_x[2] / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 4 > array_tmp3[4] := (array_tmp2[4] - array_tmp3[3] * array_x[2]) / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 4 > array_tmp4[4] := (array_tmp3[4] - array_tmp4[3] * array_x[2]) / array_x[1]; > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp5[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 > array_tmp2[5] := neg(array_tmp2[4])* array_x[2] / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 5 > array_tmp3[5] := (array_tmp2[5] - array_tmp3[4] * array_x[2]) / array_x[1]; > #emit pre div FULL - LINEAR $eq_no = 1 i = 5 > array_tmp4[5] := (array_tmp3[5] - array_tmp4[4] * array_x[2]) / array_x[1]; > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp5[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 div CONST LINEAR (NOP) $eq_no = 1 i = 1 > array_tmp2[kkk] := array_tmp1[1] * array_x[kkk]; > #emit div FULL LINEAR $eq_no = 1 i = 1 > array_tmp3[kkk] := neg(ats(kkk,array_x,array_tmp3,2)) / array_x[1]; > #emit div FULL LINEAR $eq_no = 1 i = 1 > array_tmp4[kkk] := neg(ats(kkk,array_x,array_tmp4,2)) / array_x[1]; > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp5[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_const_2D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; array_tmp1[1] := neg(array_const_2D0[1]); array_tmp2[1] := array_tmp1[1]/array_x[1]; array_tmp3[1] := array_tmp2[1]/array_x[1]; array_tmp4[1] := array_tmp3[1]/array_x[1]; array_tmp5[1] := array_const_0D0[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_tmp2[2] := neg(array_tmp2[1])*array_x[2]/array_x[1]; array_tmp3[2] := (-array_x[2]*array_tmp3[1] + array_tmp2[2])/array_x[1] ; array_tmp4[2] := (-array_x[2]*array_tmp4[1] + array_tmp3[2])/array_x[1] ; array_tmp5[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_tmp2[3] := neg(array_tmp2[2])*array_x[2]/array_x[1]; array_tmp3[3] := (-array_x[2]*array_tmp3[2] + array_tmp2[3])/array_x[1] ; array_tmp4[3] := (-array_x[2]*array_tmp4[2] + array_tmp3[3])/array_x[1] ; array_tmp5[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_tmp2[4] := neg(array_tmp2[3])*array_x[2]/array_x[1]; array_tmp3[4] := (-array_x[2]*array_tmp3[3] + array_tmp2[4])/array_x[1] ; array_tmp4[4] := (-array_x[2]*array_tmp4[3] + array_tmp3[4])/array_x[1] ; array_tmp5[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_tmp2[5] := neg(array_tmp2[4])*array_x[2]/array_x[1]; array_tmp3[5] := (-array_x[2]*array_tmp3[4] + array_tmp2[5])/array_x[1] ; array_tmp4[5] := (-array_x[2]*array_tmp4[4] + array_tmp3[5])/array_x[1] ; array_tmp5[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_tmp2[kkk] := array_tmp1[1]*array_x[kkk]; array_tmp3[kkk] := neg(ats(kkk, array_x, array_tmp3, 2))/array_x[1] ; array_tmp4[kkk] := neg(ats(kkk, array_x, array_tmp4, 2))/array_x[1] ; array_tmp5[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, > array_const_2D0, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > ATS_MAX_TERMS := 20; > # before first input block > #BEGIN FIRST INPUT BLOCK > #BEGIN BLOCK 1 > #BEGIN FIRST INPUT BLOCK > Digits:=16; > max_terms:=20; > #END BLOCK 1 > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > # before generate arrays > array_y_init:= Array(0..(20),[]); > array_norms:= Array(0..(20),[]); > array_fact_1:= Array(0..(20),[]); > array_1st_rel_error:= Array(0..(2),[]); > array_last_rel_error:= Array(0..(2),[]); > array_est_rel_error:= Array(0..(2),[]); > array_max_est_error:= Array(0..(2),[]); > array_type_pole:= Array(0..(2),[]); > array_type_real_pole:= Array(0..(2),[]); > array_type_complex_pole:= Array(0..(2),[]); > array_est_digits:= Array(0..(2),[]); > array_y:= Array(0..(20),[]); > array_x:= Array(0..(20),[]); > array_tmp0:= Array(0..(20),[]); > array_tmp1:= Array(0..(20),[]); > array_tmp2:= Array(0..(20),[]); > array_tmp3:= Array(0..(20),[]); > array_tmp4:= Array(0..(20),[]); > array_tmp5:= Array(0..(20),[]); > array_m1:= Array(0..(20),[]); > array_y_higher := Array(0..(2) ,(0..20+ 1),[]); > array_y_higher_work := Array(0..(2) ,(0..20+ 1),[]); > array_y_higher_work2 := Array(0..(2) ,(0..20+ 1),[]); > array_y_set_initial := Array(0..(2) ,(0..20+ 1),[]); > array_given_rad_poles := Array(0..(2) ,(0..3+ 1),[]); > array_given_ord_poles := Array(0..(2) ,(0..3+ 1),[]); > array_rad_test_poles := Array(0..(2) ,(0..4+ 1),[]); > array_ord_test_poles := Array(0..(2) ,(0..4+ 1),[]); > array_fact_2 := Array(0..(20) ,(0..20+ 1),[]); > # before generate constants > # before generate globals definition > #Top Generate Globals Definition > #Bottom Generate Globals Deninition > # before generate const definition > # before arrays initialized > term := 1; > while (term <= 20) do # do number 1 > array_y_init[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_norms[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_fact_1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_1st_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_last_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_est_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_max_est_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_real_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_complex_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_est_digits[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_y[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_x[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_tmp0[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_tmp1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_tmp2[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_tmp3[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_tmp4[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_tmp5[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 20) do # do number 1 > array_m1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 20) do # do number 2 > array_y_higher[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 20) do # do number 2 > array_y_higher_work[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 20) do # do number 2 > array_y_higher_work2[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 20) do # do number 2 > array_y_set_initial[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_rad_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_ord_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 4) do # do number 2 > array_rad_test_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 4) do # do number 2 > array_ord_test_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=20) do # do number 1 > term := 1; > while (term <= 20) do # do number 2 > array_fact_2[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > # before symbols initialized > #BEGIN SYMBOLS INITIALIZATED > zero_ats_ar(array_y); > zero_ats_ar(array_x); > zero_ats_ar(array_tmp0); > zero_ats_ar(array_tmp1); > zero_ats_ar(array_tmp2); > zero_ats_ar(array_tmp3); > zero_ats_ar(array_tmp4); > zero_ats_ar(array_tmp5); > zero_ats_ar(array_m1); > zero_ats_ar(array_const_1); > array_const_1[1] := c(1); > zero_ats_ar(array_const_0D0); > array_const_0D0[1] := c(0.0); > zero_ats_ar(array_const_2D0); > array_const_2D0[1] := c(2.0); > zero_ats_ar(array_m1); > array_m1[1] := glob__m1; > #END SYMBOLS INITIALIZATED > # before generate factorials init > #Initing Factorial Tables > iiif := 0; > while (iiif <= ATS_MAX_TERMS) do # do number 1 > jjjf := 0; > while (jjjf <= ATS_MAX_TERMS) do # do number 2 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 2; > iiif := iiif + 1; > od;# end do number 1; > #Done Initing Factorial Table > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := 5; > glob_yes_pole := 4; > glob_no_pole := 3; > glob_not_given := 0; > glob_no_sing_tests := 4; > glob_ratio_test := 1; > glob_three_term_test := 2; > glob_six_term_test := 3; > glob_log_10 := log(c(10.0)); > MAX_UNCHANGED := 10; > glob__small := c(0.1e-50); > glob_small_float := c(0.1e-50); > glob_smallish_float := c(0.1e-60); > glob_large_float := c(1.0e100); > glob_larger_float := c(1.1e100); > glob__m2 := c(-2); > glob__m1 := c(-1); > glob__0 := c(0); > glob__1 := c(1); > glob__2 := c(2); > glob__3 := c(3); > glob__4 := c(4); > glob__5 := c(5); > glob__8 := c(8); > glob__10 := c(10); > glob__100 := c(100); > glob__pi := c(0.0); > glob__0_5 := c(0.5); > glob__0_8 := c(0.8); > glob__m0_8 := c(-0.8); > glob__0_25 := c(0.25); > glob__0_125 := c(0.125); > glob_h := 0.1; > glob_nxt := 1; > glob_prec := c(1.0e-16); > glob_check_sign := c(1.0); > glob_desired_digits_correct := c(8.0); > glob_max_estimated_step_error := c(0.0); > glob_ratio_of_radius := c(0.1); > glob_percent_done := c(0.0); > glob_total_exp_sec := c(0.1); > glob_optimal_expect_sec := c(0.1); > glob_estimated_size_answer := c(100.0); > glob_almost_1 := c(0.9990); > glob_clock_sec := c(0.0); > glob_clock_start_sec := c(0.0); > glob_disp_incr := c(0.1); > glob_diff_rc_fm := c(0.1); > glob_diff_rc_fmm1 := c(0.1); > glob_diff_rc_fmm2 := c(0.1); > glob_diff_ord_fm := c(0.1); > glob_diff_ord_fmm1 := c(0.1); > glob_diff_ord_fmm2 := c(0.1); > glob_six_term_ord_save := c(0.1); > glob_guess_error_rc := c(0.1); > glob_guess_error_ord := c(0.1); > glob_least_given_sing := c(9.9e200); > glob_least_ratio_sing := c(9.9e200); > glob_least_3_sing := c(9.9e100); > glob_least_6_sing := c(9.9e100); > glob_last_good_h := c(0.1); > glob_max_h := c(0.1); > glob_min_h := c(0.000001); > glob_display_interval := c(0.1); > glob_abserr := c(0.1e-10); > glob_relerr := c(0.1e-10); > glob_min_pole_est := c(0.1e+10); > glob_max_rel_trunc_err := c(0.1e-10); > glob_max_trunc_err := c(0.1e-10); > glob_max_hours := c(0.0); > glob_optimal_clock_start_sec := c(0.0); > glob_optimal_start := c(0.0); > glob_upper_ratio_limit := c(1.0001); > glob_lower_ratio_limit := c(0.9999); > glob_max_sec := c(10000.0); > glob_orig_start_sec := c(0.0); > glob_normmax := c(0.0); > glob_max_minutes := c(0.0); > glob_next_display := c(0.0); > glob_est_digits := 1; > glob_subiter_method := 3; > glob_html_log := true; > glob_min_good_digits := 99999; > glob_good_digits := 0; > glob_min_apfp_est_good_digits := 99999; > glob_apfp_est_good_digits := 0; > glob_max_opt_iter := 10; > glob_dump := false; > glob_djd_debug := true; > glob_display_flag := true; > glob_djd_debug2 := true; > glob_h_reason := 0; > glob_sec_in_minute := 60 ; > glob_min_in_hour := 60; > glob_hours_in_day := 24; > glob_days_in_year := 365; > glob_sec_in_hour := 3600; > glob_sec_in_day := 86400; > glob_sec_in_year := 31536000; > glob_not_yet_finished := true; > glob_initial_pass := true; > glob_not_yet_start_msg := true; > glob_reached_optimal_h := false; > glob_optimal_done := false; > glob_type_given_pole := 0; > glob_optimize := false; > glob_look_poles := false; > glob_dump_closed_form := false; > glob_max_iter := 10000; > glob_no_eqs := 0; > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_start := 0; > glob_iter := 0; > # before generate set diff initial > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > # before generate init omniout const > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > ATS_MAX_TERMS := 20; > glob_iolevel := INFO; > # set default block > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > glob_display_flag := true; > glob_no_eqs := 1; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 10000; > glob_max_hours := (0.0); > glob_max_minutes := (15.0); > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/sing3postcpx.cpx#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = neg ( 2.0 ) / x / x / x ; "); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=16;"); > omniout_str(ALWAYS,"max_terms:=20;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := -2.1 + 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,"glob_max_h := c(0.001);"); > omniout_str(ALWAYS,"glob_min_h := c(0.001);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"glob_type_given_pole := 1;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_rad_poles[1,1] := c(0.0);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_rad_poles[1,2] := c(0.0);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_ord_poles[1,1] := c(2.0);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_ord_poles[1,2] := c(0.0);"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_desired_digits_correct:=8;"); > omniout_str(ALWAYS,"glob_max_minutes:=(3.0);"); > omniout_str(ALWAYS,"glob_subiter_method:=3;"); > omniout_str(ALWAYS,"glob_max_iter:=10000;"); > omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);"); > omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);"); > omniout_str(ALWAYS,"glob_look_poles:=true;"); > omniout_str(ALWAYS,"glob_h:=c(0.001);"); > omniout_str(ALWAYS,"glob_display_interval:=c(0.01);"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,"return(c(1.0)/c(x)/c(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > 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 := -2.1 + 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_max_h := c(0.001); > glob_min_h := c(0.001); > glob_type_given_pole := 1; > array_given_rad_poles[1,1] := c(0.0); > array_given_rad_poles[1,2] := c(0.0); > array_given_ord_poles[1,1] := c(2.0); > array_given_ord_poles[1,2] := c(0.0); > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=8; > glob_max_minutes:=(3.0); > glob_subiter_method:=3; > glob_max_iter:=10000; > glob_upper_ratio_limit:=c(1.000001); > glob_lower_ratio_limit:=c(0.999999); > glob_look_poles:=true; > glob_h:=c(0.001); > glob_display_interval:=c(0.01); > #END OVERRIDE BLOCK > #END BLOCK 2 > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_sec := (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours); > # after second input block > found_h := true; > glob_h := next_delta(); > #START ADJUST ALL SERIES > if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 9 > h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius; > omniout_str(ALWAYS,"SETTING H FOR POLE"); > glob_h_reason := 6; > if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 10 > omniout_str(ALWAYS,"SETTING H FOR MIN H"); > h_new := glob_min_h; > glob_h_reason := 5; > fi;# end if 10; > term := 1; > ratio := c(1.0); > while (term <= ATS_MAX_TERMS) do # do number 1 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / float_abs(glob_h); > term := term + 1; > od;# end do number 1; > glob_h := h_new; > fi;# end if 9; > #BOTTOM ADJUST ALL SERIES > #END OPTIMIZE CODE > if (glob_html_log) then # if number 9 > html_log_file := fopen("entry.html",WRITE,TEXT); > fi;# end if 9; > #BEGIN SOLUTION CODE > found_h := true; > if (found_h) then # if number 9 > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := c(x_start); > array_x[2] := c(glob_h); > glob_next_display := c(x_start); > glob_min_pole_est := glob_larger_float; > glob_least_given_sing := glob_larger_float; > glob_least_ratio_sing := glob_larger_float; > glob_least_3_sing := glob_larger_float; > glob_least_6_sing := glob_larger_float; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 1 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1)); > term_no := term_no + 1; > od;# end do number 1; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 1 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 2 > it := term_no + r_order - 1; > if (term_no < ATS_MAX_TERMS) then # if number 10 > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1))); > fi;# end if 10; > term_no := term_no + 1; > od;# end do number 2; > r_order := r_order + 1; > od;# end do number 1 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > glob_clock_sec := elapsed_time_seconds(); > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > found_h := true; > glob_h := next_delta(); > #START ADJUST ALL SERIES > if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 10 > h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius; > omniout_str(ALWAYS,"SETTING H FOR POLE"); > glob_h_reason := 6; > if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 11 > omniout_str(ALWAYS,"SETTING H FOR MIN H"); > h_new := glob_min_h; > glob_h_reason := 5; > fi;# end if 11; > term := 1; > ratio := c(1.0); > while (term <= ATS_MAX_TERMS) do # do number 1 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / float_abs(glob_h); > term := term + 1; > od;# end do number 1; > glob_h := h_new; > fi;# end if 10; > #BOTTOM ADJUST ALL SERIES > #END OPTIMIZE CODE > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_iter < glob_max_iter) and ((glob_iter < 10) or ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0))))) do # do number 1 > #left paren 0001C > if (true) then # if number 10 > omniout_str(INFO," "); > fi;# end if 10; > found_h := true; > glob_h := next_delta(); > #START ADJUST ALL SERIES > if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 10 > h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius; > omniout_str(ALWAYS,"SETTING H FOR POLE"); > glob_h_reason := 6; > if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 11 > omniout_str(ALWAYS,"SETTING H FOR MIN H"); > h_new := glob_min_h; > glob_h_reason := 5; > fi;# end if 11; > term := 1; > ratio := c(1.0); > while (term <= ATS_MAX_TERMS) do # do number 2 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / float_abs(glob_h); > term := term + 1; > od;# end do number 2; > glob_h := h_new; > fi;# end if 10; > #BOTTOM ADJUST ALL SERIES > #END OPTIMIZE CODE > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > atomall(); > if ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0))) then # if number 10 > display_alot(current_iter); > fi;# end if 10; > if ((glob_look_poles) and ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0)))) then # if number 10 > check_for_pole(); > fi;# end if 10; > if (true) then # if number 10 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 10; > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := ATS_MAX_TERMS; > while (term_no >= 1) do # do number 2 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 3 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 3; > term_no := term_no - 1; > od;# end do number 2; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > ; > od;# end do number 1;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 10 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 10; > if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec )) then # if number 10 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 10; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = neg ( 2.0 ) / x / x / 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,"2017-11-26T16:23:09-06:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"sing3") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = neg ( 2.0 ) / x / x / 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,"sing3 diffeq.mxt") > ; > logitem_str(html_log_file,"sing3 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_const_2D0, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; ATS_MAX_TERMS := 20; Digits := 16; max_terms := 20; glob_html_log := true; array_y_init := Array(0 .. 20, []); array_norms := Array(0 .. 20, []); array_fact_1 := Array(0 .. 20, []); array_1st_rel_error := Array(0 .. 2, []); array_last_rel_error := Array(0 .. 2, []); array_est_rel_error := Array(0 .. 2, []); array_max_est_error := Array(0 .. 2, []); array_type_pole := Array(0 .. 2, []); array_type_real_pole := Array(0 .. 2, []); array_type_complex_pole := Array(0 .. 2, []); array_est_digits := Array(0 .. 2, []); array_y := Array(0 .. 20, []); array_x := Array(0 .. 20, []); array_tmp0 := Array(0 .. 20, []); array_tmp1 := Array(0 .. 20, []); array_tmp2 := Array(0 .. 20, []); array_tmp3 := Array(0 .. 20, []); array_tmp4 := Array(0 .. 20, []); array_tmp5 := Array(0 .. 20, []); array_m1 := Array(0 .. 20, []); array_y_higher := Array(0 .. 2, 0 .. 21, []); array_y_higher_work := Array(0 .. 2, 0 .. 21, []); array_y_higher_work2 := Array(0 .. 2, 0 .. 21, []); array_y_set_initial := Array(0 .. 2, 0 .. 21, []); array_given_rad_poles := Array(0 .. 2, 0 .. 4, []); array_given_ord_poles := Array(0 .. 2, 0 .. 4, []); array_rad_test_poles := Array(0 .. 2, 0 .. 5, []); array_ord_test_poles := Array(0 .. 2, 0 .. 5, []); array_fact_2 := Array(0 .. 20, 0 .. 21, []); term := 1; while term <= 20 do array_y_init[term] := c(0.); term := term + 1 end do; term := 1; while term <= 20 do array_norms[term] := c(0.); term := term + 1 end do ; term := 1; while term <= 20 do array_fact_1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_1st_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_last_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_est_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_max_est_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_type_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_type_real_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_type_complex_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_est_digits[term] := 0; term := term + 1 end do ; term := 1; while term <= 20 do array_y[term] := c(0.); term := term + 1 end do; term := 1; while term <= 20 do array_x[term] := c(0.); term := term + 1 end do; term := 1; while term <= 20 do array_tmp0[term] := c(0.); term := term + 1 end do; term := 1; while term <= 20 do array_tmp1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 20 do array_tmp2[term] := c(0.); term := term + 1 end do; term := 1; while term <= 20 do array_tmp3[term] := c(0.); term := term + 1 end do; term := 1; while term <= 20 do array_tmp4[term] := c(0.); term := term + 1 end do; term := 1; while term <= 20 do array_tmp5[term] := c(0.); term := term + 1 end do; term := 1; while term <= 20 do array_m1[term] := c(0.); term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 20 do array_y_higher[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 20 do array_y_higher_work[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 20 do array_y_higher_work2[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 20 do array_y_set_initial[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_rad_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_ord_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 4 do array_rad_test_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 4 do array_ord_test_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 20 do term := 1; while term <= 20 do array_fact_2[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; zero_ats_ar(array_y); zero_ats_ar(array_x); zero_ats_ar(array_tmp0); zero_ats_ar(array_tmp1); zero_ats_ar(array_tmp2); zero_ats_ar(array_tmp3); zero_ats_ar(array_tmp4); zero_ats_ar(array_tmp5); zero_ats_ar(array_m1); zero_ats_ar(array_const_1); array_const_1[1] := c(1); zero_ats_ar(array_const_0D0); array_const_0D0[1] := c(0.); zero_ats_ar(array_const_2D0); array_const_2D0[1] := c(2.0); zero_ats_ar(array_m1); array_m1[1] := glob__m1; iiif := 0; while iiif <= ATS_MAX_TERMS do jjjf := 0; while jjjf <= ATS_MAX_TERMS do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := 5; glob_yes_pole := 4; glob_no_pole := 3; glob_not_given := 0; glob_no_sing_tests := 4; glob_ratio_test := 1; glob_three_term_test := 2; glob_six_term_test := 3; glob_log_10 := log(c(10.0)); MAX_UNCHANGED := 10; glob__small := c(0.1*10^(-50)); glob_small_float := c(0.1*10^(-50)); glob_smallish_float := c(0.1*10^(-60)); glob_large_float := c(0.10*10^101); glob_larger_float := c(0.11*10^101); glob__m2 := c(-2); glob__m1 := c(-1); glob__0 := c(0); glob__1 := c(1); glob__2 := c(2); glob__3 := c(3); glob__4 := c(4); glob__5 := c(5); glob__8 := c(8); glob__10 := c(10); glob__100 := c(100); glob__pi := c(0.); glob__0_5 := c(0.5); glob__0_8 := c(0.8); glob__m0_8 := c(-0.8); glob__0_25 := c(0.25); glob__0_125 := c(0.125); glob_h := 0.1; glob_nxt := 1; glob_prec := c(0.10*10^(-15)); glob_check_sign := c(1.0); glob_desired_digits_correct := c(8.0); glob_max_estimated_step_error := c(0.); glob_ratio_of_radius := c(0.1); glob_percent_done := c(0.); glob_total_exp_sec := c(0.1); glob_optimal_expect_sec := c(0.1); glob_estimated_size_answer := c(100.0); glob_almost_1 := c(0.9990); glob_clock_sec := c(0.); glob_clock_start_sec := c(0.); glob_disp_incr := c(0.1); glob_diff_rc_fm := c(0.1); glob_diff_rc_fmm1 := c(0.1); glob_diff_rc_fmm2 := c(0.1); glob_diff_ord_fm := c(0.1); glob_diff_ord_fmm1 := c(0.1); glob_diff_ord_fmm2 := c(0.1); glob_six_term_ord_save := c(0.1); glob_guess_error_rc := c(0.1); glob_guess_error_ord := c(0.1); glob_least_given_sing := c(0.99*10^201); glob_least_ratio_sing := c(0.99*10^201); glob_least_3_sing := c(0.99*10^101); glob_least_6_sing := c(0.99*10^101); glob_last_good_h := c(0.1); glob_max_h := c(0.1); glob_min_h := c(0.1*10^(-5)); glob_display_interval := c(0.1); glob_abserr := c(0.1*10^(-10)); glob_relerr := c(0.1*10^(-10)); glob_min_pole_est := c(0.1*10^10); glob_max_rel_trunc_err := c(0.1*10^(-10)); glob_max_trunc_err := c(0.1*10^(-10)); glob_max_hours := c(0.); glob_optimal_clock_start_sec := c(0.); glob_optimal_start := c(0.); glob_upper_ratio_limit := c(1.0001); glob_lower_ratio_limit := c(0.9999); glob_max_sec := c(10000.0); glob_orig_start_sec := c(0.); glob_normmax := c(0.); glob_max_minutes := c(0.); glob_next_display := c(0.); glob_est_digits := 1; glob_subiter_method := 3; glob_html_log := true; glob_min_good_digits := 99999; glob_good_digits := 0; glob_min_apfp_est_good_digits := 99999; glob_apfp_est_good_digits := 0; glob_max_opt_iter := 10; glob_dump := false; glob_djd_debug := true; glob_display_flag := true; glob_djd_debug2 := true; glob_h_reason := 0; glob_sec_in_minute := 60; glob_min_in_hour := 60; glob_hours_in_day := 24; glob_days_in_year := 365; glob_sec_in_hour := 3600; glob_sec_in_day := 86400; glob_sec_in_year := 31536000; glob_not_yet_finished := true; glob_initial_pass := true; glob_not_yet_start_msg := true; glob_reached_optimal_h := false; glob_optimal_done := false; glob_type_given_pole := 0; glob_optimize := false; glob_look_poles := false; glob_dump_closed_form := false; glob_max_iter := 10000; glob_no_eqs := 0; glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_start := 0; glob_iter := 0; array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; ATS_MAX_TERMS := 20; glob_iolevel := INFO; glob_orig_start_sec := elapsed_time_seconds(); glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 10000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/sing3postcpx.cpx#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = neg ( 2.0 ) / x / x / x ; ") ; omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=16;"); omniout_str(ALWAYS, "max_terms:=20;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := -2.1 + 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, "glob_max_h := c(0.001);"); omniout_str(ALWAYS, "glob_min_h := c(0.001);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "glob_type_given_pole := 1;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_rad_poles[1,1] := c(0.0);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_rad_poles[1,2] := c(0.0);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_ord_poles[1,1] := c(2.0);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_ord_poles[1,2] := c(0.0);"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_desired_digits_correct:=8;"); omniout_str(ALWAYS, "glob_max_minutes:=(3.0);"); omniout_str(ALWAYS, "glob_subiter_method:=3;"); omniout_str(ALWAYS, "glob_max_iter:=10000;"); omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);"); omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);"); omniout_str(ALWAYS, "glob_look_poles:=true;"); omniout_str(ALWAYS, "glob_h:=c(0.001);"); omniout_str(ALWAYS, "glob_display_interval:=c(0.01);"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, "return(c(1.0)/c(x)/c(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); 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 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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, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 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 := -2.1 + 0.1*I; x_end := 99.0 + 99.0*I; array_y_init[1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_h := c(0.001); glob_min_h := c(0.001); glob_type_given_pole := 1; array_given_rad_poles[1, 1] := c(0.); array_given_rad_poles[1, 2] := c(0.); array_given_ord_poles[1, 1] := c(2.0); array_given_ord_poles[1, 2] := c(0.); glob_desired_digits_correct := 8; glob_max_minutes := 3.0; glob_subiter_method := 3; glob_max_iter := 10000; glob_upper_ratio_limit := c(1.000001); glob_lower_ratio_limit := c(0.999999); glob_look_poles := true; glob_h := c(0.001); glob_display_interval := c(0.01); glob_last_good_h := glob_h; glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours; found_h := true; glob_h := next_delta(); if float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h) then h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius; omniout_str(ALWAYS, "SETTING H FOR POLE"); glob_h_reason := 6; if glob_check_sign*h_new < glob_check_sign*glob_min_h then omniout_str(ALWAYS, "SETTING H FOR MIN H"); h_new := glob_min_h; glob_h_reason := 5 end if; term := 1; ratio := c(1.0); while term <= ATS_MAX_TERMS do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/float_abs(glob_h); term := term + 1 end do; glob_h := h_new end if; if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT) end if; found_h := true; if found_h then omniout_str(ALWAYS, "START of Soultion"); array_x[1] := c(x_start); array_x[2] := c(glob_h); glob_next_display := c(x_start); glob_min_pole_est := glob_larger_float; glob_least_given_sing := glob_larger_float; glob_least_ratio_sing := glob_larger_float; glob_least_3_sing := glob_larger_float; glob_least_6_sing := glob_larger_float; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1)); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; if term_no < ATS_MAX_TERMS then array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, c(term_no - 1))/ c(factorial_1(term_no - 1)) end if; term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); glob_clock_sec := elapsed_time_seconds(); glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; found_h := true; glob_h := next_delta(); if float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h) then h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius ; omniout_str(ALWAYS, "SETTING H FOR POLE"); glob_h_reason := 6; if glob_check_sign*h_new < glob_check_sign*glob_min_h then omniout_str(ALWAYS, "SETTING H FOR MIN H"); h_new := glob_min_h; glob_h_reason := 5 end if; term := 1; ratio := c(1.0); while term <= ATS_MAX_TERMS do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/float_abs(glob_h); term := term + 1 end do; glob_h := h_new end if; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_iter < glob_max_iter and (glob_iter < 10 or not (Re(glob_h) = 0. and Im(glob_h) = 0.)) do omniout_str(INFO, " "); found_h := true; glob_h := next_delta(); if float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h) then h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius; omniout_str(ALWAYS, "SETTING H FOR POLE"); glob_h_reason := 6; if glob_check_sign*h_new < glob_check_sign*glob_min_h then omniout_str(ALWAYS, "SETTING H FOR MIN H"); h_new := glob_min_h; glob_h_reason := 5 end if; term := 1; ratio := c(1.0); while term <= ATS_MAX_TERMS do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/float_abs(glob_h); term := term + 1 end do; glob_h := h_new end if; glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); atomall(); if not (Re(glob_h) = 0. and Im(glob_h) = 0.) then display_alot(current_iter) end if; if glob_look_poles and not (Re(glob_h) = 0. and Im(glob_h) = 0.) then check_for_pole() end if; glob_next_display := glob_next_display + glob_display_interval; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 2; ord := 2; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_higher[2, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 2; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); term_no := ATS_MAX_TERMS; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if glob_max_sec <= elapsed_time_seconds() - glob_orig_start_sec then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y , x , 1 ) = neg ( 2.0 ) /\ x / x / 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, "2017-11-26T16:23:09-06:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "sing3"); logitem_str(html_log_file, "diff ( y , x , 1 ) = ne\ g ( 2.0 ) / x / x / 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, "sing3 diffeq.mxt"); logitem_str(html_log_file, "sing3 maple results") ; logitem_str(html_log_file, "OK"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end if end proc # End Function number 12 > main(); memory used=3.9MB, alloc=40.3MB, time=0.08 ##############ECHO OF PROBLEM################# ##############temp/sing3postcpx.cpx################# diff ( y , x , 1 ) = neg ( 2.0 ) / x / x / x ; ! #BEGIN FIRST INPUT BLOCK Digits:=16; max_terms:=20; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := -2.1 + 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_max_h := c(0.001); glob_min_h := c(0.001); glob_type_given_pole := 1; array_given_rad_poles[1,1] := c(0.0); array_given_rad_poles[1,2] := c(0.0); array_given_ord_poles[1,1] := c(2.0); array_given_ord_poles[1,2] := c(0.0); #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=8; glob_max_minutes:=(3.0); glob_subiter_method:=3; glob_max_iter:=10000; glob_upper_ratio_limit:=c(1.000001); glob_lower_ratio_limit:=c(0.999999); glob_look_poles:=true; glob_h:=c(0.001); glob_display_interval:=c(0.01); #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) return(c(1.0)/c(x)/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] = -2.1 0.1 h = 0.0001 0.005 y[1] (numeric) = 0.225220613829 0.02149833132 y[1] (closed_form) = 0.225220613829 0.02149833132 absolute error = 0 relative error = 0 % Correct digits = 14 Radius of convergence (given) for eq 1 = 2.102 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.628 Order of pole (three term test) = 1.659e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0999 0.105 h = 0.0001 0.003 y[1] (numeric) = 0.225085782276 0.0225661293499 y[1] (closed_form) = 0.225085026309 0.0225659948758 absolute error = 7.678e-07 relative error = 0.0003394 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.103 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.262 Order of pole (three term test) = 1.613e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0998 0.108 h = 0.001 0.001 y[1] (numeric) = 0.225008386399 0.0232073095974 y[1] (closed_form) = 0.225008538393 0.0232073324723 absolute error = 1.537e-07 relative error = 6.795e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.103 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9906 Order of pole (three term test) = 1.487e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0988 0.109 h = 0.001 0.003 y[1] (numeric) = 0.225187427848 0.0234533383001 y[1] (closed_form) = 0.225188050546 0.0234532879043 absolute error = 6.247e-07 relative error = 0.0002759 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.102 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.699 Order of pole (three term test) = 8.288e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0978 0.112 h = 0.0001 0.004 y[1] (numeric) = 0.225299641301 0.0241258383941 y[1] (closed_form) = 0.225299296368 0.0241258964346 absolute error = 3.498e-07 relative error = 0.0001544 % Correct digits = 6 Radius of convergence (given) for eq 1 = 2.101 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.658 Order of pole (three term test) = 1.532e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0977 0.116 h = 0.003 0.006 y[1] (numeric) = 0.225181520437 0.0249813740494 y[1] (closed_form) = 0.225180676702 0.0249807692959 absolute error = 1.038e-06 relative error = 0.0004582 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.101 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.522 Order of pole (three term test) = 8.590e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0947 0.122 h = 0.0001 0.005 y[1] (numeric) = 0.225602223628 0.0263655513837 y[1] (closed_form) = 0.225600070266 0.0263683481245 absolute error = 3.530e-06 relative error = 0.001554 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.098 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.564 Order of pole (three term test) = 1.365e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0946 0.127 h = 0.0001 0.003 y[1] (numeric) = 0.225430530901 0.0274366388602 y[1] (closed_form) = 0.225429624286 0.0274374105929 absolute error = 1.191e-06 relative error = 0.0005243 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.098 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.26 Order of pole (three term test) = 1.867e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0945 0.13 h = 0.001 0.001 y[1] (numeric) = 0.225332222888 0.0280787380778 y[1] (closed_form) = 0.225332223719 0.0280797070159 absolute error = 9.689e-07 relative error = 0.0004267 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.099 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9887 Order of pole (three term test) = 1.383e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0935 0.131 h = 0.001 0.003 y[1] (numeric) = 0.225504338388 0.0283317873136 y[1] (closed_form) = 0.225504816255 0.0283327025929 absolute error = 1.033e-06 relative error = 0.0004543 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.098 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.69 Order of pole (three term test) = 5.692e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0925 0.134 h = 0.0001 0.004 y[1] (numeric) = 0.225595620606 0.0290114188553 y[1] (closed_form) = 0.225595119644 0.0290124019382 absolute error = 1.103e-06 relative error = 0.0004851 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.097 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.653 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0924 0.138 h = 0.003 0.006 y[1] (numeric) = 0.225449487563 0.0298676240017 y[1] (closed_form) = 0.225448512806 0.0298679185148 absolute error = 1.018e-06 relative error = 0.0004478 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.097 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.516 Order of pole (three term test) = 8.533e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0894 0.144 h = 0.0001 0.005 y[1] (numeric) = 0.2258280235 0.0312723803801 y[1] (closed_form) = 0.225825584906 0.0312760427839 absolute error = 4.400e-06 relative error = 0.00193 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.094 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.561 Order of pole (three term test) = 8.605e-14 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=39.3MB, alloc=40.3MB, time=0.51 x[1] = -2.0893 0.149 h = 0.0001 0.003 y[1] (numeric) = 0.225621083477 0.0323433448597 y[1] (closed_form) = 0.225619986504 0.0323450225953 absolute error = 2.005e-06 relative error = 0.0008795 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.095 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.257 Order of pole (three term test) = 2.898e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0892 0.152 h = 0.001 0.001 y[1] (numeric) = 0.225501685712 0.032985474471 y[1] (closed_form) = 0.225501493529 0.0329873895589 absolute error = 1.925e-06 relative error = 0.0008445 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.095 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9869 Order of pole (three term test) = 1.329e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0882 0.153 h = 0.001 0.003 y[1] (numeric) = 0.225666529359 0.0332452940432 y[1] (closed_form) = 0.225666819542 0.0332471755791 absolute error = 1.904e-06 relative error = 0.0008346 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.094 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.682 Order of pole (three term test) = 3.595e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0872 0.156 h = 0.0001 0.004 y[1] (numeric) = 0.22573643739 0.0339312077129 y[1] (closed_form) = 0.225735739636 0.033933115498 absolute error = 2.031e-06 relative error = 0.0008899 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.093 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.648 Order of pole (three term test) = 4.547e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0871 0.16 h = 0.003 0.006 y[1] (numeric) = 0.225562081606 0.0347868865788 y[1] (closed_form) = 0.225560936642 0.0347880811581 absolute error = 1.655e-06 relative error = 0.000725 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.093 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.509 Order of pole (three term test) = 8.090e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0841 0.166 h = 0.0001 0.005 y[1] (numeric) = 0.225897298813 0.0362105471944 y[1] (closed_form) = 0.225894536419 0.0362150675264 absolute error = 5.298e-06 relative error = 0.002316 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.091 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.559 Order of pole (three term test) = 1.155e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.084 0.171 h = 0.0001 0.003 y[1] (numeric) = 0.225654896153 0.0372798743272 y[1] (closed_form) = 0.225653568799 0.0372824557342 absolute error = 2.903e-06 relative error = 0.001269 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.091 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.255 Order of pole (three term test) = 6.553e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0839 0.174 h = 0.001 0.001 y[1] (numeric) = 0.225514277323 0.0379211293792 y[1] (closed_form) = 0.225513849927 0.0379239884407 absolute error = 2.891e-06 relative error = 0.001264 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.091 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9852 Order of pole (three term test) = 4.952e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0829 0.175 h = 0.001 0.003 y[1] (numeric) = 0.225671513989 0.0381874486168 y[1] (closed_form) = 0.225671573249 0.0381902946679 absolute error = 2.847e-06 relative error = 0.001244 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.09 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.674 Order of pole (three term test) = 6.831e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0819 0.178 h = 0.0001 0.004 y[1] (numeric) = 0.22571964709 0.0388787648096 y[1] (closed_form) = 0.225718711473 0.0388815947598 absolute error = 2.981e-06 relative error = 0.001301 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.089 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.644 Order of pole (three term test) = 1.729e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0818 0.182 h = 0.003 0.006 y[1] (numeric) = 0.22551692065 0.0397327012789 y[1] (closed_form) = 0.225515565926 0.0397347946393 absolute error = 2.493e-06 relative error = 0.001089 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.09 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.504 Order of pole (three term test) = 1.088e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0788 0.188 h = 0.0001 0.005 y[1] (numeric) = 0.225807749056 0.0411735170155 y[1] (closed_form) = 0.225804624486 0.0411788854235 absolute error = 6.212e-06 relative error = 0.002706 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.087 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.556 Order of pole (three term test) = 2.608e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0787 0.193 h = 0.0001 0.003 y[1] (numeric) = 0.22552974839 0.0422396698667 y[1] (closed_form) = 0.225528150461 0.042243150447 absolute error = 3.830e-06 relative error = 0.001669 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.088 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.253 Order of pole (three term test) = 1.249e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0786 0.196 h = 0.001 0.001 y[1] (numeric) = 0.225367824937 0.0428791318795 y[1] (closed_form) = 0.225367119929 0.0428829304322 absolute error = 3.863e-06 relative error = 0.001684 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.088 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9837 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0776 0.197 h = 0.0001 0.004 y[1] (numeric) = 0.225517131686 0.0431516601589 y[1] (closed_form) = 0.225516916545 0.0431554666138 absolute error = 3.813e-06 relative error = 0.00166 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.087 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.905 Order of pole (three term test) = 1.022e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0775 0.201 h = 0.003 0.006 y[1] (numeric) = 0.225291143872 0.0440032125493 y[1] (closed_form) = 0.225289347614 0.0440058223585 absolute error = 3.168e-06 relative error = 0.00138 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.087 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.499 Order of pole (three term test) = 5.247e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0745 0.207 h = 0.0001 0.005 y[1] (numeric) = 0.225542798484 0.0454567964025 y[1] (closed_form) = 0.225539103298 0.045462628973 absolute error = 6.905e-06 relative error = 0.003001 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.085 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.554 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0744 0.212 h = 0.0001 0.003 y[1] (numeric) = 0.225234173502 0.0465185479351 y[1] (closed_form) = 0.225232081381 0.0465225419455 absolute error = 4.509e-06 relative error = 0.00196 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.085 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.252 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0743 0.215 h = 0.001 0.001 y[1] (numeric) = 0.22505391866 0.0471554687163 y[1] (closed_form) = 0.225052711146 0.0471598151872 absolute error = 4.511e-06 relative error = 0.001962 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.085 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9825 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0733 0.216 h = 0.001 0.003 y[1] (numeric) = 0.225196082439 0.047432994598 y[1] (closed_form) = 0.225195366415 0.0474373672382 absolute error = 4.431e-06 relative error = 0.001925 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.085 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.661 Order of pole (three term test) = 3.146e-14 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=86.0MB, alloc=44.3MB, time=1.12 x[1] = -2.0723 0.219 h = 0.0001 0.004 y[1] (numeric) = 0.225202746606 0.048131660688 y[1] (closed_form) = 0.225201029311 0.0481359367513 absolute error = 4.608e-06 relative error = 0.002001 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.084 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.637 Order of pole (three term test) = 8.010e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0722 0.223 h = 0.003 0.006 y[1] (numeric) = 0.224947112999 0.048978725755 y[1] (closed_form) = 0.224945032928 0.0489822257897 absolute error = 4.071e-06 relative error = 0.001769 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.084 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.494 Order of pole (three term test) = 2.511e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0692 0.229 h = 0.0001 0.005 y[1] (numeric) = 0.225152645551 0.0504460183107 y[1] (closed_form) = 0.225148517925 0.0504526745457 absolute error = 7.832e-06 relative error = 0.003394 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.082 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.552 Order of pole (three term test) = 4.565e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0691 0.234 h = 0.0001 0.003 y[1] (numeric) = 0.22480840916 0.0515016935763 y[1] (closed_form) = 0.224805971802 0.051506572054 absolute error = 5.453e-06 relative error = 0.002365 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.082 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.25 Order of pole (three term test) = 2.312e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.069 0.237 h = 0.001 0.001 y[1] (numeric) = 0.224606836632 0.0521350869553 y[1] (closed_form) = 0.224605272706 0.0521403578321 absolute error = 5.498e-06 relative error = 0.002384 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.083 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9812 Order of pole (three term test) = 6.562e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.068 0.238 h = 0.001 0.003 y[1] (numeric) = 0.224740510744 0.0524182268021 y[1] (closed_form) = 0.224739439429 0.0524235452566 absolute error = 5.425e-06 relative error = 0.002351 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.082 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.655 Order of pole (three term test) = 4.528e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.067 0.241 h = 0.0001 0.004 y[1] (numeric) = 0.224724518132 0.0531196318442 y[1] (closed_form) = 0.22472244516 0.053124809885 absolute error = 5.578e-06 relative error = 0.002415 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.081 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.633 Order of pole (three term test) = 7.651e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0669 0.245 h = 0.003 0.006 y[1] (numeric) = 0.224440466945 0.0539613994563 y[1] (closed_form) = 0.224438063215 0.0539657822633 absolute error = 4.999e-06 relative error = 0.002165 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.081 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.489 Order of pole (three term test) = 1.365e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0639 0.251 h = 0.0001 0.005 y[1] (numeric) = 0.224599070087 0.0554404674128 y[1] (closed_form) = 0.224594472971 0.0554479314381 absolute error = 8.766e-06 relative error = 0.003789 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.079 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.55 Order of pole (three term test) = 6.911e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0638 0.256 h = 0.0001 0.003 y[1] (numeric) = 0.224219326126 0.0564884941689 y[1] (closed_form) = 0.224216503642 0.0564942462955 absolute error = 6.407e-06 relative error = 0.002771 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.08 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.248 Order of pole (three term test) = 4.450e-15 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0637 0.259 h = 0.001 0.001 y[1] (numeric) = 0.22399649518 0.0571174204616 y[1] (closed_form) = 0.223994532729 0.0571236045272 absolute error = 6.488e-06 relative error = 0.002807 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.08 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9799 Order of pole (three term test) = 1.228e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0627 0.26 h = 0.001 0.003 y[1] (numeric) = 0.224121399297 0.0574058306427 y[1] (closed_form) = 0.224119929422 0.0574120838657 absolute error = 6.424e-06 relative error = 0.002777 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.079 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.649 Order of pole (three term test) = 1.454e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0617 0.263 h = 0.0001 0.004 y[1] (numeric) = 0.224082532516 0.0581090036058 y[1] (closed_form) = 0.224080062977 0.0581150723326 absolute error = 6.552e-06 relative error = 0.00283 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.078 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.63 Order of pole (three term test) = 1.165e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0616 0.267 h = 0.003 0.006 y[1] (numeric) = 0.223770172458 0.05894421779 y[1] (closed_form) = 0.223767405382 0.0589494737201 absolute error = 5.940e-06 relative error = 0.002567 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.079 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.485 Order of pole (three term test) = 4.650e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0586 0.273 h = 0.0001 0.005 y[1] (numeric) = 0.223881139493 0.0604330739745 y[1] (closed_form) = 0.22387603656 0.0604413278529 absolute error = 9.704e-06 relative error = 0.004185 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.077 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.548 Order of pole (three term test) = 4.715e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0585 0.278 h = 0.0001 0.003 y[1] (numeric) = 0.223466077768 0.0614718777213 y[1] (closed_form) = 0.223462830647 0.0614784904587 absolute error = 7.367e-06 relative error = 0.003179 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.077 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.247 Order of pole (three term test) = 1.121e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0584 0.281 h = 0.001 0.001 y[1] (numeric) = 0.223222098993 0.0620953958498 y[1] (closed_form) = 0.223219696294 0.06210247952 absolute error = 7.480e-06 relative error = 0.003228 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.077 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9788 Order of pole (three term test) = 5.085e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0574 0.282 h = 0.001 0.003 y[1] (numeric) = 0.223337970087 0.0623887158425 y[1] (closed_form) = 0.223336058757 0.0623958903465 absolute error = 7.425e-06 relative error = 0.003202 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.077 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.644 Order of pole (three term test) = 5.616e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0564 0.285 h = 0.0001 0.004 y[1] (numeric) = 0.223276063463 0.0630926691687 y[1] (closed_form) = 0.223273156868 0.0630996150022 absolute error = 7.529e-06 relative error = 0.003245 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.076 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.627 Order of pole (three term test) = 1.593e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0563 0.289 h = 0.003 0.006 y[1] (numeric) = 0.222935572036 0.0639200738989 y[1] (closed_form) = 0.222932402227 0.0639261911027 absolute error = 6.890e-06 relative error = 0.002971 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.077 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.481 Order of pole (three term test) = 1.006e-13 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=132.8MB, alloc=44.3MB, time=1.72 x[1] = -2.0533 0.295 h = 0.0001 0.005 y[1] (numeric) = 0.222998300989 0.0654166835325 y[1] (closed_form) = 0.222992656772 0.065425707303 absolute error = 1.064e-05 relative error = 0.00458 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.074 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.546 Order of pole (three term test) = 1.021e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0532 0.3 h = 0.0001 0.003 y[1] (numeric) = 0.222548197879 0.0664446931187 y[1] (closed_form) = 0.222544487135 0.0664521512211 absolute error = 8.330e-06 relative error = 0.003587 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.075 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.245 Order of pole (three term test) = 1.041e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0531 0.303 h = 0.001 0.001 y[1] (numeric) = 0.222283233542 0.067061863954 y[1] (closed_form) = 0.222280349423 0.06706983129 absolute error = 8.473e-06 relative error = 0.003649 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.075 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9778 Order of pole (three term test) = 2.958e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0521 0.304 h = 0.0001 0.004 y[1] (numeric) = 0.222389827075 0.0673597173867 y[1] (closed_form) = 0.222387431931 0.0673677972533 absolute error = 8.427e-06 relative error = 0.003627 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.074 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.869 Order of pole (three term test) = 8.502e-15 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.052 0.308 h = 0.003 0.006 y[1] (numeric) = 0.222026524413 0.0681797623331 y[1] (closed_form) = 0.222022801475 0.0681863060259 absolute error = 7.529e-06 relative error = 0.003242 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.075 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.479 Order of pole (three term test) = 3.080e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.049 0.314 h = 0.0001 0.005 y[1] (numeric) = 0.222047273603 0.0696808026549 y[1] (closed_form) = 0.222040961769 0.0696901663511 absolute error = 1.129e-05 relative error = 0.004852 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.073 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.545 Order of pole (three term test) = 3.160e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0489 0.319 h = 0.0001 0.003 y[1] (numeric) = 0.221567449469 0.0706978582804 y[1] (closed_form) = 0.221563133916 0.070705725751 absolute error = 8.973e-06 relative error = 0.003858 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.074 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.245 Order of pole (three term test) = 1.020e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0488 0.322 h = 0.001 0.001 y[1] (numeric) = 0.221284681665 0.0713085711498 y[1] (closed_form) = 0.221281175253 0.0713169799086 absolute error = 9.111e-06 relative error = 0.003919 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.074 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9771 Order of pole (three term test) = 1.933e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0478 0.323 h = 0.001 0.003 y[1] (numeric) = 0.22138306088 0.0716099000541 y[1] (closed_form) = 0.221380040172 0.0716184399289 absolute error = 9.058e-06 relative error = 0.003893 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.073 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.636 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0468 0.326 h = 0.0001 0.004 y[1] (numeric) = 0.221278043105 0.0723123576137 y[1] (closed_form) = 0.221274042296 0.0723205870358 absolute error = 9.150e-06 relative error = 0.003931 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.073 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.622 Order of pole (three term test) = 2.033e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0467 0.33 h = 0.003 0.006 y[1] (numeric) = 0.220886043063 0.073121579501 y[1] (closed_form) = 0.220881845607 0.0731289561387 absolute error = 8.487e-06 relative error = 0.003648 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.073 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.476 Order of pole (three term test) = 1.124e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0437 0.336 h = 0.0001 0.005 y[1] (numeric) = 0.220857750059 0.0746264791204 y[1] (closed_form) = 0.220850833985 0.0746365699671 absolute error = 1.223e-05 relative error = 0.005248 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.071 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.544 Order of pole (three term test) = 9.249e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0436 0.341 h = 0.0001 0.003 y[1] (numeric) = 0.220343647891 0.0756298511673 y[1] (closed_form) = 0.220338798308 0.0756385294045 absolute error = 9.941e-06 relative error = 0.004267 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.072 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.244 Order of pole (three term test) = 9.944e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0435 0.344 h = 0.001 0.001 y[1] (numeric) = 0.220040345147 0.0762324894397 y[1] (closed_form) = 0.220036282958 0.0762417455645 absolute error = 1.011e-05 relative error = 0.004341 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.072 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9763 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0425 0.345 h = 0.001 0.003 y[1] (numeric) = 0.220129049634 0.0765376108875 y[1] (closed_form) = 0.220125468539 0.0765470196421 absolute error = 1.007e-05 relative error = 0.00432 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.071 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.632 Order of pole (three term test) = 1.302e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0415 0.348 h = 0.0001 0.004 y[1] (numeric) = 0.220000826772 0.0772379625228 y[1] (closed_form) = 0.219996276912 0.0772470172901 absolute error = 1.013e-05 relative error = 0.004346 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.071 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.62 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0414 0.352 h = 0.003 0.006 y[1] (numeric) = 0.219581599304 0.0780358267505 y[1] (closed_form) = 0.219576889634 0.0780440182721 absolute error = 9.449e-06 relative error = 0.004055 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.072 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.473 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0384 0.358 h = 0.0001 0.005 y[1] (numeric) = 0.219503980299 0.0795424535978 y[1] (closed_form) = 0.21949642773 0.0795532461721 absolute error = 1.317e-05 relative error = 0.005642 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.07 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.543 Order of pole (three term test) = 3.012e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0383 0.363 h = 0.0001 0.003 y[1] (numeric) = 0.218956123383 0.0805306129953 y[1] (closed_form) = 0.218950703113 0.0805400806186 absolute error = 1.091e-05 relative error = 0.004676 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.07 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.243 Order of pole (three term test) = 9.538e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0382 0.366 h = 0.001 0.001 y[1] (numeric) = 0.218632595332 0.0811242624979 y[1] (closed_form) = 0.218627938658 0.0811343435048 absolute error = 1.110e-05 relative error = 0.004762 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.071 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9756 Order of pole (three term test) = 9.639e-14 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=179.4MB, alloc=44.3MB, time=2.32 x[1] = -2.0372 0.367 h = 0.001 0.003 y[1] (numeric) = 0.218711439477 0.0814327616333 y[1] (closed_form) = 0.218707258102 0.081443016581 absolute error = 1.107e-05 relative error = 0.004745 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.07 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.629 Order of pole (three term test) = 1.369e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0362 0.37 h = 0.0001 0.004 y[1] (numeric) = 0.218560055905 0.0821299885339 y[1] (closed_form) = 0.218554919507 0.0821398464815 absolute error = 1.112e-05 relative error = 0.004761 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.07 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.619 Order of pole (three term test) = 3.241e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0361 0.374 h = 0.003 0.006 y[1] (numeric) = 0.218114044053 0.0829152821772 y[1] (closed_form) = 0.218108785332 0.0829242684099 absolute error = 1.041e-05 relative error = 0.004462 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.07 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.471 Order of pole (three term test) = 5.803e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0331 0.38 h = 0.0001 0.005 y[1] (numeric) = 0.217986931055 0.0844214836796 y[1] (closed_form) = 0.217978711093 0.0844329507856 absolute error = 1.411e-05 relative error = 0.006036 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.068 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.542 Order of pole (three term test) = 1.592e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.033 0.385 h = 0.0001 0.003 y[1] (numeric) = 0.21740592747 0.0853929267148 y[1] (closed_form) = 0.217399900938 0.0854031602902 absolute error = 1.188e-05 relative error = 0.005085 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.069 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.242 Order of pole (three term test) = 7.648e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0329 0.388 h = 0.001 0.001 y[1] (numeric) = 0.217062534349 0.0859766883442 y[1] (closed_form) = 0.217057245632 0.0859875695592 absolute error = 1.210e-05 relative error = 0.005182 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.07 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9751 Order of pole (three term test) = 1.814e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0319 0.389 h = 0.001 0.003 y[1] (numeric) = 0.217131354847 0.0862881393448 y[1] (closed_form) = 0.217126534459 0.0862992155305 absolute error = 1.208e-05 relative error = 0.00517 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.069 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.626 Order of pole (three term test) = 2.507e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0309 0.392 h = 0.0001 0.004 y[1] (numeric) = 0.216956910756 0.0869812231182 y[1] (closed_form) = 0.216951151462 0.0869918599721 absolute error = 1.210e-05 relative error = 0.005175 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.068 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.617 Order of pole (three term test) = 6.375e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0308 0.396 h = 0.003 0.006 y[1] (numeric) = 0.216484624742 0.0877527552297 y[1] (closed_form) = 0.216478781135 0.0877625139375 absolute error = 1.137e-05 relative error = 0.004869 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.069 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.469 Order of pole (three term test) = 8.075e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0278 0.402 h = 0.0001 0.005 y[1] (numeric) = 0.216307967164 0.0892563658669 y[1] (closed_form) = 0.216299050383 0.0892684786239 absolute error = 1.504e-05 relative error = 0.006428 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.067 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.541 Order of pole (three term test) = 8.734e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0277 0.407 h = 0.0001 0.003 y[1] (numeric) = 0.215694508274 0.0902096198037 y[1] (closed_form) = 0.21568784112 0.0902205939108 absolute error = 1.284e-05 relative error = 0.005492 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.068 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.241 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0276 0.41 h = 0.001 0.001 y[1] (numeric) = 0.215331660018 0.090782612874 y[1] (closed_form) = 0.215325702996 0.0907942675045 absolute error = 1.309e-05 relative error = 0.005601 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.069 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9746 Order of pole (three term test) = 8.947e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0266 0.411 h = 0.0001 0.004 y[1] (numeric) = 0.215390316631 0.091096580397 y[1] (closed_form) = 0.21538481981 0.0911084506697 absolute error = 1.308e-05 relative error = 0.005594 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.068 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.851 Order of pole (three term test) = 1.592e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0265 0.415 h = 0.003 0.006 y[1] (numeric) = 0.214896992155 0.0918559523072 y[1] (closed_form) = 0.214890508252 0.0918660186504 absolute error = 1.197e-05 relative error = 0.005124 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.069 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.468 Order of pole (three term test) = 6.897e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0235 0.421 h = 0.0001 0.005 y[1] (numeric) = 0.214677804195 0.0933550057193 y[1] (closed_form) = 0.214668157852 0.0933673107192 absolute error = 1.564e-05 relative error = 0.006679 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.067 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.541 Order of pole (three term test) = 1.043e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0234 0.426 h = 0.0001 0.003 y[1] (numeric) = 0.214037264504 0.094291077589 y[1] (closed_form) = 0.214029910856 0.09430232872 absolute error = 1.344e-05 relative error = 0.005747 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.068 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.241 Order of pole (three term test) = 1.325e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0233 0.429 h = 0.001 0.001 y[1] (numeric) = 0.213658177424 0.0948538884956 y[1] (closed_form) = 0.213651508255 0.0948658469015 absolute error = 1.369e-05 relative error = 0.005857 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.068 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9745 Order of pole (three term test) = 1.259e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0223 0.43 h = 0.001 0.003 y[1] (numeric) = 0.213707968323 0.0951695444839 y[1] (closed_form) = 0.213701751207 0.0951817358645 absolute error = 1.369e-05 relative error = 0.00585 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.068 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.623 Order of pole (three term test) = 1.740e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0213 0.433 h = 0.0001 0.004 y[1] (numeric) = 0.213491149614 0.0958519558022 y[1] (closed_form) = 0.213484030235 0.0958636316858 absolute error = 1.368e-05 relative error = 0.005844 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.067 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.616 Order of pole (three term test) = 2.818e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0212 0.437 h = 0.003 0.006 y[1] (numeric) = 0.212971751856 0.0965945092865 y[1] (closed_form) = 0.212964619837 0.0966053010612 absolute error = 1.294e-05 relative error = 0.005532 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.068 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.467 Order of pole (three term test) = 8.879e-14 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=226.1MB, alloc=44.3MB, time=2.92 x[1] = -2.0182 0.443 h = 0.0001 0.005 y[1] (numeric) = 0.212703266491 0.0980869369813 y[1] (closed_form) = 0.212692873245 0.0980998294419 absolute error = 1.656e-05 relative error = 0.00707 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.066 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.54 Order of pole (three term test) = 1.721e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0181 0.448 h = 0.0001 0.003 y[1] (numeric) = 0.212031789075 0.0990021910264 y[1] (closed_form) = 0.212023734917 0.099014130003 absolute error = 1.440e-05 relative error = 0.006154 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.067 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.241 Order of pole (three term test) = 1.881e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.018 0.451 h = 0.001 0.001 y[1] (numeric) = 0.211634147604 0.0995526610423 y[1] (closed_form) = 0.211626746963 0.0995653372747 absolute error = 1.468e-05 relative error = 0.006276 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.068 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9742 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.017 0.452 h = 0.001 0.003 y[1] (numeric) = 0.21167358257 0.099870002343 y[1] (closed_form) = 0.21166662377 0.0998829313393 absolute error = 1.468e-05 relative error = 0.006273 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.067 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.622 Order of pole (three term test) = 1.222e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.016 0.455 h = 0.0001 0.004 y[1] (numeric) = 0.211434309396 0.100545395701 y[1] (closed_form) = 0.211426470964 0.100557769698 absolute error = 1.465e-05 relative error = 0.006256 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.067 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.615 Order of pole (three term test) = 1.675e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0159 0.459 h = 0.003 0.006 y[1] (numeric) = 0.210890467602 0.101270949976 y[1] (closed_form) = 0.210882655259 0.101282439432 absolute error = 1.389e-05 relative error = 0.005939 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.067 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.466 Order of pole (three term test) = 7.895e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0129 0.465 h = 0.0001 0.005 y[1] (numeric) = 0.210572973521 0.10275459352 y[1] (closed_form) = 0.210561808748 0.102768040325 absolute error = 1.748e-05 relative error = 0.007459 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.066 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.54 Order of pole (three term test) = 1.142e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0128 0.47 h = 0.0001 0.003 y[1] (numeric) = 0.209871475247 0.10364767642 y[1] (closed_form) = 0.209862690435 0.103660272618 absolute error = 1.536e-05 relative error = 0.006561 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.067 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.241 Order of pole (three term test) = 1.855e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0127 0.473 h = 0.001 0.001 y[1] (numeric) = 0.209455823898 0.104184995892 y[1] (closed_form) = 0.209447660017 0.104198357615 absolute error = 1.566e-05 relative error = 0.006693 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.068 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9741 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0117 0.474 h = 0.001 0.003 y[1] (numeric) = 0.209484831904 0.104503568701 y[1] (closed_form) = 0.209477098576 0.104517202405 absolute error = 1.567e-05 relative error = 0.006695 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.067 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.621 Order of pole (three term test) = 3.287e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0107 0.477 h = 0.0001 0.004 y[1] (numeric) = 0.209223417839 0.105170962347 y[1] (closed_form) = 0.209214829656 0.105184002816 absolute error = 1.561e-05 relative error = 0.006668 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.067 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.615 Order of pole (three term test) = 1.118e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0106 0.481 h = 0.003 0.006 y[1] (numeric) = 0.208655885506 0.10587845273 y[1] (closed_form) = 0.208647362136 0.105890610346 absolute error = 1.485e-05 relative error = 0.006346 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.067 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.466 Order of pole (three term test) = 3.938e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0076 0.487 h = 0.0001 0.005 y[1] (numeric) = 0.208289789345 0.107351170702 y[1] (closed_form) = 0.208277830269 0.107365137469 absolute error = 1.839e-05 relative error = 0.007847 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.066 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.54 Order of pole (three term test) = 5.702e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0075 0.492 h = 0.0001 0.003 y[1] (numeric) = 0.207559260517 0.108220780416 y[1] (closed_form) = 0.207549716597 0.10823400158 absolute error = 1.631e-05 relative error = 0.006966 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.067 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.241 Order of pole (three term test) = 2.777e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0074 0.495 h = 0.001 0.001 y[1] (numeric) = 0.207126187628 0.108744170199 y[1] (closed_form) = 0.207117230547 0.10875818334 absolute error = 1.663e-05 relative error = 0.007109 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.068 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9741 Order of pole (three term test) = 6.163e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0064 0.496 h = 0.001 0.003 y[1] (numeric) = 0.207144722541 0.109063517248 y[1] (closed_form) = 0.207136183684 0.109077820947 absolute error = 1.666e-05 relative error = 0.007116 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.067 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.622 Order of pole (three term test) = 6.087e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0054 0.499 h = 0.0001 0.004 y[1] (numeric) = 0.206861534611 0.10972194752 y[1] (closed_form) = 0.20685216774 0.109735621151 absolute error = 1.657e-05 relative error = 0.007078 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.067 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.615 Order of pole (three term test) = 6.940e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0053 0.503 h = 0.003 0.006 y[1] (numeric) = 0.206271122727 0.110410351696 y[1] (closed_form) = 0.206261859247 0.110423146279 absolute error = 1.580e-05 relative error = 0.006752 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.067 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.466 Order of pole (three term test) = 1.183e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0023 0.509 h = 0.0001 0.005 y[1] (numeric) = 0.205856947789 0.111870027411 y[1] (closed_form) = 0.205844173561 0.111884478612 absolute error = 1.929e-05 relative error = 0.008233 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.066 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.54 Order of pole (three term test) = 1.143e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0022 0.514 h = 0.0001 0.003 y[1] (numeric) = 0.205098448654 0.112714917918 y[1] (closed_form) = 0.205088118969 0.11272873027 absolute error = 1.725e-05 relative error = 0.00737 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.067 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.241 Order of pole (three term test) = 9.285e-14 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=272.7MB, alloc=44.3MB, time=3.51 x[1] = -2.0021 0.517 h = 0.001 0.001 y[1] (numeric) = 0.204648584311 0.113223632196 y[1] (closed_form) = 0.204638805985 0.113238261067 absolute error = 1.760e-05 relative error = 0.007524 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.068 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9742 Order of pole (three term test) = 8.836e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.0011 0.518 h = 0.0001 0.004 y[1] (numeric) = 0.20465662507 0.113543294393 y[1] (closed_form) = 0.20464725165 0.11355823169 absolute error = 1.763e-05 relative error = 0.007535 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.067 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.848 Order of pole (three term test) = 3.053e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -2.001 0.522 h = 0.003 0.006 y[1] (numeric) = 0.204048174342 0.114215328644 y[1] (closed_form) = 0.204038216358 0.114228291511 absolute error = 1.635e-05 relative error = 0.00699 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.068 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.467 Order of pole (three term test) = 1.590e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.998 0.528 h = 0.0001 0.005 y[1] (numeric) = 0.203593310611 0.115661545429 y[1] (closed_form) = 0.203579785955 0.115676029815 absolute error = 1.982e-05 relative error = 0.008463 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.067 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.541 Order of pole (three term test) = 2.883e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9979 0.533 h = 0.0001 0.003 y[1] (numeric) = 0.202811948678 0.116483891985 y[1] (closed_form) = 0.202800887843 0.116497830771 absolute error = 1.779e-05 relative error = 0.007608 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.068 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.241 Order of pole (three term test) = 9.373e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9978 0.536 h = 0.001 0.001 y[1] (numeric) = 0.202348351785 0.116979215186 y[1] (closed_form) = 0.202337810499 0.116993989576 absolute error = 1.815e-05 relative error = 0.007765 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.068 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9745 Order of pole (three term test) = 8.923e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9968 0.537 h = 0.001 0.003 y[1] (numeric) = 0.202347365542 0.117298655967 y[1] (closed_form) = 0.202337216738 0.117313753376 absolute error = 1.819e-05 relative error = 0.007778 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.068 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.624 Order of pole (three term test) = 1.234e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9958 0.54 h = 0.0001 0.004 y[1] (numeric) = 0.202024948712 0.117937672386 y[1] (closed_form) = 0.202014027378 0.117952075749 absolute error = 1.808e-05 relative error = 0.007727 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.068 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.616 Order of pole (three term test) = 6.299e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9957 0.544 h = 0.003 0.006 y[1] (numeric) = 0.201394560356 0.11858775371 y[1] (closed_form) = 0.201383813233 0.118601291131 absolute error = 1.728e-05 relative error = 0.007396 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.069 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.468 Order of pole (three term test) = 8.012e-15 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9927 0.55 h = 0.0001 0.005 y[1] (numeric) = 0.200892919445 0.120017090733 y[1] (closed_form) = 0.200878546631 0.120031990664 absolute error = 2.070e-05 relative error = 0.008847 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.067 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.541 Order of pole (three term test) = 6.164e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9926 0.555 h = 0.0001 0.003 y[1] (numeric) = 0.200085745887 0.120812578088 y[1] (closed_form) = 0.200073855226 0.120827041323 absolute error = 1.872e-05 relative error = 0.008011 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.068 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.242 Order of pole (three term test) = 9.653e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9925 0.558 h = 0.001 0.001 y[1] (numeric) = 0.199606640928 0.121291944232 y[1] (closed_form) = 0.199595232132 0.121307263825 absolute error = 1.910e-05 relative error = 0.008178 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.069 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9749 Order of pole (three term test) = 1.275e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9915 0.559 h = 0.001 0.003 y[1] (numeric) = 0.199595193624 0.121610847146 y[1] (closed_form) = 0.199584162287 0.121626506134 absolute error = 1.915e-05 relative error = 0.008195 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.068 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.625 Order of pole (three term test) = 8.731e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9905 0.562 h = 0.0001 0.004 y[1] (numeric) = 0.199252345949 0.122238280305 y[1] (closed_form) = 0.199240574231 0.122253213156 absolute error = 1.901e-05 relative error = 0.008134 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.068 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.617 Order of pole (three term test) = 1.007e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9904 0.566 h = 0.003 0.006 y[1] (numeric) = 0.198601698734 0.12286662851 y[1] (closed_form) = 0.198590138606 0.122880705156 absolute error = 1.822e-05 relative error = 0.0078 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.069 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.469 Order of pole (three term test) = 5.731e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9874 0.572 h = 0.0001 0.005 y[1] (numeric) = 0.198054124833 0.124277082493 y[1] (closed_form) = 0.198038888857 0.124292359931 absolute error = 2.158e-05 relative error = 0.009228 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.068 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.542 Order of pole (three term test) = 8.332e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9873 0.577 h = 0.0001 0.003 y[1] (numeric) = 0.197222376826 0.125044649102 y[1] (closed_form) = 0.197209635331 0.125059599379 absolute error = 1.964e-05 relative error = 0.008412 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.069 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.242 Order of pole (three term test) = 1.343e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9872 0.58 h = 0.001 0.001 y[1] (numeric) = 0.196728499517 0.125507422139 y[1] (closed_form) = 0.196716201203 0.1255232474 absolute error = 2.004e-05 relative error = 0.008589 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.07 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9753 Order of pole (three term test) = 4.570e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9862 0.581 h = 0.001 0.003 y[1] (numeric) = 0.196706641658 0.125825332263 y[1] (closed_form) = 0.196694704941 0.125841512418 absolute error = 2.011e-05 relative error = 0.008611 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.069 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.627 Order of pole (three term test) = 1.274e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9852 0.584 h = 0.0001 0.004 y[1] (numeric) = 0.19634392177 0.126440320445 y[1] (closed_form) = 0.196331278455 0.12645574424 absolute error = 1.994e-05 relative error = 0.00854 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.069 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.618 Order of pole (three term test) = 9.138e-14 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=319.4MB, alloc=44.3MB, time=4.11 x[1] = -1.9851 0.588 h = 0.003 0.006 y[1] (numeric) = 0.195674018454 0.12704610975 y[1] (closed_form) = 0.19566162344 0.127060689078 absolute error = 1.914e-05 relative error = 0.008202 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.07 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.471 Order of pole (three term test) = 8.229e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9821 0.594 h = 0.0001 0.005 y[1] (numeric) = 0.195081462008 0.128435730357 y[1] (closed_form) = 0.19506534999 0.12845134664 absolute error = 2.244e-05 relative error = 0.009607 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.069 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.543 Order of pole (three term test) = 1.339e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.982 0.599 h = 0.0001 0.003 y[1] (numeric) = 0.194226430078 0.129174386055 y[1] (closed_form) = 0.194212818851 0.129189784949 absolute error = 2.055e-05 relative error = 0.008811 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.071 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.243 Order of pole (three term test) = 1.091e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9819 0.602 h = 0.001 0.001 y[1] (numeric) = 0.193718548003 0.129619972405 y[1] (closed_form) = 0.193705340418 0.129636262727 absolute error = 2.097e-05 relative error = 0.008998 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.071 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9759 Order of pole (three term test) = 1.002e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9809 0.603 h = 0.001 0.003 y[1] (numeric) = 0.193686354673 0.129936439304 y[1] (closed_form) = 0.193673492044 0.129953099095 absolute error = 2.105e-05 relative error = 0.009024 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.071 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.63 Order of pole (three term test) = 6.437e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9799 0.606 h = 0.0001 0.004 y[1] (numeric) = 0.193304366011 0.130538154539 y[1] (closed_form) = 0.193290832073 0.130554029709 absolute error = 2.086e-05 relative error = 0.008944 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.071 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.62 Order of pole (three term test) = 9.305e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9798 0.61 h = 0.003 0.006 y[1] (numeric) = 0.192616250377 0.131120617039 y[1] (closed_form) = 0.192603000655 0.131135661429 absolute error = 2.005e-05 relative error = 0.008604 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.072 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.473 Order of pole (three term test) = 4.192e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9768 0.616 h = 0.0001 0.005 y[1] (numeric) = 0.191979764113 0.132487513557 y[1] (closed_form) = 0.191962765321 0.132503429546 absolute error = 2.329e-05 relative error = 0.009984 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.071 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.544 Order of pole (three term test) = 6.107e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9767 0.621 h = 0.0001 0.003 y[1] (numeric) = 0.191102787201 0.133196342681 y[1] (closed_form) = 0.191088289512 0.133212150893 absolute error = 2.145e-05 relative error = 0.009208 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.072 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.244 Order of pole (three term test) = 1.408e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9766 0.624 h = 0.001 0.001 y[1] (numeric) = 0.190581696874 0.133624193091 y[1] (closed_form) = 0.190567562577 0.133640906953 absolute error = 2.189e-05 relative error = 0.009404 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.073 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9766 Order of pole (three term test) = 9.498e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9756 0.625 h = 0.0001 0.004 y[1] (numeric) = 0.19053926731 0.133938772402 y[1] (closed_form) = 0.190525460614 0.133955869331 absolute error = 2.198e-05 relative error = 0.009436 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.072 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.863 Order of pole (three term test) = 8.574e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9755 0.629 h = 0.003 0.006 y[1] (numeric) = 0.189837096441 0.134501603572 y[1] (closed_form) = 0.189823136032 0.134516667503 absolute error = 2.054e-05 relative error = 0.008828 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.073 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.476 Order of pole (three term test) = 4.619e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9725 0.635 h = 0.0001 0.005 y[1] (numeric) = 0.189164014768 0.13584697171 y[1] (closed_form) = 0.189146286985 0.135862763916 absolute error = 2.374e-05 relative error = 0.01019 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.072 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.545 Order of pole (three term test) = 9.888e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9724 0.64 h = 0.0001 0.003 y[1] (numeric) = 0.188269622407 0.136529213869 y[1] (closed_form) = 0.188254389931 0.136544992133 absolute error = 2.193e-05 relative error = 0.00943 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.074 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.245 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9723 0.643 h = 0.001 0.001 y[1] (numeric) = 0.187738039833 0.136941249048 y[1] (closed_form) = 0.187723135517 0.136957942905 absolute error = 2.238e-05 relative error = 0.009631 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.074 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9774 Order of pole (three term test) = 9.735e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9713 0.644 h = 0.001 0.003 y[1] (numeric) = 0.187686926317 0.137253733631 y[1] (closed_form) = 0.187672333999 0.137270821236 absolute error = 2.247e-05 relative error = 0.009664 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.074 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.637 Order of pole (three term test) = 6.740e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9703 0.647 h = 0.0001 0.004 y[1] (numeric) = 0.187271011848 0.137828463551 y[1] (closed_form) = 0.187255817696 0.137844719926 absolute error = 2.225e-05 relative error = 0.00957 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.074 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.624 Order of pole (three term test) = 1.463e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9702 0.651 h = 0.003 0.006 y[1] (numeric) = 0.186552205765 0.138365498401 y[1] (closed_form) = 0.186537359916 0.138380954825 absolute error = 2.143e-05 relative error = 0.009227 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.075 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.479 Order of pole (three term test) = 8.299e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9672 0.657 h = 0.0001 0.005 y[1] (numeric) = 0.185837430345 0.139684819576 y[1] (closed_form) = 0.185818802058 0.1397008378 absolute error = 2.457e-05 relative error = 0.01057 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.074 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.546 Order of pole (three term test) = 7.328e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9671 0.662 h = 0.0001 0.003 y[1] (numeric) = 0.184923704274 0.140335755708 y[1] (closed_form) = 0.184907560601 0.140351868204 absolute error = 2.281e-05 relative error = 0.009825 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.076 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.246 Order of pole (three term test) = 1.095e-13 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=366.2MB, alloc=44.3MB, time=4.72 x[1] = -1.967 0.665 h = 0.001 0.001 y[1] (numeric) = 0.184380467242 0.14072916643 y[1] (closed_form) = 0.184364610587 0.140746204519 absolute error = 2.328e-05 relative error = 0.01003 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.076 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9783 Order of pole (three term test) = 1.001e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.966 0.666 h = 0.001 0.003 y[1] (numeric) = 0.184319369557 0.141038959773 y[1] (closed_form) = 0.184303806414 0.141056403291 absolute error = 2.338e-05 relative error = 0.01007 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.076 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.642 Order of pole (three term test) = 2.772e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.965 0.669 h = 0.0001 0.004 y[1] (numeric) = 0.18388614572 0.141598266913 y[1] (closed_form) = 0.183870019537 0.141614857018 absolute error = 2.314e-05 relative error = 0.009969 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.076 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.626 Order of pole (three term test) = 7.093e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9649 0.673 h = 0.003 0.006 y[1] (numeric) = 0.183152310137 0.142110131299 y[1] (closed_form) = 0.183136565223 0.142125940318 absolute error = 2.231e-05 relative error = 0.009625 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.077 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.482 Order of pole (three term test) = 1.012e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9619 0.679 h = 0.0001 0.005 y[1] (numeric) = 0.18239715924 0.143401720027 y[1] (closed_form) = 0.182377625912 0.143417924564 absolute error = 2.538e-05 relative error = 0.01094 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.076 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.548 Order of pole (three term test) = 3.308e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9618 0.684 h = 0.0001 0.003 y[1] (numeric) = 0.181465546983 0.144020661589 y[1] (closed_form) = 0.181448481797 0.144037067361 absolute error = 2.367e-05 relative error = 0.01022 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.078 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.247 Order of pole (three term test) = 1.129e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9617 0.687 h = 0.001 0.001 y[1] (numeric) = 0.180911516969 0.144395033745 y[1] (closed_form) = 0.180894697377 0.144412372825 absolute error = 2.416e-05 relative error = 0.01044 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.079 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9793 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9607 0.688 h = 0.001 0.003 y[1] (numeric) = 0.180840599959 0.144701717402 y[1] (closed_form) = 0.180824054878 0.144719472519 absolute error = 2.427e-05 relative error = 0.01048 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.078 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.646 Order of pole (three term test) = 1.574e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9597 0.691 h = 0.0001 0.004 y[1] (numeric) = 0.180390818124 0.145244928327 y[1] (closed_form) = 0.180373749749 0.145261810084 absolute error = 2.401e-05 relative error = 0.01037 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.078 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.629 Order of pole (three term test) = 3.661e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9596 0.695 h = 0.003 0.006 y[1] (numeric) = 0.179643115667 0.145731097323 y[1] (closed_form) = 0.179626460293 0.145747218516 absolute error = 2.318e-05 relative error = 0.01002 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.079 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.486 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9566 0.701 h = 0.0001 0.005 y[1] (numeric) = 0.178848990237 0.146993349892 y[1] (closed_form) = 0.17882854948 0.147009701102 absolute error = 2.618e-05 relative error = 0.01131 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.078 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.549 Order of pole (three term test) = 4.836e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9565 0.706 h = 0.0001 0.003 y[1] (numeric) = 0.17790096707 0.14757969099 y[1] (closed_form) = 0.177882972326 0.14759634878 absolute error = 2.452e-05 relative error = 0.01061 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.08 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.248 Order of pole (three term test) = 2.240e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9564 0.709 h = 0.001 0.001 y[1] (numeric) = 0.177337022186 0.147934659648 y[1] (closed_form) = 0.177319231484 0.147952256177 absolute error = 2.502e-05 relative error = 0.01084 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.081 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9804 Order of pole (three term test) = 4.274e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9554 0.71 h = 0.001 0.003 y[1] (numeric) = 0.177256472147 0.148237826837 y[1] (closed_form) = 0.177238936518 0.148255848916 absolute error = 2.515e-05 relative error = 0.01088 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.08 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.652 Order of pole (three term test) = 1.488e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9544 0.713 h = 0.0001 0.004 y[1] (numeric) = 0.176790914989 0.14876431312 y[1] (closed_form) = 0.176772896607 0.14878144417 absolute error = 2.486e-05 relative error = 0.01076 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.08 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.632 Order of pole (three term test) = 1.934e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9543 0.717 h = 0.003 0.006 y[1] (numeric) = 0.176030528703 0.149224328018 y[1] (closed_form) = 0.176012953725 0.149240720589 absolute error = 2.403e-05 relative error = 0.01041 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.082 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.49 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9513 0.723 h = 0.0001 0.005 y[1] (numeric) = 0.175198906396 0.150455727154 y[1] (closed_form) = 0.175177557943 0.150472185596 absolute error = 2.696e-05 relative error = 0.01167 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.081 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.551 Order of pole (three term test) = 7.096e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9512 0.728 h = 0.0001 0.003 y[1] (numeric) = 0.174235969764 0.151008945632 y[1] (closed_form) = 0.174217039697 0.151025814032 absolute error = 2.536e-05 relative error = 0.011 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.083 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.25 Order of pole (three term test) = 1.161e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9511 0.731 h = 0.001 0.001 y[1] (numeric) = 0.173663001445 0.151344195687 y[1] (closed_form) = 0.173644233884 0.151362005987 absolute error = 2.587e-05 relative error = 0.01123 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.084 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9816 Order of pole (three term test) = 2.220e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9501 0.732 h = 0.0001 0.004 y[1] (numeric) = 0.173573025191 0.151643452576 y[1] (closed_form) = 0.1735544929 0.151661696823 absolute error = 2.601e-05 relative error = 0.01128 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.083 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.893 Order of pole (three term test) = 6.724e-14 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=413.0MB, alloc=44.3MB, time=5.32 x[1] = -1.95 0.736 h = 0.003 0.006 y[1] (numeric) = 0.172803197418 0.152081767171 y[1] (closed_form) = 0.172784934348 0.152098033354 absolute error = 2.446e-05 relative error = 0.01062 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.084 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.494 Order of pole (three term test) = 1.050e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.947 0.742 h = 0.0001 0.005 y[1] (numeric) = 0.171940926706 0.15328504139 y[1] (closed_form) = 0.171918909312 0.153301233945 absolute error = 2.733e-05 relative error = 0.01187 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.084 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.553 Order of pole (three term test) = 1.106e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9469 0.747 h = 0.0001 0.003 y[1] (numeric) = 0.170966766424 0.153809242247 y[1] (closed_form) = 0.170947138175 0.153825931498 absolute error = 2.576e-05 relative error = 0.0112 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.085 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.252 Order of pole (three term test) = 1.624e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9468 0.75 h = 0.001 0.001 y[1] (numeric) = 0.170386991645 0.154127212345 y[1] (closed_form) = 0.170367490275 0.154144843923 absolute error = 2.629e-05 relative error = 0.01144 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.086 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9829 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9458 0.751 h = 0.001 0.003 y[1] (numeric) = 0.170289134839 0.154422690208 y[1] (closed_form) = 0.170269851377 0.154440761819 absolute error = 2.643e-05 relative error = 0.0115 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.086 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.664 Order of pole (three term test) = 1.608e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9448 0.754 h = 0.0001 0.004 y[1] (numeric) = 0.169796615232 0.15491637934 y[1] (closed_form) = 0.169776926191 0.154933533708 absolute error = 2.611e-05 relative error = 0.01136 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.086 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.639 Order of pole (three term test) = 1.231e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9447 0.758 h = 0.0001 0.004 y[1] (numeric) = 0.169016148736 0.155326619141 y[1] (closed_form) = 0.168996955539 0.155343080256 absolute error = 2.529e-05 relative error = 0.01102 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.087 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.087 Order of pole (three term test) = 2.950e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9446 0.762 h = 0.003 0.006 y[1] (numeric) = 0.168235501173 0.155731149641 y[1] (closed_form) = 0.168216307977 0.155747610756 absolute error = 2.529e-05 relative error = 0.01103 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.089 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.502 Order of pole (three term test) = 6.853e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9416 0.768 h = 0.0001 0.005 y[1] (numeric) = 0.167334145438 0.156893864916 y[1] (closed_form) = 0.167311237364 0.1569100662 absolute error = 2.806e-05 relative error = 0.01223 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.088 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.557 Order of pole (three term test) = 1.194e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9415 0.773 h = 0.0001 0.003 y[1] (numeric) = 0.166347230136 0.157377921597 y[1] (closed_form) = 0.16632666332 0.157394733643 absolute error = 2.656e-05 relative error = 0.0116 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.09 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.254 Order of pole (three term test) = 1.029e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9414 0.776 h = 0.001 0.001 y[1] (numeric) = 0.165759692629 0.15767197787 y[1] (closed_form) = 0.165739204631 0.157689729344 absolute error = 2.711e-05 relative error = 0.01185 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.091 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.985 Order of pole (three term test) = 4.923e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9404 0.777 h = 0.001 0.003 y[1] (numeric) = 0.165651501464 0.157961695797 y[1] (closed_form) = 0.165631207379 0.157979893813 absolute error = 2.726e-05 relative error = 0.01191 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.09 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.674 Order of pole (three term test) = 3.413e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9394 0.78 h = 0.0001 0.004 y[1] (numeric) = 0.165144056792 0.158433458914 y[1] (closed_form) = 0.165123406694 0.158450728564 absolute error = 2.692e-05 relative error = 0.01176 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.09 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.645 Order of pole (three term test) = 2.769e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9393 0.784 h = 0.003 0.006 y[1] (numeric) = 0.164353904891 0.158811602221 y[1] (closed_form) = 0.16433378013 0.15882821012 absolute error = 2.609e-05 relative error = 0.01142 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.092 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.507 Order of pole (three term test) = 1.121e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9363 0.79 h = 0.0001 0.005 y[1] (numeric) = 0.163419996765 0.15993951324 y[1] (closed_form) = 0.163396194603 0.159955705001 absolute error = 2.879e-05 relative error = 0.01259 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.091 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.559 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9362 0.795 h = 0.0001 0.003 y[1] (numeric) = 0.162422799992 0.160389455105 y[1] (closed_form) = 0.162401296115 0.16040635283 absolute error = 2.735e-05 relative error = 0.01198 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.093 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.256 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9361 0.798 h = 0.001 0.001 y[1] (numeric) = 0.16182899749 0.160663189098 y[1] (closed_form) = 0.161807531933 0.16068102273 absolute error = 2.791e-05 relative error = 0.01224 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.094 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9866 Order of pole (three term test) = 2.583e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9351 0.799 h = 0.001 0.003 y[1] (numeric) = 0.161712138726 0.160947906266 y[1] (closed_form) = 0.161690846686 0.160966191399 absolute error = 2.807e-05 relative error = 0.0123 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.094 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.681 Order of pole (three term test) = 1.791e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9341 0.802 h = 0.0001 0.004 y[1] (numeric) = 0.161192347473 0.161400939324 y[1] (closed_form) = 0.161170741499 0.161418287811 absolute error = 2.771e-05 relative error = 0.01215 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.094 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.649 Order of pole (three term test) = 4.597e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.934 0.806 h = 0.003 0.006 y[1] (numeric) = 0.160394407809 0.161751819947 y[1] (closed_form) = 0.160373351353 0.161768533923 absolute error = 2.688e-05 relative error = 0.0118 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.095 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.513 Order of pole (three term test) = 1.316e-13 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=459.8MB, alloc=44.3MB, time=5.92 x[1] = -1.931 0.812 h = 0.0001 0.005 y[1] (numeric) = 0.159429663695 0.162843797368 y[1] (closed_form) = 0.159404975249 0.162859942361 absolute error = 2.950e-05 relative error = 0.01294 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.095 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.562 Order of pole (three term test) = 4.329e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9309 0.817 h = 0.0001 0.003 y[1] (numeric) = 0.158423711754 0.163259442241 y[1] (closed_form) = 0.158401273987 0.163276385206 absolute error = 2.812e-05 relative error = 0.01236 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.097 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.258 Order of pole (three term test) = 5.682e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9308 0.82 h = 0.001 0.001 y[1] (numeric) = 0.157824553409 0.163512741187 y[1] (closed_form) = 0.157802114044 0.16353061443 absolute error = 2.869e-05 relative error = 0.01262 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.098 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9883 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9298 0.821 h = 0.001 0.003 y[1] (numeric) = 0.1576993046 0.16379212795 y[1] (closed_form) = 0.157677018293 0.163810456524 absolute error = 2.886e-05 relative error = 0.01269 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.097 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.689 Order of pole (three term test) = 2.109e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9288 0.824 h = 0.0001 0.004 y[1] (numeric) = 0.15716805487 0.164226049163 y[1] (closed_form) = 0.157145496732 0.16424343512 absolute error = 2.848e-05 relative error = 0.01253 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.097 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.654 Order of pole (three term test) = 4.844e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9287 0.828 h = 0.003 0.006 y[1] (numeric) = 0.156363542778 0.164549545762 y[1] (closed_form) = 0.156341556664 0.164566325457 absolute error = 2.766e-05 relative error = 0.01218 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.099 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.519 Order of pole (three term test) = 6.207e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9257 0.834 h = 0.0001 0.005 y[1] (numeric) = 0.155369722253 0.165604561986 y[1] (closed_form) = 0.155344157179 0.165620623776 absolute error = 3.019e-05 relative error = 0.0133 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.099 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.564 Order of pole (three term test) = 4.568e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9256 0.839 h = 0.0001 0.003 y[1] (numeric) = 0.154356536015 0.165985810247 y[1] (closed_form) = 0.15433316964 0.166002758571 absolute error = 2.887e-05 relative error = 0.01274 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.1 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.261 Order of pole (three term test) = 1.756e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9255 0.842 h = 0.001 0.001 y[1] (numeric) = 0.153752927886 0.166218610518 y[1] (closed_form) = 0.153729520699 0.166236481444 absolute error = 2.945e-05 relative error = 0.01301 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.102 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9901 Order of pole (three term test) = 1.437e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9245 0.843 h = 0.001 0.003 y[1] (numeric) = 0.153619581217 0.166492355175 y[1] (closed_form) = 0.153596306638 0.166510684146 absolute error = 2.963e-05 relative error = 0.01308 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.101 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.698 Order of pole (three term test) = 9.965e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9235 0.846 h = 0.0001 0.004 y[1] (numeric) = 0.153077772381 0.166906833492 y[1] (closed_form) = 0.153054267956 0.166924216154 absolute error = 2.923e-05 relative error = 0.01291 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.101 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.659 Order of pole (three term test) = 1.054e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9234 0.85 h = 0.003 0.006 y[1] (numeric) = 0.152267897313 0.167202890102 y[1] (closed_form) = 0.152244985693 0.167219695642 absolute error = 2.841e-05 relative error = 0.01256 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.103 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.525 Order of pole (three term test) = 6.565e-15 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9204 0.856 h = 0.0001 0.005 y[1] (numeric) = 0.151246796166 0.168220020755 y[1] (closed_form) = 0.151220365893 0.168235963824 absolute error = 3.087e-05 relative error = 0.01365 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.103 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.567 Order of pole (three term test) = 1.104e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9203 0.861 h = 0.0001 0.003 y[1] (numeric) = 0.15022788591 0.168566853966 y[1] (closed_form) = 0.150203598258 0.168583768452 absolute error = 2.960e-05 relative error = 0.01311 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.104 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.263 Order of pole (three term test) = 6.357e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9202 0.864 h = 0.001 0.001 y[1] (numeric) = 0.149620727904 0.168779140259 y[1] (closed_form) = 0.14959636105 0.168796967696 absolute error = 3.019e-05 relative error = 0.01339 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.106 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9921 Order of pole (three term test) = 1.530e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9192 0.865 h = 0.0001 0.004 y[1] (numeric) = 0.14947958887 0.169046949755 y[1] (closed_form) = 0.149455334251 0.169065236847 absolute error = 3.038e-05 relative error = 0.01346 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.105 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.956 Order of pole (three term test) = 3.959e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9191 0.869 h = 0.003 0.006 y[1] (numeric) = 0.148666262079 0.169320563073 y[1] (closed_form) = 0.148642739433 0.169337082578 absolute error = 2.874e-05 relative error = 0.01276 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.107 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.532 Order of pole (three term test) = 1.250e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9161 0.875 h = 0.0001 0.005 y[1] (numeric) = 0.147623603545 0.170304127085 y[1] (closed_form) = 0.147596621344 0.170319664303 absolute error = 3.114e-05 relative error = 0.01382 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.106 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.57 Order of pole (three term test) = 7.986e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.916 0.88 h = 0.0001 0.003 y[1] (numeric) = 0.146601372657 0.170621338915 y[1] (closed_form) = 0.146576480793 0.170637916781 absolute error = 2.991e-05 relative error = 0.0133 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.108 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.266 Order of pole (three term test) = 1.714e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9159 0.883 h = 0.001 0.001 y[1] (numeric) = 0.145992116505 0.170815963483 y[1] (closed_form) = 0.145967113288 0.170833444026 absolute error = 3.051e-05 relative error = 0.01358 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.11 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9939 Order of pole (three term test) = 6.444e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9149 0.884 h = 0.001 0.003 y[1] (numeric) = 0.145844598956 0.171078356538 y[1] (closed_form) = 0.14581969055 0.171096297015 absolute error = 3.070e-05 relative error = 0.01365 % Correct digits = 4 memory used=506.7MB, alloc=44.3MB, time=6.52 Radius of convergence (given) for eq 1 = 2.109 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.716 Order of pole (three term test) = 3.162e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9139 0.887 h = 0.0001 0.004 y[1] (numeric) = 0.145285799059 0.171455848743 y[1] (closed_form) = 0.145260738114 0.171472842469 absolute error = 3.028e-05 relative error = 0.01347 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.109 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.669 Order of pole (three term test) = 1.150e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9138 0.891 h = 0.003 0.006 y[1] (numeric) = 0.144469452306 0.171700885257 y[1] (closed_form) = 0.144445017781 0.171717358244 absolute error = 2.947e-05 relative error = 0.01313 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.111 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.539 Order of pole (three term test) = 7.377e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9108 0.897 h = 0.0001 0.005 y[1] (numeric) = 0.143402935308 0.172645143355 y[1] (closed_form) = 0.143375114008 0.172660498707 absolute error = 3.178e-05 relative error = 0.01416 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.111 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.574 Order of pole (three term test) = 7.701e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9107 0.902 h = 0.0001 0.003 y[1] (numeric) = 0.142377743648 0.172928133171 y[1] (closed_form) = 0.142351949797 0.172944606631 absolute error = 3.061e-05 relative error = 0.01366 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.113 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.268 Order of pole (three term test) = 1.827e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9106 0.905 h = 0.001 0.001 y[1] (numeric) = 0.141766584597 0.173102350663 y[1] (closed_form) = 0.141740642852 0.1731197137 absolute error = 3.122e-05 relative error = 0.01395 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.114 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.996 Order of pole (three term test) = 2.097e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9096 0.906 h = 0.001 0.003 y[1] (numeric) = 0.141611876874 0.17335831875 y[1] (closed_form) = 0.141586009906 0.17337614134 absolute error = 3.141e-05 relative error = 0.01403 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.114 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.726 Order of pole (three term test) = 4.775e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9086 0.909 h = 0.0001 0.004 y[1] (numeric) = 0.141045125209 0.173715711635 y[1] (closed_form) = 0.141019146554 0.173732590061 absolute error = 3.098e-05 relative error = 0.01385 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.114 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.675 Order of pole (three term test) = 1.371e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9085 0.913 h = 0.003 0.006 y[1] (numeric) = 0.140226805522 0.173933510963 y[1] (closed_form) = 0.140201468984 0.173949899657 absolute error = 3.017e-05 relative error = 0.01351 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.116 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.547 Order of pole (three term test) = 1.114e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9055 0.919 h = 0.0001 0.005 y[1] (numeric) = 0.139138289884 0.174837837704 y[1] (closed_form) = 0.139109645506 0.174852978816 absolute error = 3.240e-05 relative error = 0.0145 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.116 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.577 Order of pole (three term test) = 8.229e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9054 0.924 h = 0.0001 0.003 y[1] (numeric) = 0.138111589829 0.175086808288 y[1] (closed_form) = 0.138084906757 0.175103140765 absolute error = 3.128e-05 relative error = 0.01403 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.118 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.271 Order of pole (three term test) = 1.915e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9053 0.927 h = 0.001 0.001 y[1] (numeric) = 0.137499393761 0.175240735134 y[1] (closed_form) = 0.137472527382 0.175257942353 absolute error = 3.190e-05 relative error = 0.01432 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.119 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9983 Order of pole (three term test) = 1.837e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9043 0.928 h = 0.001 0.003 y[1] (numeric) = 0.137337831689 0.175490041514 y[1] (closed_form) = 0.137311020318 0.175507706872 absolute error = 3.211e-05 relative error = 0.01441 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.118 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.737 Order of pole (three term test) = 1.275e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9033 0.931 h = 0.0001 0.004 y[1] (numeric) = 0.136764039668 0.17582719834 y[1] (closed_form) = 0.136737156824 0.175843924207 absolute error = 3.166e-05 relative error = 0.01421 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.119 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.681 Order of pole (three term test) = 1.313e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9032 0.935 h = 0.003 0.006 y[1] (numeric) = 0.135944896529 0.176017942916 y[1] (closed_form) = 0.135918669703 0.176034210483 absolute error = 3.086e-05 relative error = 0.01388 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.12 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.555 Order of pole (three term test) = 9.427e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9002 0.941 h = 0.0001 0.005 y[1] (numeric) = 0.134836251763 0.176881816825 y[1] (closed_form) = 0.134806801757 0.176896712567 absolute error = 3.300e-05 relative error = 0.01484 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.12 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.581 Order of pole (three term test) = 6.237e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9001 0.946 h = 0.0001 0.003 y[1] (numeric) = 0.133809467155 0.177097043627 y[1] (closed_form) = 0.133781909371 0.177113199649 absolute error = 3.194e-05 relative error = 0.01439 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.123 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.274 Order of pole (three term test) = 6.163e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.9 0.949 h = 0.001 0.001 y[1] (numeric) = 0.133197083131 0.177230839542 y[1] (closed_form) = 0.133169307841 0.177247853836 absolute error = 3.257e-05 relative error = 0.01469 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.124 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.001 Order of pole (three term test) = 9.855e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.899 0.95 h = 0.001 0.003 y[1] (numeric) = 0.133029010555 0.177473267782 y[1] (closed_form) = 0.13300127083 0.1774907378 absolute error = 3.278e-05 relative error = 0.01478 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.123 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.748 Order of pole (three term test) = 5.474e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.898 0.953 h = 0.0001 0.004 y[1] (numeric) = 0.132449085222 0.177790100615 y[1] (closed_form) = 0.132421313483 0.177806637827 absolute error = 3.232e-05 relative error = 0.01458 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.124 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.687 Order of pole (three term test) = 7.082e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8979 0.957 h = 0.003 0.006 y[1] (numeric) = 0.131630244174 0.177954029902 y[1] (closed_form) = 0.131603140554 0.177970140556 absolute error = 3.153e-05 relative error = 0.01424 % Correct digits = 4 memory used=553.6MB, alloc=44.3MB, time=7.12 Radius of convergence (given) for eq 1 = 2.126 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.564 Order of pole (three term test) = 9.456e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8949 0.963 h = 0.0001 0.005 y[1] (numeric) = 0.130503342897 0.178777032486 y[1] (closed_form) = 0.130473106044 0.178791653042 absolute error = 3.359e-05 relative error = 0.01517 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.126 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.585 Order of pole (three term test) = 1.341e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8948 0.968 h = 0.0001 0.003 y[1] (numeric) = 0.129477864998 0.178958860737 y[1] (closed_form) = 0.129449448652 0.178974806029 absolute error = 3.258e-05 relative error = 0.01475 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.128 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.277 Order of pole (three term test) = 4.941e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8947 0.971 h = 0.001 0.001 y[1] (numeric) = 0.128866122847 0.17907272701 y[1] (closed_form) = 0.128837456094 0.17908951257 absolute error = 3.322e-05 relative error = 0.01506 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.129 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.003 Order of pole (three term test) = 1.544e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8937 0.972 h = 0.0001 0.004 y[1] (numeric) = 0.128691890257 0.179308081158 y[1] (closed_form) = 0.128663240007 0.179325319063 absolute error = 3.344e-05 relative error = 0.01515 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.129 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.022 Order of pole (three term test) = 1.288e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8936 0.976 h = 0.003 0.006 y[1] (numeric) = 0.127874154563 0.179450299461 y[1] (closed_form) = 0.127846530945 0.179466022572 absolute error = 3.178e-05 relative error = 0.01442 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.13 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.572 Order of pole (three term test) = 1.130e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8906 0.982 h = 0.0001 0.005 y[1] (numeric) = 0.126733527643 0.180237676645 y[1] (closed_form) = 0.126702853411 0.180251813953 absolute error = 3.378e-05 relative error = 0.01533 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.13 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.588 Order of pole (three term test) = 7.323e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8905 0.987 h = 0.0001 0.003 y[1] (numeric) = 0.125710651952 0.180391121399 y[1] (closed_form) = 0.125681733939 0.180406634401 absolute error = 3.282e-05 relative error = 0.01493 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.133 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.28 Order of pole (three term test) = 2.144e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8904 0.99 h = 0.001 0.001 y[1] (numeric) = 0.125100343871 0.180488045163 y[1] (closed_form) = 0.125071148463 0.180504381413 absolute error = 3.346e-05 relative error = 0.01523 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.134 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.005 Order of pole (three term test) = 5.083e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8894 0.991 h = 0.001 0.003 y[1] (numeric) = 0.124921180735 0.180717101354 y[1] (closed_form) = 0.124891985822 0.180733886079 absolute error = 3.368e-05 relative error = 0.01533 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.134 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.771 Order of pole (three term test) = 7.062e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8884 0.994 h = 0.0001 0.004 y[1] (numeric) = 0.124332472121 0.180995996709 y[1] (closed_form) = 0.124303316097 0.18101186659 absolute error = 3.320e-05 relative error = 0.01512 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.134 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.7 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8883 0.998 h = 0.003 0.006 y[1] (numeric) = 0.12351740416 0.181110885588 y[1] (closed_form) = 0.123488933649 0.181126388504 absolute error = 3.242e-05 relative error = 0.01479 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.136 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.581 Order of pole (three term test) = 1.127e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8853 1.004 h = 0.0001 0.005 y[1] (numeric) = 0.12236199396 0.181856903671 y[1] (closed_form) = 0.122330571332 0.181870714243 absolute error = 3.432e-05 relative error = 0.01566 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.136 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.592 Order of pole (three term test) = 7.803e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8852 1.009 h = 0.0001 0.003 y[1] (numeric) = 0.121342908472 0.181977782607 y[1] (closed_form) = 0.121313166355 0.181993024801 absolute error = 3.342e-05 relative error = 0.01528 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.138 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.283 Order of pole (three term test) = 1.287e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8851 1.012 h = 0.001 0.001 y[1] (numeric) = 0.120734724179 0.182055264741 y[1] (closed_form) = 0.12070467438 0.182071309619 absolute error = 3.407e-05 relative error = 0.01559 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.14 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.008 Order of pole (three term test) = 7.779e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8841 1.013 h = 0.001 0.003 y[1] (numeric) = 0.120550067989 0.182276941221 y[1] (closed_form) = 0.12052000048 0.182293429514 absolute error = 3.429e-05 relative error = 0.01569 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.139 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.783 Order of pole (three term test) = 4.173e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8831 1.016 h = 0.0001 0.004 y[1] (numeric) = 0.119957770205 0.18253553089 y[1] (closed_form) = 0.11992777827 0.182551116311 absolute error = 3.380e-05 relative error = 0.01547 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.14 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.707 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.883 1.02 h = 0.003 0.006 y[1] (numeric) = 0.119146060011 0.182624594687 y[1] (closed_form) = 0.119116760632 0.182639845124 absolute error = 3.303e-05 relative error = 0.01515 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.142 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.59 Order of pole (three term test) = 1.134e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.88 1.026 h = 0.0001 0.005 y[1] (numeric) = 0.117977712419 0.183329120173 y[1] (closed_form) = 0.117945563394 0.18334257824 absolute error = 3.485e-05 relative error = 0.01599 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.142 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.597 Order of pole (three term test) = 1.191e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8799 1.031 h = 0.0001 0.003 y[1] (numeric) = 0.116963694719 0.183417959659 y[1] (closed_form) = 0.11693314877 0.183432900637 absolute error = 3.400e-05 relative error = 0.01563 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.144 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.287 Order of pole (three term test) = 2.779e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8798 1.034 h = 0.001 0.001 y[1] (numeric) = 0.116358396847 0.183476309439 y[1] (closed_form) = 0.116327514411 0.18349203131 absolute error = 3.465e-05 relative error = 0.01595 % Correct digits = 4 memory used=600.3MB, alloc=44.3MB, time=7.72 Radius of convergence (given) for eq 1 = 2.145 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.011 Order of pole (three term test) = 7.552e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8788 1.035 h = 0.001 0.003 y[1] (numeric) = 0.116168609401 0.183690468962 y[1] (closed_form) = 0.116137691572 0.183706628341 absolute error = 3.489e-05 relative error = 0.01605 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.145 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.796 Order of pole (three term test) = 7.422e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8778 1.038 h = 0.0001 0.004 y[1] (numeric) = 0.115573585722 0.183928841897 y[1] (closed_form) = 0.11554277901 0.183944112051 absolute error = 3.438e-05 relative error = 0.01583 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.146 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.715 Order of pole (three term test) = 1.353e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8777 1.042 h = 0.003 0.006 y[1] (numeric) = 0.114766238518 0.183992516041 y[1] (closed_form) = 0.114736129691 0.184007483078 absolute error = 3.362e-05 relative error = 0.01551 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.147 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.6 Order of pole (three term test) = 1.238e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8747 1.048 h = 0.0001 0.005 y[1] (numeric) = 0.113586779251 0.184655510518 y[1] (closed_form) = 0.113553926759 0.1846685918 absolute error = 3.536e-05 relative error = 0.01631 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.148 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.601 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8746 1.053 h = 0.0001 0.003 y[1] (numeric) = 0.112579061517 0.184712893552 y[1] (closed_form) = 0.112547733251 0.184727504372 absolute error = 3.457e-05 relative error = 0.01598 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.15 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.291 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8745 1.056 h = 0.001 0.001 y[1] (numeric) = 0.111977385836 0.184752454034 y[1] (closed_form) = 0.111945693802 0.184767822839 absolute error = 3.522e-05 relative error = 0.0163 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.151 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.014 Order of pole (three term test) = 6.498e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8735 1.057 h = 0.001 0.003 y[1] (numeric) = 0.111782830455 0.184958979581 y[1] (closed_form) = 0.11175108591 0.184974779192 absolute error = 3.546e-05 relative error = 0.01641 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.151 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.81 Order of pole (three term test) = 4.040e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8725 1.06 h = 0.0001 0.004 y[1] (numeric) = 0.111185926832 0.185177266833 y[1] (closed_form) = 0.111154327725 0.185192192441 absolute error = 3.495e-05 relative error = 0.01618 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.152 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.723 Order of pole (three term test) = 1.165e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8724 1.064 h = 0.003 0.006 y[1] (numeric) = 0.110383910917 0.185216030746 y[1] (closed_form) = 0.110353013344 0.185230684883 absolute error = 3.420e-05 relative error = 0.01586 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.154 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.611 Order of pole (three term test) = 6.712e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8694 1.07 h = 0.0001 0.005 y[1] (numeric) = 0.109195140162 0.185837547956 y[1] (closed_form) = 0.109161607953 0.185850229682 absolute error = 3.585e-05 relative error = 0.01663 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.154 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.606 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8693 1.075 h = 0.0001 0.003 y[1] (numeric) = 0.108194906589 0.185864110394 y[1] (closed_form) = 0.108162818647 0.185878363629 absolute error = 3.511e-05 relative error = 0.01633 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.156 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.294 Order of pole (three term test) = 7.378e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8692 1.078 h = 0.001 0.001 y[1] (numeric) = 0.107597560469 0.185885256187 y[1] (closed_form) = 0.107565083045 0.185900243492 absolute error = 3.577e-05 relative error = 0.01665 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.158 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.017 Order of pole (three term test) = 4.486e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8682 1.079 h = 0.0001 0.004 y[1] (numeric) = 0.107398600759 0.186084050688 y[1] (closed_form) = 0.107366054304 0.186099461349 absolute error = 3.601e-05 relative error = 0.01676 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.157 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.104 Order of pole (three term test) = 2.207e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8681 1.083 h = 0.003 0.006 y[1] (numeric) = 0.106601674637 0.186102837753 y[1] (closed_form) = 0.106570364326 0.186117032643 absolute error = 3.438e-05 relative error = 0.01603 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.159 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.62 Order of pole (three term test) = 4.362e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8651 1.089 h = 0.0001 0.005 y[1] (numeric) = 0.105406798745 0.186688681417 y[1] (closed_form) = 0.105372950658 0.186700836074 absolute error = 3.596e-05 relative error = 0.01678 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.16 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.61 Order of pole (three term test) = 1.082e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.865 1.094 h = 0.0001 0.003 y[1] (numeric) = 0.104414273174 0.186689368614 y[1] (closed_form) = 0.104381799443 0.186703126228 absolute error = 3.527e-05 relative error = 0.01649 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.162 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.298 Order of pole (three term test) = 2.605e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8649 1.097 h = 0.001 0.001 y[1] (numeric) = 0.103821410299 0.18669504852 y[1] (closed_form) = 0.103788526528 0.186709518621 absolute error = 3.593e-05 relative error = 0.01682 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.164 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.019 Order of pole (three term test) = 1.240e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8639 1.098 h = 0.001 0.003 y[1] (numeric) = 0.10361904329 0.18688707904 y[1] (closed_form) = 0.103586076873 0.186901965336 absolute error = 3.617e-05 relative error = 0.01693 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.163 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.837 Order of pole (three term test) = 1.070e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8629 1.101 h = 0.0001 0.004 y[1] (numeric) = 0.103021058394 0.187068477311 y[1] (closed_form) = 0.102988297568 0.18708252214 absolute error = 3.564e-05 relative error = 0.01669 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.164 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.738 Order of pole (three term test) = 8.648e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8628 1.105 h = 0.003 0.006 y[1] (numeric) = 0.102231686897 0.187062391992 y[1] (closed_form) = 0.102199629727 0.187076223331 absolute error = 3.491e-05 relative error = 0.01638 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.166 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.631 Order of pole (three term test) = 3.185e-14 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=647.2MB, alloc=44.3MB, time=8.32 x[1] = -1.8598 1.111 h = 0.0001 0.005 y[1] (numeric) = 0.101030761218 0.187607112858 y[1] (closed_form) = 0.100996279672 0.187618829972 absolute error = 3.642e-05 relative error = 0.01709 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.166 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.615 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8597 1.116 h = 0.0001 0.003 y[1] (numeric) = 0.10004777924 0.187578302712 y[1] (closed_form) = 0.100014590871 0.187591656156 absolute error = 3.577e-05 relative error = 0.01683 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.169 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.302 Order of pole (three term test) = 8.315e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8596 1.119 h = 0.001 0.001 y[1] (numeric) = 0.0994604768811 0.187566348654 y[1] (closed_form) = 0.0994268557506 0.187580389121 absolute error = 3.644e-05 relative error = 0.01716 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.17 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.023 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8586 1.12 h = 0.001 0.003 y[1] (numeric) = 0.0992543794403 0.187750523592 y[1] (closed_form) = 0.0992206603542 0.18776497155 absolute error = 3.668e-05 relative error = 0.01727 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.17 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.852 Order of pole (three term test) = 5.354e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8576 1.123 h = 0.0001 0.004 y[1] (numeric) = 0.0986568169029 0.187912436066 y[1] (closed_form) = 0.0986233338541 0.187926061695 absolute error = 3.615e-05 relative error = 0.01703 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.171 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.747 Order of pole (three term test) = 1.416e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8575 1.127 h = 0.003 0.006 y[1] (numeric) = 0.0978753192276 0.187883037494 y[1] (closed_form) = 0.0978425389594 0.187896480127 absolute error = 3.543e-05 relative error = 0.01672 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.173 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.643 Order of pole (three term test) = 1.120e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8545 1.133 h = 0.0001 0.005 y[1] (numeric) = 0.0966700433019 0.188386933627 y[1] (closed_form) = 0.0966349538126 0.188398194835 absolute error = 3.685e-05 relative error = 0.0174 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.173 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.62 Order of pole (three term test) = 2.608e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8544 1.138 h = 0.0001 0.003 y[1] (numeric) = 0.0956976400059 0.188329391028 y[1] (closed_form) = 0.0956637622341 0.188342317401 absolute error = 3.626e-05 relative error = 0.01716 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.176 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.306 Order of pole (three term test) = 9.649e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8543 1.141 h = 0.001 0.001 y[1] (numeric) = 0.0951165172213 0.188300254718 y[1] (closed_form) = 0.0950821855948 0.188313841964 absolute error = 3.692e-05 relative error = 0.0175 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.177 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.026 Order of pole (three term test) = 1.432e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8533 1.142 h = 0.001 0.003 y[1] (numeric) = 0.0949070471296 0.188476531786 y[1] (closed_form) = 0.0948726029193 0.188490517218 absolute error = 3.718e-05 relative error = 0.01762 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.177 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.868 Order of pole (three term test) = 2.311e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8523 1.145 h = 0.0001 0.004 y[1] (numeric) = 0.0943106664955 0.188619233768 y[1] (closed_form) = 0.0942764873204 0.188632417176 absolute error = 3.663e-05 relative error = 0.01737 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.178 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.755 Order of pole (three term test) = 1.493e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8522 1.149 h = 0.003 0.006 y[1] (numeric) = 0.0935378519554 0.188567141747 y[1] (closed_form) = 0.0935043732114 0.188580172094 absolute error = 3.593e-05 relative error = 0.01707 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.18 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.654 Order of pole (three term test) = 1.292e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8492 1.155 h = 0.0001 0.005 y[1] (numeric) = 0.092329882293 0.189030589397 y[1] (closed_form) = 0.0922942108037 0.189041377876 absolute error = 3.727e-05 relative error = 0.01772 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.18 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.625 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8491 1.16 h = 0.0001 0.003 y[1] (numeric) = 0.0913690378691 0.188945116878 y[1] (closed_form) = 0.0913344966301 0.188957594897 absolute error = 3.673e-05 relative error = 0.0175 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.183 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.31 Order of pole (three term test) = 4.758e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.849 1.163 h = 0.001 0.001 y[1] (numeric) = 0.0907946811884 0.188899272556 y[1] (closed_form) = 0.0907596666342 0.188912384722 absolute error = 3.739e-05 relative error = 0.01784 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.184 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.029 Order of pole (three term test) = 1.651e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.848 1.164 h = 0.001 0.003 y[1] (numeric) = 0.0905821922074 0.189067627623 y[1] (closed_form) = 0.0905470511451 0.18908112812 absolute error = 3.765e-05 relative error = 0.01796 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.184 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.884 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.847 1.167 h = 0.0001 0.004 y[1] (numeric) = 0.0899877266715 0.189191426763 y[1] (closed_form) = 0.0899528781558 0.189204146598 absolute error = 3.710e-05 relative error = 0.01771 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.185 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.764 Order of pole (three term test) = 4.942e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8469 1.171 h = 0.003 0.006 y[1] (numeric) = 0.0892243605625 0.189117289912 y[1] (closed_form) = 0.0891902087167 0.189129885991 absolute error = 3.640e-05 relative error = 0.01741 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.187 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.666 Order of pole (three term test) = 8.764e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8439 1.177 h = 0.0001 0.005 y[1] (numeric) = 0.0880153069698 0.189540739391 y[1] (closed_form) = 0.0879790797553 0.189551039851 absolute error = 3.766e-05 relative error = 0.01802 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.188 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.631 Order of pole (three term test) = 3.176e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8438 1.182 h = 0.0001 0.003 y[1] (numeric) = 0.0870669456606 0.189428173151 y[1] (closed_form) = 0.0870317674797 0.18944018316 absolute error = 3.717e-05 relative error = 0.01783 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.19 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.315 Order of pole (three term test) = 7.438e-14 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=693.9MB, alloc=44.3MB, time=8.91 x[1] = -1.8437 1.185 h = 0.001 0.001 y[1] (numeric) = 0.0864999084515 0.189366115227 y[1] (closed_form) = 0.0864642391273 0.189378732187 absolute error = 3.784e-05 relative error = 0.01817 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.192 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.033 Order of pole (three term test) = 7.161e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8427 1.186 h = 0.0001 0.004 y[1] (numeric) = 0.0862847493537 0.189526541705 y[1] (closed_form) = 0.0862489403177 0.189539536642 absolute error = 3.809e-05 relative error = 0.01829 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.191 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.2 Order of pole (three term test) = 5.922e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8426 1.19 h = 0.003 0.006 y[1] (numeric) = 0.0855296803877 0.189434892327 y[1] (closed_form) = 0.0854952293915 0.189446988365 absolute error = 3.651e-05 relative error = 0.01757 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.193 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.677 Order of pole (three term test) = 8.146e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8396 1.196 h = 0.0001 0.005 y[1] (numeric) = 0.0843214126318 0.189824338966 y[1] (closed_form) = 0.0842849882454 0.189834099813 absolute error = 3.771e-05 relative error = 0.01816 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.194 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.636 Order of pole (three term test) = 3.480e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8395 1.201 h = 0.0001 0.003 y[1] (numeric) = 0.0833848018356 0.189689306371 y[1] (closed_form) = 0.0833493567935 0.189700789617 absolute error = 3.726e-05 relative error = 0.01798 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.197 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.319 Order of pole (three term test) = 1.730e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8394 1.204 h = 0.001 0.001 y[1] (numeric) = 0.0828246672382 0.189613797433 y[1] (closed_form) = 0.0827887173376 0.189625863739 absolute error = 3.792e-05 relative error = 0.01833 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.198 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.036 Order of pole (three term test) = 5.552e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8384 1.205 h = 0.001 0.003 y[1] (numeric) = 0.0826075788406 0.189767380612 y[1] (closed_form) = 0.0825714785804 0.189779815478 absolute error = 3.818e-05 relative error = 0.01845 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.198 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.915 Order of pole (three term test) = 7.728e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8374 1.208 h = 0.0001 0.004 y[1] (numeric) = 0.0820187477887 0.189856968484 y[1] (closed_form) = 0.0819829869362 0.189868665171 absolute error = 3.763e-05 relative error = 0.01819 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.199 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.782 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8373 1.212 h = 0.003 0.006 y[1] (numeric) = 0.0812750893816 0.1897437552 y[1] (closed_form) = 0.0812400143454 0.189755380664 absolute error = 3.695e-05 relative error = 0.0179 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.201 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.69 Order of pole (three term test) = 5.163e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8343 1.218 h = 0.0001 0.005 y[1] (numeric) = 0.0800685905698 0.190094241734 y[1] (closed_form) = 0.0800316600524 0.19010349045 absolute error = 3.807e-05 relative error = 0.01846 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.202 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.641 Order of pole (three term test) = 1.941e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8342 1.223 h = 0.0001 0.003 y[1] (numeric) = 0.0791460206774 0.189933756893 y[1] (closed_form) = 0.0791099894478 0.189944740199 absolute error = 3.767e-05 relative error = 0.01831 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.205 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.323 Order of pole (three term test) = 4.482e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8341 1.226 h = 0.001 0.001 y[1] (numeric) = 0.0785941391922 0.189843005649 y[1] (closed_form) = 0.0785575882885 0.189854544239 absolute error = 3.833e-05 relative error = 0.01865 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.206 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.039 Order of pole (three term test) = 6.167e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8331 1.227 h = 0.001 0.003 y[1] (numeric) = 0.0783750129491 0.189988696339 y[1] (closed_form) = 0.0783382998595 0.190000592356 absolute error = 3.859e-05 relative error = 0.01878 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.206 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.932 Order of pole (three term test) = 8.586e-15 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8321 1.23 h = 0.0001 0.004 y[1] (numeric) = 0.0777900330877 0.1900604278 y[1] (closed_form) = 0.0777536825196 0.190071609414 absolute error = 3.803e-05 relative error = 0.01852 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.207 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.792 Order of pole (three term test) = 6.285e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.832 1.234 h = 0.003 0.006 y[1] (numeric) = 0.077057755026 0.189927163518 y[1] (closed_form) = 0.0770220828619 0.189938301035 absolute error = 3.737e-05 relative error = 0.01823 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.209 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.703 Order of pole (three term test) = 5.740e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.829 1.24 h = 0.0001 0.005 y[1] (numeric) = 0.0758544836569 0.190239327538 y[1] (closed_form) = 0.0758170737079 0.190248053111 absolute error = 3.841e-05 relative error = 0.01876 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.21 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.647 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8289 1.245 h = 0.0001 0.003 y[1] (numeric) = 0.0749467154013 0.190054300628 y[1] (closed_form) = 0.0749101256002 0.190064768964 absolute error = 3.806e-05 relative error = 0.01863 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.212 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.328 Order of pole (three term test) = 2.138e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8288 1.248 h = 0.001 0.001 y[1] (numeric) = 0.0744035434307 0.189948845945 y[1] (closed_form) = 0.07436642073 0.189959841609 absolute error = 3.872e-05 relative error = 0.01898 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.214 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.043 Order of pole (three term test) = 1.375e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8278 1.249 h = 0.001 0.003 y[1] (numeric) = 0.0741827088942 0.190086683844 y[1] (closed_form) = 0.0741454129286 0.190098025451 absolute error = 3.898e-05 relative error = 0.0191 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.214 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.95 Order of pole (three term test) = 1.167e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8268 1.252 h = 0.0001 0.004 y[1] (numeric) = 0.0736022005708 0.190140970098 y[1] (closed_form) = 0.0735652886835 0.190151621726 absolute error = 3.842e-05 relative error = 0.01884 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.215 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.802 Order of pole (three term test) = 7.002e-14 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=740.7MB, alloc=44.3MB, time=9.51 x[1] = -1.8267 1.256 h = 0.003 0.006 y[1] (numeric) = 0.072881893043 0.189988384818 y[1] (closed_form) = 0.0728456510075 0.189999018612 absolute error = 3.777e-05 relative error = 0.01856 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.217 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.717 Order of pole (three term test) = 1.865e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8237 1.262 h = 0.0001 0.005 y[1] (numeric) = 0.0716832502332 0.190262920956 y[1] (closed_form) = 0.0716453875415 0.190271113817 absolute error = 3.874e-05 relative error = 0.01905 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.218 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.653 Order of pole (three term test) = 7.192e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8236 1.267 h = 0.0001 0.003 y[1] (numeric) = 0.070790987051 0.190054280902 y[1] (closed_form) = 0.0707538664898 0.190064220825 absolute error = 3.843e-05 relative error = 0.01895 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.221 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.333 Order of pole (three term test) = 7.954e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8235 1.27 h = 0.001 0.001 y[1] (numeric) = 0.0702569470039 0.189934672967 y[1] (closed_form) = 0.0702192818812 0.189945112174 absolute error = 3.909e-05 relative error = 0.0193 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.222 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.047 Order of pole (three term test) = 7.703e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8225 1.271 h = 0.001 0.003 y[1] (numeric) = 0.0700347256274 0.190064712532 y[1] (closed_form) = 0.0699968769109 0.190075485899 absolute error = 3.935e-05 relative error = 0.01943 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.222 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.968 Order of pole (three term test) = 3.203e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8215 1.274 h = 0.0001 0.004 y[1] (numeric) = 0.069459278087 0.1901019862 y[1] (closed_form) = 0.0694218334483 0.190112094553 absolute error = 3.879e-05 relative error = 0.01916 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.223 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.813 Order of pole (three term test) = 6.182e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8214 1.278 h = 0.003 0.006 y[1] (numeric) = 0.0687514857503 0.189930823792 y[1] (closed_form) = 0.0687147013456 0.189940939672 absolute error = 3.815e-05 relative error = 0.01889 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.225 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.73 Order of pole (three term test) = 1.288e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8184 1.284 h = 0.0001 0.005 y[1] (numeric) = 0.0675588133342 0.190168479187 y[1] (closed_form) = 0.0675205244996 0.190176131178 absolute error = 3.905e-05 relative error = 0.01935 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.226 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.66 Order of pole (three term test) = 8.041e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8183 1.289 h = 0.0001 0.003 y[1] (numeric) = 0.0666827016337 0.189937170011 y[1] (closed_form) = 0.0666450782254 0.189946569638 absolute error = 3.878e-05 relative error = 0.01926 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.229 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.338 Order of pole (three term test) = 8.896e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8182 1.292 h = 0.001 0.001 y[1] (numeric) = 0.0661581820756 0.189803968163 y[1] (closed_form) = 0.0661200039762 0.189813839033 absolute error = 3.943e-05 relative error = 0.01962 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.23 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.051 Order of pole (three term test) = 8.574e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8172 1.293 h = 0.0001 0.004 y[1] (numeric) = 0.0659348865746 0.189926277811 y[1] (closed_form) = 0.0658965153015 0.189936470806 absolute error = 3.970e-05 relative error = 0.01975 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.23 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.31 Order of pole (three term test) = 7.461e-15 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8171 1.297 h = 0.003 0.006 y[1] (numeric) = 0.0652377296038 0.189740503631 y[1] (closed_form) = 0.0652007571136 0.189750107512 absolute error = 3.820e-05 relative error = 0.01904 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.233 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.743 Order of pole (three term test) = 8.835e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8141 1.303 h = 0.0001 0.005 y[1] (numeric) = 0.0640516507164 0.189947140084 y[1] (closed_form) = 0.0640132730563 0.189954266363 absolute error = 3.903e-05 relative error = 0.01947 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.234 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.665 Order of pole (three term test) = 1.069e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.814 1.308 h = 0.0001 0.003 y[1] (numeric) = 0.0631901706394 0.189697284766 y[1] (closed_form) = 0.0631523936175 0.18970615543 absolute error = 3.880e-05 relative error = 0.01941 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.236 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.342 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8139 1.311 h = 0.001 0.001 y[1] (numeric) = 0.0626742842567 0.189552954156 y[1] (closed_form) = 0.062635945356 0.189562271896 absolute error = 3.945e-05 relative error = 0.01976 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.238 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.054 Order of pole (three term test) = 1.342e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8129 1.312 h = 0.001 0.003 y[1] (numeric) = 0.0624503982308 0.189668667097 y[1] (closed_form) = 0.0624118586542 0.189678296335 absolute error = 3.972e-05 relative error = 0.01989 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.238 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.004 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8119 1.315 h = 0.0001 0.004 y[1] (numeric) = 0.0618860171471 0.189675575176 y[1] (closed_form) = 0.0618479144348 0.189684587158 absolute error = 3.915e-05 relative error = 0.01962 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.239 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.833 Order of pole (three term test) = 4.847e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8118 1.319 h = 0.003 0.006 y[1] (numeric) = 0.0612030075499 0.189472022842 y[1] (closed_form) = 0.0611655443233 0.189481086866 absolute error = 3.854e-05 relative error = 0.01936 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.241 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.757 Order of pole (three term test) = 1.675e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8088 1.325 h = 0.0001 0.005 y[1] (numeric) = 0.0600252228806 0.189643307289 y[1] (closed_form) = 0.0599864681447 0.189649881436 absolute error = 3.931e-05 relative error = 0.01976 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.242 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.672 Order of pole (three term test) = 3.722e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8087 1.33 h = 0.0001 0.003 y[1] (numeric) = 0.0591809356738 0.189372573736 y[1] (closed_form) = 0.0591427078107 0.189380886372 absolute error = 3.912e-05 relative error = 0.01972 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.245 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.348 Order of pole (three term test) = 1.106e-14 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=787.7MB, alloc=44.3MB, time=10.12 x[1] = -1.8086 1.333 h = 0.001 0.001 y[1] (numeric) = 0.0586751969876 0.189215710935 y[1] (closed_form) = 0.058636399864 0.189224442847 absolute error = 3.977e-05 relative error = 0.02007 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.247 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.059 Order of pole (three term test) = 1.066e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8076 1.334 h = 0.001 0.003 y[1] (numeric) = 0.0584507923977 0.189323859082 y[1] (closed_form) = 0.0584117864017 0.189332890124 absolute error = 4.004e-05 relative error = 0.02021 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.247 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.023 Order of pole (three term test) = 1.515e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8066 1.337 h = 0.0001 0.004 y[1] (numeric) = 0.0578929765713 0.189315096312 y[1] (closed_form) = 0.0578544230358 0.189323536062 absolute error = 3.947e-05 relative error = 0.01994 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.248 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.844 Order of pole (three term test) = 3.852e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8065 1.341 h = 0.003 0.006 y[1] (numeric) = 0.0572237829405 0.189095150932 y[1] (closed_form) = 0.0571858566547 0.189103665296 absolute error = 3.887e-05 relative error = 0.01968 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.25 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.772 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8035 1.347 h = 0.0001 0.005 y[1] (numeric) = 0.0560554568547 0.18923195503 y[1] (closed_form) = 0.0560163509776 0.189237972681 absolute error = 3.957e-05 relative error = 0.02005 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.251 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.678 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8034 1.352 h = 0.0001 0.003 y[1] (numeric) = 0.0552288492087 0.188941310728 y[1] (closed_form) = 0.0551901982117 0.18894905773 absolute error = 3.942e-05 relative error = 0.02003 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.254 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.353 Order of pole (three term test) = 1.244e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8033 1.355 h = 0.001 0.001 y[1] (numeric) = 0.0547335519505 0.188772489551 y[1] (closed_form) = 0.0546943257269 0.188780628263 absolute error = 4.006e-05 relative error = 0.02038 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.256 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.063 Order of pole (three term test) = 1.224e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8023 1.356 h = 0.001 0.003 y[1] (numeric) = 0.0545089134639 0.188873176597 y[1] (closed_form) = 0.0544694709014 0.188881601951 absolute error = 4.033e-05 relative error = 0.02052 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.255 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.043 Order of pole (three term test) = 1.673e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8013 1.359 h = 0.0001 0.004 y[1] (numeric) = 0.0539581288001 0.188849237205 y[1] (closed_form) = 0.0539191527945 0.188857097407 absolute error = 3.976e-05 relative error = 0.02024 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.256 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.855 Order of pole (three term test) = 9.699e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.8012 1.363 h = 0.003 0.006 y[1] (numeric) = 0.0533031241639 0.188613669674 y[1] (closed_form) = 0.0532647623983 0.188621626043 absolute error = 3.918e-05 relative error = 0.01999 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.259 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.787 Order of pole (three term test) = 5.613e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7982 1.369 h = 0.0001 0.005 y[1] (numeric) = 0.0521453576145 0.188716900286 y[1] (closed_form) = 0.0521059261808 0.188722358319 absolute error = 3.981e-05 relative error = 0.02033 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.26 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.685 Order of pole (three term test) = 1.791e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7981 1.374 h = 0.0001 0.003 y[1] (numeric) = 0.0513368622778 0.188407314943 y[1] (closed_form) = 0.0512978156358 0.188414490122 absolute error = 3.970e-05 relative error = 0.02033 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.263 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.358 Order of pole (three term test) = 5.613e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.798 1.377 h = 0.001 0.001 y[1] (numeric) = 0.0508522681336 0.188227110713 y[1] (closed_form) = 0.0508126416668 0.188234650338 absolute error = 4.034e-05 relative error = 0.02069 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.265 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.067 Order of pole (three term test) = 3.385e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.797 1.378 h = 0.001 0.003 y[1] (numeric) = 0.0506276698603 0.188320451105 y[1] (closed_form) = 0.0505878203062 0.188328264805 absolute error = 4.061e-05 relative error = 0.02082 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.265 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.064 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.796 1.381 h = 0.0001 0.004 y[1] (numeric) = 0.0500843502715 0.188281840227 y[1] (closed_form) = 0.0500449798988 0.188289115007 absolute error = 4.004e-05 relative error = 0.02055 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.266 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.867 Order of pole (three term test) = 9.791e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7959 1.385 h = 0.003 0.006 y[1] (numeric) = 0.0494438650795 0.188031422363 y[1] (closed_form) = 0.0494050952381 0.18803881383 absolute error = 3.947e-05 relative error = 0.0203 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.268 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.802 Order of pole (three term test) = 2.004e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7929 1.391 h = 0.0001 0.005 y[1] (numeric) = 0.0482976952776 0.188102017256 y[1] (closed_form) = 0.0482579634652 0.188106913736 absolute error = 4.003e-05 relative error = 0.02061 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.269 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.692 Order of pole (three term test) = 6.746e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7928 1.396 h = 0.0001 0.003 y[1] (numeric) = 0.0475076922871 0.187774459827 y[1] (closed_form) = 0.0474682771996 0.187781058363 absolute error = 3.996e-05 relative error = 0.02063 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.272 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.364 Order of pole (three term test) = 4.758e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7927 1.399 h = 0.001 0.001 y[1] (numeric) = 0.04703403162 0.187583447606 y[1] (closed_form) = 0.0469940334262 0.187590383692 absolute error = 4.060e-05 relative error = 0.02099 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.274 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.071 Order of pole (three term test) = 1.560e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7917 1.4 h = 0.003 0.006 y[1] (numeric) = 0.0468097367979 0.187669565704 y[1] (closed_form) = 0.0467695094727 0.187676763263 absolute error = 4.087e-05 relative error = 0.02113 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.274 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.79 Order of pole (three term test) = 4.741e-14 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=834.7MB, alloc=44.3MB, time=10.72 x[1] = -1.7887 1.406 h = 0.0001 0.005 y[1] (numeric) = 0.0456694563088 0.187719387954 y[1] (closed_form) = 0.0456302032977 0.187722652908 absolute error = 3.939e-05 relative error = 0.02039 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.275 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.696 Order of pole (three term test) = 7.295e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7886 1.411 h = 0.0001 0.003 y[1] (numeric) = 0.0448919438816 0.187379552646 y[1] (closed_form) = 0.0448529615388 0.187384509347 absolute error = 3.930e-05 relative error = 0.02039 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.278 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.367 Order of pole (three term test) = 1.249e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7885 1.414 h = 0.001 0.001 y[1] (numeric) = 0.0444256668646 0.187181157125 y[1] (closed_form) = 0.04438609923 0.187186433164 absolute error = 3.992e-05 relative error = 0.02075 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.28 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.074 Order of pole (three term test) = 1.655e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7875 1.415 h = 0.001 0.003 y[1] (numeric) = 0.0442015498192 0.187262368843 y[1] (closed_form) = 0.0441617489785 0.187267897816 absolute error = 4.018e-05 relative error = 0.02088 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.28 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.098 Order of pole (three term test) = 2.308e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7865 1.418 h = 0.0001 0.004 y[1] (numeric) = 0.0436713851284 0.187199954558 y[1] (closed_form) = 0.0436320821908 0.187204988633 absolute error = 3.962e-05 relative error = 0.02061 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.281 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.886 Order of pole (three term test) = 5.990e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7864 1.422 h = 0.003 0.006 y[1] (numeric) = 0.0430557095629 0.186925836264 y[1] (closed_form) = 0.0430169830944 0.186931019659 absolute error = 3.907e-05 relative error = 0.02037 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.283 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.828 Order of pole (three term test) = 2.373e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7834 1.428 h = 0.0001 0.005 y[1] (numeric) = 0.04193052027 0.186943201403 y[1] (closed_form) = 0.0418910083266 0.186945903482 absolute error = 3.960e-05 relative error = 0.02067 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.285 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.703 Order of pole (three term test) = 8.268e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7833 1.433 h = 0.0001 0.003 y[1] (numeric) = 0.0411720501362 0.186587013258 y[1] (closed_form) = 0.0411327443679 0.18659138748 absolute error = 3.955e-05 relative error = 0.0207 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.288 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.373 Order of pole (three term test) = 9.724e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7832 1.436 h = 0.001 0.001 y[1] (numeric) = 0.0407170410077 0.186378771044 y[1] (closed_form) = 0.0406771487793 0.186383438435 absolute error = 4.016e-05 relative error = 0.02105 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.29 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.079 Order of pole (three term test) = 7.964e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7822 1.437 h = 0.001 0.003 y[1] (numeric) = 0.0404936500015 0.186452984535 y[1] (closed_form) = 0.0404535196751 0.186457892263 absolute error = 4.043e-05 relative error = 0.02119 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.289 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.119 Order of pole (three term test) = 1.888e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7812 1.44 h = 0.0001 0.004 y[1] (numeric) = 0.0399719734677 0.186377286936 y[1] (closed_form) = 0.0399323498803 0.186381725891 absolute error = 3.987e-05 relative error = 0.02092 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.29 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.898 Order of pole (three term test) = 1.359e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7811 1.444 h = 0.003 0.006 y[1] (numeric) = 0.0393715219738 0.186090374886 y[1] (closed_form) = 0.0393324595997 0.186094980867 absolute error = 3.933e-05 relative error = 0.02068 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.293 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.844 Order of pole (three term test) = 9.841e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7781 1.45 h = 0.0001 0.005 y[1] (numeric) = 0.0382604273045 0.186077724877 y[1] (closed_form) = 0.0382206802976 0.186079865097 absolute error = 3.980e-05 relative error = 0.02095 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.294 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.71 Order of pole (three term test) = 6.673e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.778 1.455 h = 0.0001 0.003 y[1] (numeric) = 0.0375212447937 0.185706138608 y[1] (closed_form) = 0.0374816417369 0.185709928968 absolute error = 3.978e-05 relative error = 0.021 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.297 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.379 Order of pole (three term test) = 1.250e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7779 1.458 h = 0.001 0.001 y[1] (numeric) = 0.0370776538259 0.185488616796 y[1] (closed_form) = 0.0370374643109 0.185492674676 absolute error = 4.039e-05 relative error = 0.02135 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.299 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.083 Order of pole (three term test) = 8.793e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7769 1.459 h = 0.001 0.003 y[1] (numeric) = 0.0368552219686 0.185555979256 y[1] (closed_form) = 0.0368147901213 0.18556026494 absolute error = 4.066e-05 relative error = 0.02149 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.299 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.141 Order of pole (three term test) = 4.207e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7759 1.462 h = 0.0001 0.004 y[1] (numeric) = 0.0363423523475 0.185467527787 y[1] (closed_form) = 0.0363024347399 0.185471370633 absolute error = 4.010e-05 relative error = 0.02122 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.3 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.911 Order of pole (three term test) = 4.635e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7758 1.466 h = 0.003 0.006 y[1] (numeric) = 0.0357573078326 0.185168579195 y[1] (closed_form) = 0.0357179357451 0.18517260572 absolute error = 3.958e-05 relative error = 0.02099 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.303 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.861 Order of pole (three term test) = 1.001e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7728 1.472 h = 0.0001 0.005 y[1] (numeric) = 0.0346611118205 0.185126931988 y[1] (closed_form) = 0.0346211530441 0.185128512354 absolute error = 3.999e-05 relative error = 0.02123 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.304 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.718 Order of pole (three term test) = 3.021e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7727 1.477 h = 0.0001 0.003 y[1] (numeric) = 0.0339414151963 0.184740892012 y[1] (closed_form) = 0.0339015404781 0.1847440983 absolute error = 4.000e-05 relative error = 0.0213 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.307 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.385 Order of pole (three term test) = 1.813e-13 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=881.5MB, alloc=44.3MB, time=11.32 x[1] = -1.7726 1.48 h = 0.001 0.001 y[1] (numeric) = 0.0335093646585 0.184514651759 y[1] (closed_form) = 0.0334689045958 0.184518100487 absolute error = 4.061e-05 relative error = 0.02165 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.309 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.088 Order of pole (three term test) = 6.866e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7716 1.481 h = 0.0001 0.004 y[1] (numeric) = 0.0332881135208 0.184575317288 y[1] (closed_form) = 0.0332474075285 0.18457898138 absolute error = 4.087e-05 relative error = 0.02179 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.309 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.533 Order of pole (three term test) = 9.460e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7715 1.485 h = 0.003 0.006 y[1] (numeric) = 0.0327157962193 0.184267105723 y[1] (closed_form) = 0.0326764058492 0.184270654606 absolute error = 3.955e-05 relative error = 0.02113 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.312 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.875 Order of pole (three term test) = 1.145e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7685 1.491 h = 0.0001 0.005 y[1] (numeric) = 0.0316333496934 0.184201512705 y[1] (closed_form) = 0.0315934542246 0.184202636463 absolute error = 3.991e-05 relative error = 0.02136 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.313 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.724 Order of pole (three term test) = 8.479e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7684 1.496 h = 0.0001 0.003 y[1] (numeric) = 0.030930707116 0.183804012752 y[1] (closed_form) = 0.0308908463819 0.183806739275 absolute error = 3.995e-05 relative error = 0.02144 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.316 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.39 Order of pole (three term test) = 3.445e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7683 1.499 h = 0.001 0.001 y[1] (numeric) = 0.0305087623958 0.18357085078 y[1] (closed_form) = 0.0304683184098 0.183573798671 absolute error = 4.055e-05 relative error = 0.02179 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.318 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.092 Order of pole (three term test) = 8.361e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7673 1.5 h = 0.001 0.003 y[1] (numeric) = 0.0302887733259 0.183625897345 y[1] (closed_form) = 0.030248080953 0.183629049959 absolute error = 4.081e-05 relative error = 0.02193 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.318 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.183 Order of pole (three term test) = 1.545e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7663 1.503 h = 0.0001 0.004 y[1] (numeric) = 0.0297931741689 0.183515241844 y[1] (closed_form) = 0.0297530062949 0.183517999223 absolute error = 4.026e-05 relative error = 0.02166 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.319 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.935 Order of pole (three term test) = 9.881e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7662 1.507 h = 0.003 0.006 y[1] (numeric) = 0.0292372823139 0.183196067036 y[1] (closed_form) = 0.0291976296513 0.183199036097 absolute error = 3.976e-05 relative error = 0.02143 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.322 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.892 Order of pole (three term test) = 1.281e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7632 1.513 h = 0.0001 0.005 y[1] (numeric) = 0.0281710540892 0.183103408968 y[1] (closed_form) = 0.0281309885012 0.183103979313 absolute error = 4.007e-05 relative error = 0.02163 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.323 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.732 Order of pole (three term test) = 1.369e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7631 1.518 h = 0.0001 0.003 y[1] (numeric) = 0.0274881363837 0.182693179085 y[1] (closed_form) = 0.0274480501295 0.18269532436 absolute error = 4.014e-05 relative error = 0.02173 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.327 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.396 Order of pole (three term test) = 1.019e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.763 1.521 h = 0.001 0.001 y[1] (numeric) = 0.0270778822685 0.182452323429 y[1] (closed_form) = 0.0270372157791 0.182454666169 absolute error = 4.073e-05 relative error = 0.02208 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.328 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.097 Order of pole (three term test) = 1.044e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.762 1.522 h = 0.001 0.003 y[1] (numeric) = 0.026859453375 0.182500977823 y[1] (closed_form) = 0.0268185360252 0.182503513107 absolute error = 4.100e-05 relative error = 0.02222 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.328 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.206 Order of pole (three term test) = 8.688e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.761 1.525 h = 0.0001 0.004 y[1] (numeric) = 0.0263734030541 0.182379092358 y[1] (closed_form) = 0.0263330141467 0.182381257456 absolute error = 4.045e-05 relative error = 0.02195 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.33 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.948 Order of pole (three term test) = 1.129e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7609 1.529 h = 0.003 0.006 y[1] (numeric) = 0.0258332338091 0.182049993814 y[1] (closed_form) = 0.0257933435393 0.182052384269 absolute error = 3.996e-05 relative error = 0.02173 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.332 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.91 Order of pole (three term test) = 1.492e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7579 1.535 h = 0.0001 0.005 y[1] (numeric) = 0.0247838535556 0.181931313971 y[1] (closed_form) = 0.0247436393122 0.181931335428 absolute error = 4.021e-05 relative error = 0.0219 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.334 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.74 Order of pole (three term test) = 1.106e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7578 1.54 h = 0.0001 0.003 y[1] (numeric) = 0.0241207346814 0.181509257275 y[1] (closed_form) = 0.0240804468176 0.181510824119 absolute error = 4.032e-05 relative error = 0.02202 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.337 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.403 Order of pole (three term test) = 1.648e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7577 1.543 h = 0.001 0.001 y[1] (numeric) = 0.0237222194258 0.181261245044 y[1] (closed_form) = 0.0236813552843 0.181262986125 absolute error = 4.090e-05 relative error = 0.02237 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.339 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.102 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7567 1.544 h = 0.001 0.003 y[1] (numeric) = 0.0235055391138 0.181303676728 y[1] (closed_form) = 0.0234644222092 0.18130559835 absolute error = 4.116e-05 relative error = 0.02252 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.339 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.23 Order of pole (three term test) = 4.969e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7557 1.547 h = 0.0001 0.004 y[1] (numeric) = 0.0230292443893 0.181171090294 y[1] (closed_form) = 0.0229886587227 0.18117266637 absolute error = 4.062e-05 relative error = 0.02224 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.34 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.961 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=928.4MB, alloc=44.3MB, time=11.92 x[1] = -1.7556 1.551 h = 0.003 0.006 y[1] (numeric) = 0.0225048463528 0.180832782144 y[1] (closed_form) = 0.0224647425549 0.180834596241 absolute error = 4.014e-05 relative error = 0.02203 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.343 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.927 Order of pole (three term test) = 6.698e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7526 1.557 h = 0.0001 0.005 y[1] (numeric) = 0.0214728852436 0.180689126529 y[1] (closed_form) = 0.0214325431249 0.180688604399 absolute error = 4.035e-05 relative error = 0.02217 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.344 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.748 Order of pole (three term test) = 7.602e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7525 1.562 h = 0.0001 0.003 y[1] (numeric) = 0.02082959939 0.180256128463 y[1] (closed_form) = 0.0207891331612 0.180257120641 absolute error = 4.048e-05 relative error = 0.02231 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.348 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.409 Order of pole (three term test) = 4.221e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7524 1.565 h = 0.001 0.001 y[1] (numeric) = 0.0204428475491 0.180001486429 y[1] (closed_form) = 0.0204018098809 0.180002630318 absolute error = 4.105e-05 relative error = 0.02266 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.349 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.107 Order of pole (three term test) = 1.223e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7514 1.566 h = 0.001 0.003 y[1] (numeric) = 0.0202280927622 0.180037868876 y[1] (closed_form) = 0.0201868009742 0.180039181502 absolute error = 4.131e-05 relative error = 0.0228 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.349 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.253 Order of pole (three term test) = 5.693e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7504 1.569 h = 0.0001 0.004 y[1] (numeric) = 0.0197617333924 0.179895106953 y[1] (closed_form) = 0.0197209745428 0.179896098219 absolute error = 4.077e-05 relative error = 0.02253 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.351 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.974 Order of pole (three term test) = 1.924e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7503 1.573 h = 0.003 0.006 y[1] (numeric) = 0.0192531240764 0.179548288863 y[1] (closed_form) = 0.0192128301878 0.179549529817 absolute error = 4.031e-05 relative error = 0.02232 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.353 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.945 Order of pole (three term test) = 8.253e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7473 1.579 h = 0.0001 0.005 y[1] (numeric) = 0.0182390962751 0.17938070319 y[1] (closed_form) = 0.0181986463587 0.179379643496 absolute error = 4.046e-05 relative error = 0.02244 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.355 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.756 Order of pole (three term test) = 1.453e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7472 1.584 h = 0.0001 0.003 y[1] (numeric) = 0.0176156398572 0.178937630025 y[1] (closed_form) = 0.0175750178131 0.178938052187 absolute error = 4.062e-05 relative error = 0.02259 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.358 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.416 Order of pole (three term test) = 4.842e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7471 1.587 h = 0.001 0.001 y[1] (numeric) = 0.017240653465 0.178676873725 y[1] (closed_form) = 0.0171994656406 0.178677425802 absolute error = 4.119e-05 relative error = 0.02295 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.36 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.112 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7461 1.588 h = 0.0001 0.004 y[1] (numeric) = 0.0170279898051 0.178707383737 y[1] (closed_form) = 0.0169865470253 0.178708092965 absolute error = 4.145e-05 relative error = 0.02309 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.36 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.678 Order of pole (three term test) = 4.100e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.746 1.592 h = 0.003 0.006 y[1] (numeric) = 0.016532296886 0.178354139513 y[1] (closed_form) = 0.0164920601097 0.17835494474 absolute error = 4.024e-05 relative error = 0.02247 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.363 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.961 Order of pole (three term test) = 1.084e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.743 1.598 h = 0.0001 0.005 y[1] (numeric) = 0.0155343430294 0.178167011643 y[1] (closed_form) = 0.0154940178714 0.178165549829 absolute error = 4.035e-05 relative error = 0.02256 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.365 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.763 Order of pole (three term test) = 3.284e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7429 1.603 h = 0.0001 0.003 y[1] (numeric) = 0.0149280312589 0.177716179714 y[1] (closed_form) = 0.014887495025 0.177716170317 absolute error = 4.054e-05 relative error = 0.02273 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.368 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.421 Order of pole (three term test) = 9.414e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7428 1.606 h = 0.001 0.001 y[1] (numeric) = 0.0145632221854 0.177450703906 y[1] (closed_form) = 0.0145221259022 0.177450806337 absolute error = 4.110e-05 relative error = 0.02308 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.37 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.117 Order of pole (three term test) = 5.287e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7418 1.607 h = 0.001 0.003 y[1] (numeric) = 0.014352549599 0.17747633014 y[1] (closed_form) = 0.0143111981729 0.177476579941 absolute error = 4.135e-05 relative error = 0.02322 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.37 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.299 Order of pole (three term test) = 1.479e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7408 1.61 h = 0.0001 0.004 y[1] (numeric) = 0.0139051741389 0.177316137626 y[1] (closed_form) = 0.0138643558099 0.177316109714 absolute error = 4.082e-05 relative error = 0.02295 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.371 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3 Order of pole (three term test) = 3.841e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7407 1.614 h = 0.003 0.006 y[1] (numeric) = 0.0134259731678 0.176955479701 y[1] (closed_form) = 0.0133855880367 0.176955720413 absolute error = 4.039e-05 relative error = 0.02276 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.374 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.98 Order of pole (three term test) = 4.983e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7377 1.62 h = 0.0001 0.005 y[1] (numeric) = 0.0124467509112 0.176746361889 y[1] (closed_form) = 0.0124063533079 0.176744375666 absolute error = 4.045e-05 relative error = 0.02283 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.376 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.771 Order of pole (three term test) = 1.888e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7376 1.625 h = 0.0001 0.003 y[1] (numeric) = 0.0118601585645 0.176287010296 y[1] (closed_form) = 0.0118195064663 0.17628644194 absolute error = 4.066e-05 relative error = 0.02301 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.379 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.428 Order of pole (three term test) = 6.571e-14 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=975.3MB, alloc=44.3MB, time=12.53 x[1] = -1.7375 1.628 h = 0.001 0.001 y[1] (numeric) = 0.0115070570804 0.176016346398 y[1] (closed_form) = 0.0114658519538 0.176015869485 absolute error = 4.121e-05 relative error = 0.02336 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.381 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.122 Order of pole (three term test) = 1.825e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7365 1.629 h = 0.001 0.003 y[1] (numeric) = 0.0112987519682 0.176036437477 y[1] (closed_form) = 0.011257291761 0.176036096815 absolute error = 4.146e-05 relative error = 0.0235 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.381 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.324 Order of pole (three term test) = 1.705e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7355 1.632 h = 0.0001 0.004 y[1] (numeric) = 0.0108616794758 0.175867543695 y[1] (closed_form) = 0.0108207512364 0.175866947979 absolute error = 4.093e-05 relative error = 0.02323 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.382 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.014 Order of pole (three term test) = 3.126e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7354 1.636 h = 0.003 0.006 y[1] (numeric) = 0.010398152292 0.175500286905 y[1] (closed_form) = 0.0103576402401 0.175499968761 absolute error = 4.051e-05 relative error = 0.02304 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.385 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.998 Order of pole (three term test) = 2.867e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7324 1.642 h = 0.0001 0.005 y[1] (numeric) = 0.00943802208829 0.175270208451 y[1] (closed_form) = 0.00939757003111 0.175267705596 absolute error = 4.053e-05 relative error = 0.02309 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.387 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.779 Order of pole (three term test) = 6.876e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7323 1.647 h = 0.0001 0.003 y[1] (numeric) = 0.00887104895692 0.174803141419 y[1] (closed_form) = 0.00883030142589 0.174802020956 absolute error = 4.076e-05 relative error = 0.02329 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.39 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.435 Order of pole (three term test) = 5.074e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7322 1.65 h = 0.001 0.001 y[1] (numeric) = 0.00852959942741 0.174527768522 y[1] (closed_form) = 0.00848830654298 0.17452671989 absolute error = 4.131e-05 relative error = 0.02364 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.392 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.127 Order of pole (three term test) = 7.315e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7312 1.651 h = 0.001 0.003 y[1] (numeric) = 0.00832379589723 0.174542507126 y[1] (closed_form) = 0.00828224844137 0.174541583894 absolute error = 4.156e-05 relative error = 0.02378 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.392 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.349 Order of pole (three term test) = 9.788e-15 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7302 1.654 h = 0.0001 0.004 y[1] (numeric) = 0.00789711105545 0.17436541283 y[1] (closed_form) = 0.00785609355168 0.174364256613 absolute error = 4.103e-05 relative error = 0.02351 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.394 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.029 Order of pole (three term test) = 5.695e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7301 1.658 h = 0.003 0.006 y[1] (numeric) = 0.00744917040401 0.173992191095 y[1] (closed_form) = 0.00740855212734 0.173991320498 absolute error = 4.063e-05 relative error = 0.02333 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.396 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.017 Order of pole (three term test) = 1.402e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7271 1.664 h = 0.0001 0.005 y[1] (numeric) = 0.00650844250114 0.173742171137 y[1] (closed_form) = 0.00646795324136 0.173739159944 absolute error = 4.060e-05 relative error = 0.02335 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.398 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.788 Order of pole (three term test) = 3.546e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.727 1.669 h = 0.0001 0.003 y[1] (numeric) = 0.00596095841705 0.173268169456 y[1] (closed_form) = 0.00592013511797 0.173266504397 absolute error = 4.086e-05 relative error = 0.02357 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.402 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.442 Order of pole (three term test) = 1.182e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7269 1.672 h = 0.001 0.001 y[1] (numeric) = 0.00563108730541 0.172988552859 y[1] (closed_form) = 0.00558972692589 0.1729869408 absolute error = 4.139e-05 relative error = 0.02392 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.404 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.132 Order of pole (three term test) = 1.617e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7259 1.673 h = 0.001 0.003 y[1] (numeric) = 0.00542790889757 0.172998122639 y[1] (closed_form) = 0.00538629487684 0.172996625414 absolute error = 4.164e-05 relative error = 0.02406 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.404 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.375 Order of pole (three term test) = 2.259e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7249 1.676 h = 0.0001 0.004 y[1] (numeric) = 0.00501167424412 0.172813319884 y[1] (closed_form) = 0.00497058732758 0.172811611125 absolute error = 4.112e-05 relative error = 0.02379 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.405 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.043 Order of pole (three term test) = 9.294e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7248 1.68 h = 0.003 0.006 y[1] (numeric) = 0.00457920958248 0.172434748286 y[1] (closed_form) = 0.00453850502396 0.172433332325 absolute error = 4.073e-05 relative error = 0.02361 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.408 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.037 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7218 1.686 h = 0.0001 0.005 y[1] (numeric) = 0.00365814596947 0.17216579369 y[1] (closed_form) = 0.00361763601568 0.172162282919 absolute error = 4.066e-05 relative error = 0.02361 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.41 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.797 Order of pole (three term test) = 1.158e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7217 1.691 h = 0.0001 0.003 y[1] (numeric) = 0.00312999280119 0.171685613961 y[1] (closed_form) = 0.00308911262261 0.171683412423 absolute error = 4.094e-05 relative error = 0.02384 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.413 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.448 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7216 1.694 h = 0.001 0.001 y[1] (numeric) = 0.00281160984977 0.171402204718 y[1] (closed_form) = 0.00277020140705 0.171400038137 absolute error = 4.147e-05 relative error = 0.02419 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.415 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.138 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7206 1.695 h = 0.0001 0.004 y[1] (numeric) = 0.0026111697991 0.171406789768 y[1] (closed_form) = 0.0025695090406 0.171404727749 absolute error = 4.171e-05 relative error = 0.02433 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.415 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.834 Order of pole (three term test) = 8.776e-14 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1022.1MB, alloc=44.3MB, time=13.12 x[1] = -1.7205 1.699 h = 0.003 0.006 y[1] (numeric) = 0.00219127136232 0.171024310172 y[1] (closed_form) = 0.00215068244621 0.17102250917 absolute error = 4.063e-05 relative error = 0.02375 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.418 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.054 Order of pole (three term test) = 1.033e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7175 1.705 h = 0.0001 0.005 y[1] (numeric) = 0.00128751802691 0.170740090368 y[1] (closed_form) = 0.00124717686927 0.17073623587 absolute error = 4.052e-05 relative error = 0.02373 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.42 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.804 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7174 1.71 h = 0.0001 0.003 y[1] (numeric) = 0.000775919531159 0.170255406952 y[1] (closed_form) = 0.000735179324543 0.170252829114 absolute error = 4.082e-05 relative error = 0.02398 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.424 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.455 Order of pole (three term test) = 1.552e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7173 1.713 h = 0.001 0.001 y[1] (numeric) = 0.000467379160694 0.169969218263 y[1] (closed_form) = 0.000426118875314 0.169966660596 absolute error = 4.134e-05 relative error = 0.02432 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.426 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.143 Order of pole (three term test) = 1.061e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7163 1.714 h = 0.001 0.003 y[1] (numeric) = 0.000269435606875 0.169969694275 y[1] (closed_form) = 0.00022792456095 0.169967232595 absolute error = 4.158e-05 relative error = 0.02447 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.426 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.424 Order of pole (three term test) = 7.413e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7153 1.717 h = 0.0001 0.004 y[1] (numeric) = -0.000127180214902 0.169771949698 y[1] (closed_form) = -0.000168171724898 0.169769314637 absolute error = 4.108e-05 relative error = 0.0242 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.427 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.071 Order of pole (three term test) = 8.811e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7152 1.721 h = 0.003 0.006 y[1] (numeric) = -0.000531167746652 0.16938517382 y[1] (closed_form) = -0.000571807977094 0.169382842496 absolute error = 4.071e-05 relative error = 0.02403 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.43 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.074 Order of pole (three term test) = 1.033e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7122 1.727 h = 0.0001 0.005 y[1] (numeric) = -0.00141490242858 0.169083855618 y[1] (closed_form) = -0.00145523565018 0.169079519097 absolute error = 4.057e-05 relative error = 0.02399 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.432 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.813 Order of pole (three term test) = 4.257e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7121 1.732 h = 0.0001 0.003 y[1] (numeric) = -0.00190754026819 0.168594333058 y[1] (closed_form) = -0.00194830440228 0.168591235469 absolute error = 4.088e-05 relative error = 0.02425 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.435 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.462 Order of pole (three term test) = 1.420e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.712 1.735 h = 0.001 0.001 y[1] (numeric) = -0.00220480591018 0.168305150415 y[1] (closed_form) = -0.00224608044514 0.168302056428 absolute error = 4.139e-05 relative error = 0.02459 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.437 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.148 Order of pole (three term test) = 1.228e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.711 1.736 h = 0.001 0.003 y[1] (numeric) = -0.00239982903343 0.168300984808 y[1] (closed_form) = -0.0024413523396 0.168297977114 absolute error = 4.163e-05 relative error = 0.02473 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.437 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.45 Order of pole (three term test) = 1.717e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.71 1.739 h = 0.0001 0.004 y[1] (numeric) = -0.00278593396838 0.168096884511 y[1] (closed_form) = -0.00282694266541 0.168093723012 absolute error = 4.113e-05 relative error = 0.02447 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.439 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.086 Order of pole (three term test) = 6.321e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7099 1.743 h = 0.003 0.006 y[1] (numeric) = -0.00317488285764 0.167706407694 y[1] (closed_form) = -0.00321555667051 0.167703554788 absolute error = 4.077e-05 relative error = 0.02431 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.442 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.094 Order of pole (three term test) = 1.298e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7069 1.749 h = 0.0001 0.005 y[1] (numeric) = -0.00403846359224 0.167388952278 y[1] (closed_form) = -0.00407877448666 0.167384143562 absolute error = 4.060e-05 relative error = 0.02425 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.444 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.822 Order of pole (three term test) = 8.834e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7068 1.754 h = 0.0001 0.003 y[1] (numeric) = -0.00451236784766 0.166895274781 y[1] (closed_form) = -0.00455313926858 0.166891666982 absolute error = 4.093e-05 relative error = 0.02452 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.447 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.469 Order of pole (three term test) = 1.472e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7067 1.757 h = 0.001 0.001 y[1] (numeric) = -0.00479849030868 0.166603506545 y[1] (closed_form) = -0.00483976205644 0.166599886564 absolute error = 4.143e-05 relative error = 0.02486 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.449 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.154 Order of pole (three term test) = 2.847e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7057 1.758 h = 0.001 0.003 y[1] (numeric) = -0.00499050761654 0.166594881915 y[1] (closed_form) = -0.00503202582312 0.166591338852 absolute error = 4.167e-05 relative error = 0.025 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.449 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.477 Order of pole (three term test) = 2.320e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7047 1.761 h = 0.0001 0.004 y[1] (numeric) = -0.00536611447181 0.166384877387 y[1] (closed_form) = -0.00540712362535 0.166381199416 absolute error = 4.117e-05 relative error = 0.02473 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.451 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.101 Order of pole (three term test) = 7.328e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7046 1.765 h = 0.003 0.006 y[1] (numeric) = -0.0057402103469 0.165991237489 y[1] (closed_form) = -0.00578090078784 0.165987872215 absolute error = 4.083e-05 relative error = 0.02458 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.454 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.114 Order of pole (three term test) = 6.728e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7016 1.771 h = 0.0001 0.005 y[1] (numeric) = -0.00658354220889 0.165658587286 y[1] (closed_form) = -0.0066238171122 0.165653316493 absolute error = 4.062e-05 relative error = 0.0245 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.456 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.831 Order of pole (three term test) = 7.236e-14 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1069.0MB, alloc=44.3MB, time=13.73 x[1] = -1.7015 1.776 h = 0.0001 0.003 y[1] (numeric) = -0.00703896052444 0.165161413213 y[1] (closed_form) = -0.00707972337341 0.165157305146 absolute error = 4.097e-05 relative error = 0.02478 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.46 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.476 Order of pole (three term test) = 1.991e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7014 1.779 h = 0.001 0.001 y[1] (numeric) = -0.00731408369605 0.164867452489 y[1] (closed_form) = -0.00735533644952 0.164863317237 absolute error = 4.146e-05 relative error = 0.02512 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.462 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.16 Order of pole (three term test) = 3.303e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.7004 1.78 h = 0.001 0.003 y[1] (numeric) = -0.00750301892628 0.164854550125 y[1] (closed_form) = -0.00754451552741 0.164850482739 absolute error = 4.170e-05 relative error = 0.02527 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.462 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.504 Order of pole (three term test) = 6.926e-15 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6994 1.783 h = 0.0001 0.004 y[1] (numeric) = -0.00786815746144 0.164639081051 y[1] (closed_form) = -0.00790915114498 0.16463489697 absolute error = 4.121e-05 relative error = 0.025 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.463 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.117 Order of pole (three term test) = 2.168e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6993 1.787 h = 0.003 0.006 y[1] (numeric) = -0.0082276018331 0.164242795345 y[1] (closed_form) = -0.00826829272437 0.164238927346 absolute error = 4.087e-05 relative error = 0.02486 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.466 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.134 Order of pole (three term test) = 1.562e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6963 1.793 h = 0.0001 0.005 y[1] (numeric) = -0.00905062819219 0.163895872743 y[1] (closed_form) = -0.0090908541586 0.163890150244 absolute error = 4.063e-05 relative error = 0.02475 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.468 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.84 Order of pole (three term test) = 8.403e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6962 1.798 h = 0.0001 0.003 y[1] (numeric) = -0.0094878269841 0.163395834456 y[1] (closed_form) = -0.00952856617909 0.16339123642 absolute error = 4.100e-05 relative error = 0.02505 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.472 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.484 Order of pole (three term test) = 7.149e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6961 1.801 h = 0.001 0.001 y[1] (numeric) = -0.00975210603471 0.163100058991 y[1] (closed_form) = -0.00979332440944 0.163095419539 absolute error = 4.148e-05 relative error = 0.02539 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.474 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.166 Order of pole (three term test) = 1.918e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6951 1.802 h = 0.0001 0.004 y[1] (numeric) = -0.0099378917125 0.163083058503 y[1] (closed_form) = -0.00997935104866 0.163078478194 absolute error = 4.171e-05 relative error = 0.02553 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.474 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7 Order of pole (three term test) = 1.059e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.695 1.806 h = 0.003 0.006 y[1] (numeric) = -0.0102855106481 0.162685001186 y[1] (closed_form) = -0.0103260435449 0.162680802747 absolute error = 4.075e-05 relative error = 0.025 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.477 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.152 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.692 1.812 h = 0.0001 0.005 y[1] (numeric) = -0.0110908856179 0.162326757995 y[1] (closed_form) = -0.0111309142335 0.162320749962 absolute error = 4.048e-05 relative error = 0.02488 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.479 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.848 Order of pole (three term test) = 6.782e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6919 1.817 h = 0.0001 0.003 y[1] (numeric) = -0.0115126036824 0.161824953167 y[1] (closed_form) = -0.0115531651707 0.161820036413 absolute error = 4.086e-05 relative error = 0.02519 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.483 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.49 Order of pole (three term test) = 6.790e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6918 1.82 h = 0.001 0.001 y[1] (numeric) = -0.0117676647959 0.161528032837 y[1] (closed_form) = -0.0118086958667 0.16152306316 absolute error = 4.133e-05 relative error = 0.02552 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.485 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.171 Order of pole (three term test) = 6.923e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6908 1.821 h = 0.001 0.003 y[1] (numeric) = -0.0119506459254 0.161507685565 y[1] (closed_form) = -0.011991915172 0.161502767823 absolute error = 4.156e-05 relative error = 0.02566 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.485 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.556 Order of pole (three term test) = 8.659e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6898 1.824 h = 0.0001 0.004 y[1] (numeric) = -0.0122963849644 0.161283299523 y[1] (closed_form) = -0.0123371642839 0.16127829704 absolute error = 4.109e-05 relative error = 0.0254 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.486 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.146 Order of pole (three term test) = 8.592e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6897 1.828 h = 0.003 0.006 y[1] (numeric) = -0.0126291332388 0.160883564684 y[1] (closed_form) = -0.0126696386601 0.160878882607 absolute error = 4.078e-05 relative error = 0.02527 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.489 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.173 Order of pole (three term test) = 2.072e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6867 1.834 h = 0.0001 0.005 y[1] (numeric) = -0.0134142025556 0.160512708063 y[1] (closed_form) = -0.0134541601469 0.160506268285 absolute error = 4.047e-05 relative error = 0.02513 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.492 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.858 Order of pole (three term test) = 7.889e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6866 1.839 h = 0.0001 0.003 y[1] (numeric) = -0.0138182476657 0.160009142751 y[1] (closed_form) = -0.0138587596068 0.160003756138 absolute error = 4.087e-05 relative error = 0.02545 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.495 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.498 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6865 1.842 h = 0.001 0.001 y[1] (numeric) = -0.0140627839536 0.159711067491 y[1] (closed_form) = -0.0141037543134 0.159705615135 absolute error = 4.133e-05 relative error = 0.02578 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.497 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.177 Order of pole (three term test) = 5.696e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6855 1.843 h = 0.001 0.003 y[1] (numeric) = -0.0142425142617 0.159686951252 y[1] (closed_form) = -0.014283719464 0.159681542723 absolute error = 4.156e-05 relative error = 0.02592 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.498 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.585 Order of pole (three term test) = 7.125e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6845 1.846 h = 0.0001 0.004 y[1] (numeric) = -0.0145779591414 0.159458288959 y[1] (closed_form) = -0.0146186819376 0.159452811911 absolute error = 4.109e-05 relative error = 0.02566 % Correct digits = 4 memory used=1115.9MB, alloc=44.3MB, time=14.32 Radius of convergence (given) for eq 1 = 2.499 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.162 Order of pole (three term test) = 3.714e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6844 1.85 h = 0.003 0.006 y[1] (numeric) = -0.0148967129575 0.159057270966 y[1] (closed_form) = -0.0149371769222 0.159052115845 absolute error = 4.079e-05 relative error = 0.02553 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.502 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.195 Order of pole (three term test) = 1.348e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6814 1.856 h = 0.0001 0.005 y[1] (numeric) = -0.0156615179037 0.15867465989 y[1] (closed_form) = -0.0157013935156 0.158667799235 absolute error = 4.046e-05 relative error = 0.02538 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.504 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.867 Order of pole (three term test) = 9.894e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6813 1.861 h = 0.0001 0.003 y[1] (numeric) = -0.0160482004408 0.158169891922 y[1] (closed_form) = -0.0160886499287 0.158164046509 absolute error = 4.087e-05 relative error = 0.02571 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.508 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.505 Order of pole (three term test) = 1.564e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6812 1.864 h = 0.001 0.001 y[1] (numeric) = -0.0162823935571 0.157870995413 y[1] (closed_form) = -0.0163232901175 0.157865072175 absolute error = 4.132e-05 relative error = 0.02604 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.51 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.183 Order of pole (three term test) = 6.633e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6802 1.865 h = 0.001 0.003 y[1] (numeric) = -0.0164588287638 0.157843283122 y[1] (closed_form) = -0.0164999566222 0.157837395934 absolute error = 4.155e-05 relative error = 0.02618 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.51 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.613 Order of pole (three term test) = 1.174e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6792 1.868 h = 0.0001 0.004 y[1] (numeric) = -0.0167840648415 0.15761073527 y[1] (closed_form) = -0.0168247182148 0.157604795091 absolute error = 4.109e-05 relative error = 0.02592 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.512 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.178 Order of pole (three term test) = 1.209e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6791 1.872 h = 0.003 0.006 y[1] (numeric) = -0.0170890739216 0.157208871564 y[1] (closed_form) = -0.0171294831977 0.157203254244 absolute error = 4.080e-05 relative error = 0.0258 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.515 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.216 Order of pole (three term test) = 1.412e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6761 1.878 h = 0.0001 0.005 y[1] (numeric) = -0.0178336861914 0.156815341442 y[1] (closed_form) = -0.0178734695364 0.156808070887 absolute error = 4.044e-05 relative error = 0.02562 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.517 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.877 Order of pole (three term test) = 1.207e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.676 1.883 h = 0.0001 0.003 y[1] (numeric) = -0.0182033289134 0.156309902935 y[1] (closed_form) = -0.0182437037789 0.156303609969 absolute error = 4.086e-05 relative error = 0.02597 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.521 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.513 Order of pole (three term test) = 1.430e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6759 1.886 h = 0.001 0.001 y[1] (numeric) = -0.0184273679949 0.156010503646 y[1] (closed_form) = -0.0184681784414 0.156004121496 absolute error = 4.131e-05 relative error = 0.02629 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.523 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.189 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6749 1.887 h = 0.001 0.003 y[1] (numeric) = -0.0186004712559 0.155979365375 y[1] (closed_form) = -0.0186415092659 0.155973011828 absolute error = 4.153e-05 relative error = 0.02644 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.523 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.642 Order of pole (three term test) = 6.841e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6739 1.89 h = 0.0001 0.004 y[1] (numeric) = -0.0189155959135 0.155743309476 y[1] (closed_form) = -0.0189561677169 0.155736917778 absolute error = 4.107e-05 relative error = 0.02618 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.525 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.195 Order of pole (three term test) = 1.261e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6738 1.894 h = 0.003 0.006 y[1] (numeric) = -0.0192071194332 0.155341017133 y[1] (closed_form) = -0.0192474615261 0.155334948669 absolute error = 4.080e-05 relative error = 0.02606 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.528 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.238 Order of pole (three term test) = 3.276e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6708 1.9 h = 0.0001 0.005 y[1] (numeric) = -0.0199316391653 0.154937379213 y[1] (closed_form) = -0.0199713206074 0.154929709814 absolute error = 4.042e-05 relative error = 0.02587 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.53 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.886 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6707 1.905 h = 0.0001 0.003 y[1] (numeric) = -0.0202845757067 0.154431776836 y[1] (closed_form) = -0.0203248645023 0.154425047716 absolute error = 4.085e-05 relative error = 0.02622 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.534 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.521 Order of pole (three term test) = 5.897e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6706 1.908 h = 0.001 0.001 y[1] (numeric) = -0.0204986564817 0.15413217817 y[1] (closed_form) = -0.0205393692574 0.154125349215 absolute error = 4.128e-05 relative error = 0.02655 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.536 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.195 Order of pole (three term test) = 5.705e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6696 1.909 h = 0.0001 0.004 y[1] (numeric) = -0.0206683980351 0.154097780918 y[1] (closed_form) = -0.0207093344697 0.154090973446 absolute error = 4.150e-05 relative error = 0.02669 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.536 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.175 Order of pole (three term test) = 4.985e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6695 1.913 h = 0.003 0.006 y[1] (numeric) = -0.0209490913935 0.15369545422 y[1] (closed_form) = -0.0209892476217 0.153689110003 absolute error = 4.065e-05 relative error = 0.02621 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.539 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.257 Order of pole (three term test) = 5.931e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6665 1.919 h = 0.0001 0.005 y[1] (numeric) = -0.0216563089121 0.153283983898 y[1] (closed_form) = -0.0216957774457 0.153276084039 absolute error = 4.025e-05 relative error = 0.026 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.542 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.895 Order of pole (three term test) = 1.459e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6664 1.924 h = 0.0001 0.003 y[1] (numeric) = -0.0219951455368 0.152778820424 y[1] (closed_form) = -0.0220352332185 0.152771828894 absolute error = 4.069e-05 relative error = 0.02636 % Correct digits = 4 memory used=1162.6MB, alloc=44.3MB, time=14.92 Radius of convergence (given) for eq 1 = 2.545 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.528 Order of pole (three term test) = 6.754e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6663 1.927 h = 0.001 0.001 y[1] (numeric) = -0.0222008179382 0.152479397079 y[1] (closed_form) = -0.022241319437 0.152472297238 absolute error = 4.112e-05 relative error = 0.02669 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.548 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.2 Order of pole (three term test) = 9.526e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6653 1.928 h = 0.001 0.003 y[1] (numeric) = -0.0223676109855 0.152442366234 y[1] (closed_form) = -0.022408332581 0.152435282055 absolute error = 4.133e-05 relative error = 0.02683 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.548 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.697 Order of pole (three term test) = 6.634e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6643 1.931 h = 0.0001 0.004 y[1] (numeric) = -0.0226641853189 0.152200859078 y[1] (closed_form) = -0.0227044570831 0.152193762446 absolute error = 4.089e-05 relative error = 0.02657 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.549 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.226 Order of pole (three term test) = 3.770e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6642 1.935 h = 0.003 0.006 y[1] (numeric) = -0.0229313383831 0.15179896342 y[1] (closed_form) = -0.0229714062293 0.151792189187 absolute error = 4.064e-05 relative error = 0.02647 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.552 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.279 Order of pole (three term test) = 6.195e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6612 1.941 h = 0.0001 0.005 y[1] (numeric) = -0.0236187278072 0.151378827098 y[1] (closed_form) = -0.0236580783156 0.151370549174 absolute error = 4.021e-05 relative error = 0.02625 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.555 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.905 Order of pole (three term test) = 1.671e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6611 1.946 h = 0.0001 0.003 y[1] (numeric) = -0.023941508498 0.150874371767 y[1] (closed_form) = -0.0239814908128 0.150866965693 absolute error = 4.066e-05 relative error = 0.02662 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.559 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.536 Order of pole (three term test) = 1.697e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.661 1.949 h = 0.001 0.001 y[1] (numeric) = -0.0241376046563 0.150575271707 y[1] (closed_form) = -0.0241779890793 0.150567747939 absolute error = 4.108e-05 relative error = 0.02694 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.561 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.206 Order of pole (three term test) = 1.169e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.66 1.95 h = 0.001 0.003 y[1] (numeric) = -0.0243010001531 0.150535283922 y[1] (closed_form) = -0.0243416005062 0.150527769297 absolute error = 4.129e-05 relative error = 0.02708 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.561 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.726 Order of pole (three term test) = 9.674e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.659 1.953 h = 0.0001 0.004 y[1] (numeric) = -0.0245878036963 0.150291273564 y[1] (closed_form) = -0.0246279632926 0.150283759394 absolute error = 4.086e-05 relative error = 0.02683 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.563 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.242 Order of pole (three term test) = 1.970e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6589 1.957 h = 0.003 0.006 y[1] (numeric) = -0.0248422587476 0.149890028825 y[1] (closed_form) = -0.024882227748 0.149882836019 absolute error = 4.061e-05 relative error = 0.02673 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.566 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.301 Order of pole (three term test) = 5.119e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6559 1.963 h = 0.0001 0.005 y[1] (numeric) = -0.0255099908157 0.149461966138 y[1] (closed_form) = -0.0255492154301 0.149453321266 absolute error = 4.017e-05 relative error = 0.02649 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.568 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.915 Order of pole (three term test) = 1.381e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6558 1.968 h = 0.0001 0.003 y[1] (numeric) = -0.0258170723623 0.148958654751 y[1] (closed_form) = -0.025856939836 0.148950845766 absolute error = 4.063e-05 relative error = 0.02687 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.572 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.544 Order of pole (three term test) = 1.459e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6557 1.971 h = 0.001 0.001 y[1] (numeric) = -0.0260038021314 0.148660139393 y[1] (closed_form) = -0.0260440599855 0.148652203985 absolute error = 4.103e-05 relative error = 0.02719 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.574 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.213 Order of pole (three term test) = 8.491e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6547 1.972 h = 0.001 0.003 y[1] (numeric) = -0.0261637885952 0.14861735174 y[1] (closed_form) = -0.0262042580954 0.148609419273 absolute error = 4.124e-05 relative error = 0.02733 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.574 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.756 Order of pole (three term test) = 9.008e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6537 1.975 h = 0.0001 0.004 y[1] (numeric) = -0.0264409564048 0.148371164114 y[1] (closed_form) = -0.0264809944328 0.148363244355 absolute error = 4.081e-05 relative error = 0.02708 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.576 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.259 Order of pole (three term test) = 1.401e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6536 1.979 h = 0.003 0.006 y[1] (numeric) = -0.0266829983656 0.147970911239 y[1] (closed_form) = -0.0267228587334 0.147963311372 absolute error = 4.058e-05 relative error = 0.02699 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.579 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.324 Order of pole (three term test) = 1.821e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6506 1.985 h = 0.0001 0.005 y[1] (numeric) = -0.0273312650964 0.147535636454 y[1] (closed_form) = -0.0273703565299 0.147526635724 absolute error = 4.011e-05 relative error = 0.02673 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.582 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.925 Order of pole (three term test) = 5.110e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6505 1.99 h = 0.0001 0.003 y[1] (numeric) = -0.0276230100223 0.147033880946 y[1] (closed_form) = -0.027662753835 0.147025680708 absolute error = 4.058e-05 relative error = 0.02713 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.585 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.552 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6504 1.993 h = 0.001 0.001 y[1] (numeric) = -0.0278005867899 0.146736197558 y[1] (closed_form) = -0.0278407092635 0.146727862803 absolute error = 4.098e-05 relative error = 0.02744 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.588 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.219 Order of pole (three term test) = 7.383e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6494 1.994 h = 0.001 0.003 y[1] (numeric) = -0.0279571584764 0.146690763373 y[1] (closed_form) = -0.0279974882114 0.146682425668 absolute error = 4.118e-05 relative error = 0.02758 % Correct digits = 4 memory used=1209.4MB, alloc=44.3MB, time=15.52 Radius of convergence (given) for eq 1 = 2.588 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.786 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6484 1.997 h = 0.0001 0.004 y[1] (numeric) = -0.0282248333314 0.146442711152 y[1] (closed_form) = -0.0282647410556 0.146434397765 absolute error = 4.076e-05 relative error = 0.02733 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.589 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.276 Order of pole (three term test) = 3.813e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6483 2.001 h = 0.003 0.006 y[1] (numeric) = -0.0284547513905 0.146043772254 y[1] (closed_form) = -0.0284944939979 0.146035776883 absolute error = 4.054e-05 relative error = 0.02725 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.592 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.346 Order of pole (three term test) = 4.953e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6453 2.007 h = 0.0001 0.005 y[1] (numeric) = -0.0290837643608 0.145601974193 y[1] (closed_form) = -0.0291227158887 0.145592628649 absolute error = 4.006e-05 relative error = 0.02698 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.595 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.935 Order of pole (three term test) = 3.783e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6452 2.012 h = 0.0001 0.003 y[1] (numeric) = -0.0293605397578 0.145102163158 y[1] (closed_form) = -0.0294001517235 0.145093583322 absolute error = 4.053e-05 relative error = 0.02738 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.599 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.56 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6451 2.015 h = 0.001 0.001 y[1] (numeric) = -0.0295291797508 0.144805545161 y[1] (closed_form) = -0.0295691586923 0.144796823328 absolute error = 4.092e-05 relative error = 0.02769 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.601 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.226 Order of pole (three term test) = 8.644e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6441 2.016 h = 0.0001 0.004 y[1] (numeric) = -0.0296823363185 0.144757613926 y[1] (closed_form) = -0.0297225180521 0.144748883556 absolute error = 4.112e-05 relative error = 0.02783 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.601 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.36 Order of pole (three term test) = 1.512e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.644 2.02 h = 0.003 0.006 y[1] (numeric) = -0.0299025591688 0.144359994298 y[1] (closed_form) = -0.0299421002878 0.144351775184 absolute error = 4.039e-05 relative error = 0.02739 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.604 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.366 Order of pole (three term test) = 1.223e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.641 2.026 h = 0.0001 0.005 y[1] (numeric) = -0.0305151152624 0.143913338973 y[1] (closed_form) = -0.0305538486842 0.143903813074 absolute error = 3.989e-05 relative error = 0.02711 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.607 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.944 Order of pole (three term test) = 6.871e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6409 2.031 h = 0.0001 0.003 y[1] (numeric) = -0.0307793310602 0.143415667738 y[1] (closed_form) = -0.0308187303372 0.143406878054 absolute error = 4.037e-05 relative error = 0.02752 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.611 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.567 Order of pole (three term test) = 1.026e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6408 2.034 h = 0.001 0.001 y[1] (numeric) = -0.0309404696327 0.143120246289 y[1] (closed_form) = -0.0309802257932 0.143111308782 absolute error = 4.075e-05 relative error = 0.02783 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.613 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.231 Order of pole (three term test) = 9.928e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6398 2.035 h = 0.001 0.003 y[1] (numeric) = -0.0310906627938 0.143070322956 y[1] (closed_form) = -0.0311306177814 0.143061372398 absolute error = 4.095e-05 relative error = 0.02797 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.613 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.844 Order of pole (three term test) = 1.112e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6388 2.038 h = 0.0001 0.004 y[1] (numeric) = -0.0313410626443 0.142819697146 y[1] (closed_form) = -0.0313806137094 0.142810790729 absolute error = 4.054e-05 relative error = 0.02773 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.615 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.309 Order of pole (three term test) = 5.129e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6387 2.042 h = 0.003 0.006 y[1] (numeric) = -0.0315492253692 0.142424134003 y[1] (closed_form) = -0.0315886335689 0.14241554099 absolute error = 4.033e-05 relative error = 0.02765 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.618 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.39 Order of pole (three term test) = 4.805e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6357 2.048 h = 0.0001 0.005 y[1] (numeric) = -0.0321429752961 0.141972166505 y[1] (closed_form) = -0.0321815578577 0.141962316209 absolute error = 3.982e-05 relative error = 0.02736 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.621 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.954 Order of pole (three term test) = 7.630e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6356 2.053 h = 0.0001 0.003 y[1] (numeric) = -0.0323929170846 0.141477098172 y[1] (closed_form) = -0.0324321710388 0.141467950563 absolute error = 4.031e-05 relative error = 0.02777 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.625 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.575 Order of pole (three term test) = 1.202e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6355 2.056 h = 0.001 0.001 y[1] (numeric) = -0.0325455289845 0.141183138107 y[1] (closed_form) = -0.032585128269 0.14117383628 absolute error = 4.068e-05 relative error = 0.02808 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.627 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.238 Order of pole (three term test) = 1.565e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6345 2.057 h = 0.001 0.003 y[1] (numeric) = -0.0326923213193 0.141130985165 y[1] (closed_form) = -0.032732114847 0.141121665253 absolute error = 4.087e-05 relative error = 0.02821 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.627 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.875 Order of pole (three term test) = 1.629e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6335 2.06 h = 0.0001 0.004 y[1] (numeric) = -0.032933675599 0.140879315139 y[1] (closed_form) = -0.0329730749936 0.140870049214 absolute error = 4.047e-05 relative error = 0.02798 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.629 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.327 Order of pole (three term test) = 4.251e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6334 2.064 h = 0.003 0.006 y[1] (numeric) = -0.0331305605053 0.140485883835 y[1] (closed_form) = -0.033169828435 0.140476928438 absolute error = 4.028e-05 relative error = 0.0279 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.632 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.413 Order of pole (three term test) = 7.811e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6304 2.07 h = 0.0001 0.005 y[1] (numeric) = -0.0337057625286 0.140029220328 y[1] (closed_form) = -0.033744189003 0.140019056425 absolute error = 3.975e-05 relative error = 0.0276 % Correct digits = 4 memory used=1256.2MB, alloc=44.3MB, time=16.11 Radius of convergence (given) for eq 1 = 2.635 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.964 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6303 2.075 h = 0.0001 0.003 y[1] (numeric) = -0.0339418043813 0.139537079872 y[1] (closed_form) = -0.033980906527 0.139527585842 absolute error = 4.024e-05 relative error = 0.02802 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.639 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.584 Order of pole (three term test) = 1.417e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6302 2.078 h = 0.001 0.001 y[1] (numeric) = -0.034086110332 0.139244776849 y[1] (closed_form) = -0.0341255463518 0.139235122758 absolute error = 4.060e-05 relative error = 0.02832 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.641 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.244 Order of pole (three term test) = 1.371e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6292 2.079 h = 0.001 0.003 y[1] (numeric) = -0.0342295151184 0.139190532232 y[1] (closed_form) = -0.0342691407535 0.139180855307 absolute error = 4.079e-05 relative error = 0.02846 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.641 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.906 Order of pole (three term test) = 1.920e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6282 2.082 h = 0.0001 0.004 y[1] (numeric) = -0.034461989167 0.138938080673 y[1] (closed_form) = -0.0345012305222 0.138928466996 absolute error = 4.040e-05 relative error = 0.02822 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.643 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.344 Order of pole (three term test) = 4.985e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6281 2.086 h = 0.003 0.006 y[1] (numeric) = -0.0346478936735 0.13854703481 y[1] (closed_form) = -0.0346870145646 0.138537728486 absolute error = 4.021e-05 relative error = 0.02816 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.646 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.436 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6251 2.092 h = 0.0001 0.005 y[1] (numeric) = -0.0352048195478 0.138086266466 y[1] (closed_form) = -0.0352430851935 0.13807579963 absolute error = 3.967e-05 relative error = 0.02784 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.649 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.975 Order of pole (three term test) = 7.005e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.625 2.097 h = 0.0001 0.003 y[1] (numeric) = -0.0354273362427 0.137597357834 y[1] (closed_form) = -0.035466280648 0.137587528795 absolute error = 4.017e-05 relative error = 0.02827 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.653 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.592 Order of pole (three term test) = 1.158e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6249 2.1 h = 0.001 0.001 y[1] (numeric) = -0.0355635575033 0.137306895018 y[1] (closed_form) = -0.035602824442 0.137296900606 absolute error = 4.052e-05 relative error = 0.02857 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.655 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.251 Order of pole (three term test) = 3.201e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6239 2.101 h = 0.001 0.003 y[1] (numeric) = -0.0357035921977 0.137250692536 y[1] (closed_form) = -0.0357430440926 0.13724067082 absolute error = 4.070e-05 relative error = 0.0287 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.655 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.938 Order of pole (three term test) = 5.116e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6229 2.104 h = 0.0001 0.004 y[1] (numeric) = -0.0359273555641 0.136997709664 y[1] (closed_form) = -0.0359664330706 0.136987759884 absolute error = 4.032e-05 relative error = 0.02847 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.657 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.362 Order of pole (three term test) = 8.273e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6228 2.108 h = 0.003 0.006 y[1] (numeric) = -0.0361025774457 0.136609286297 y[1] (closed_form) = -0.0361415450906 0.136599640424 absolute error = 4.014e-05 relative error = 0.02841 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.66 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.46 Order of pole (three term test) = 1.075e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6198 2.114 h = 0.0001 0.005 y[1] (numeric) = -0.0366415110019 0.136144979573 y[1] (closed_form) = -0.0366796115426 0.136134220342 absolute error = 3.959e-05 relative error = 0.02808 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.663 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.985 Order of pole (three term test) = 5.813e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6197 2.119 h = 0.0001 0.003 y[1] (numeric) = -0.0368508771759 0.135659586334 y[1] (closed_form) = -0.036889658441 0.135649433584 absolute error = 4.009e-05 relative error = 0.02852 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.667 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.601 Order of pole (three term test) = 1.980e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6196 2.122 h = 0.001 0.001 y[1] (numeric) = -0.0369792350361 0.135371134778 y[1] (closed_form) = -0.0370183276266 0.135360811855 absolute error = 4.043e-05 relative error = 0.02881 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.669 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.258 Order of pole (three term test) = 3.945e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6186 2.123 h = 0.0001 0.004 y[1] (numeric) = -0.0371159209781 0.135313104085 y[1] (closed_form) = -0.037155193846 0.135302749658 absolute error = 4.061e-05 relative error = 0.02895 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.67 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.553 Order of pole (three term test) = 1.039e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6185 2.127 h = 0.003 0.006 y[1] (numeric) = -0.0372826320291 0.134927006338 y[1] (closed_form) = -0.0373213924038 0.134917184275 absolute error = 3.999e-05 relative error = 0.02856 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.673 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.481 Order of pole (three term test) = 8.746e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6155 2.133 h = 0.0001 0.005 y[1] (numeric) = -0.0378062804856 0.134460298388 y[1] (closed_form) = -0.0378441655697 0.134449402961 absolute error = 3.942e-05 relative error = 0.02822 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.676 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.995 Order of pole (three term test) = 1.338e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6154 2.138 h = 0.0001 0.003 y[1] (numeric) = -0.0380046725463 0.133978293676 y[1] (closed_form) = -0.0380432388366 0.133967978394 absolute error = 3.992e-05 relative error = 0.02867 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.68 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.608 Order of pole (three term test) = 1.303e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6153 2.141 h = 0.001 0.001 y[1] (numeric) = -0.0381264652463 0.133691791451 y[1] (closed_form) = -0.0381653332828 0.133681302385 absolute error = 4.026e-05 relative error = 0.02896 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.682 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.264 Order of pole (three term test) = 4.324e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6143 2.142 h = 0.001 0.003 y[1] (numeric) = -0.0382602687825 0.133632327212 y[1] (closed_form) = -0.0382993130161 0.133621803293 absolute error = 4.044e-05 relative error = 0.02909 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.682 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.998 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1303.1MB, alloc=44.3MB, time=16.72 x[1] = -1.6133 2.145 h = 0.0001 0.004 y[1] (numeric) = -0.0384682868563 0.133379078807 y[1] (closed_form) = -0.0385069752196 0.133368641418 absolute error = 4.007e-05 relative error = 0.02887 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.684 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.396 Order of pole (three term test) = 1.118e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6132 2.149 h = 0.003 0.006 y[1] (numeric) = -0.0386244590965 0.132996230633 y[1] (closed_form) = -0.0386630562273 0.132986089972 absolute error = 3.991e-05 relative error = 0.02882 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.687 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.505 Order of pole (three term test) = 1.072e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6102 2.155 h = 0.0001 0.005 y[1] (numeric) = -0.0391306770156 0.132526970055 y[1] (closed_form) = -0.0391683903283 0.132515801482 absolute error = 3.933e-05 relative error = 0.02846 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.69 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.006 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6101 2.16 h = 0.0001 0.003 y[1] (numeric) = -0.0393166154834 0.132048952002 y[1] (closed_form) = -0.03935501006 0.132038333734 absolute error = 3.984e-05 relative error = 0.02891 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.694 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.617 Order of pole (three term test) = 1.114e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.61 2.163 h = 0.001 0.001 y[1] (numeric) = -0.039430956768 0.131764745816 y[1] (closed_form) = -0.0394696421741 0.131753949851 absolute error = 4.016e-05 relative error = 0.0292 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.696 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.27 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.609 2.164 h = 0.001 0.003 y[1] (numeric) = -0.0395614620509 0.131703683169 y[1] (closed_form) = -0.039600318971 0.131692848635 absolute error = 4.034e-05 relative error = 0.02933 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.697 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.03 Order of pole (three term test) = 7.955e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.608 2.167 h = 0.0001 0.004 y[1] (numeric) = -0.0397612748072 0.131450550506 y[1] (closed_form) = -0.0397997857292 0.131439809656 absolute error = 3.998e-05 relative error = 0.02911 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.698 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.414 Order of pole (three term test) = 1.000e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6079 2.171 h = 0.003 0.006 y[1] (numeric) = -0.0399076147914 0.1310709128 y[1] (closed_form) = -0.039946043957 0.131060464582 absolute error = 3.982e-05 relative error = 0.02907 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.702 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.529 Order of pole (three term test) = 4.826e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6049 2.177 h = 0.0001 0.005 y[1] (numeric) = -0.0403967130452 0.130599597209 y[1] (closed_form) = -0.0404342515293 0.130588165575 absolute error = 3.924e-05 relative error = 0.0287 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.705 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.016 Order of pole (three term test) = 9.642e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6048 2.182 h = 0.0001 0.003 y[1] (numeric) = -0.0405705678056 0.130125794807 y[1] (closed_form) = -0.0406087866714 0.130114884442 absolute error = 3.975e-05 relative error = 0.02916 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.709 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.626 Order of pole (three term test) = 1.272e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6047 2.185 h = 0.001 0.001 y[1] (numeric) = -0.0406776764531 0.129844023252 y[1] (closed_form) = -0.0407161754037 0.129832931726 absolute error = 4.006e-05 relative error = 0.02944 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.711 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.277 Order of pole (three term test) = 4.220e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6037 2.186 h = 0.001 0.003 y[1] (numeric) = -0.0408049143389 0.129781479889 y[1] (closed_form) = -0.0408435801302 0.129770346324 absolute error = 4.024e-05 relative error = 0.02958 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.711 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.062 Order of pole (three term test) = 9.348e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6027 2.189 h = 0.0001 0.004 y[1] (numeric) = -0.0409967019102 0.129528667433 y[1] (closed_form) = -0.0410350315332 0.129517634203 absolute error = 3.989e-05 relative error = 0.02936 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.713 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.433 Order of pole (three term test) = 1.211e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6026 2.193 h = 0.003 0.006 y[1] (numeric) = -0.0411335028882 0.129152418346 y[1] (closed_form) = -0.0411717598466 0.129141673466 absolute error = 3.974e-05 relative error = 0.02932 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.716 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.554 Order of pole (three term test) = 1.375e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5996 2.199 h = 0.0001 0.005 y[1] (numeric) = -0.0416057995814 0.128679522165 y[1] (closed_form) = -0.041643160569 0.128667837375 absolute error = 3.915e-05 relative error = 0.02895 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.719 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.027 Order of pole (three term test) = 1.091e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5995 2.204 h = 0.0001 0.003 y[1] (numeric) = -0.0417679376779 0.128210146636 y[1] (closed_form) = -0.0418059772856 0.128198954894 absolute error = 3.965e-05 relative error = 0.02941 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.723 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.635 Order of pole (three term test) = 5.127e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5994 2.207 h = 0.001 0.001 y[1] (numeric) = -0.0418680308805 0.127930937728 y[1] (closed_form) = -0.0419063400114 0.127919561788 absolute error = 3.996e-05 relative error = 0.02969 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.726 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.284 Order of pole (three term test) = 7.016e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5984 2.208 h = 0.001 0.003 y[1] (numeric) = -0.0419920350625 0.127867027197 y[1] (closed_form) = -0.0420305063795 0.127855605986 absolute error = 4.013e-05 relative error = 0.02982 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.726 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.095 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5974 2.211 h = 0.0001 0.004 y[1] (numeric) = -0.0421759790866 0.127614728264 y[1] (closed_form) = -0.0422141240051 0.127603413554 absolute error = 3.979e-05 relative error = 0.0296 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.728 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.451 Order of pole (three term test) = 1.382e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5973 2.215 h = 0.003 0.006 y[1] (numeric) = -0.0423035319193 0.127242031998 y[1] (closed_form) = -0.0423416128864 0.127231001192 absolute error = 3.965e-05 relative error = 0.02957 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.731 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.578 Order of pole (three term test) = 1.667e-14 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1349.7MB, alloc=44.3MB, time=17.31 x[1] = -1.5943 2.221 h = 0.0001 0.005 y[1] (numeric) = -0.0427593512899 0.126768006938 y[1] (closed_form) = -0.0427965324834 0.126756078713 absolute error = 3.905e-05 relative error = 0.02919 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.734 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.038 Order of pole (three term test) = 6.681e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5942 2.226 h = 0.0001 0.003 y[1] (numeric) = -0.0429101363561 0.126303252421 y[1] (closed_form) = -0.0429479935874 0.126291789842 absolute error = 3.955e-05 relative error = 0.02965 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.738 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.643 Order of pole (three term test) = 1.279e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5941 2.229 h = 0.001 0.001 y[1] (numeric) = -0.0430034293799 0.126026724001 y[1] (closed_form) = -0.0430415457658 0.126015074594 absolute error = 3.986e-05 relative error = 0.02993 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.74 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.291 Order of pole (three term test) = 5.833e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5931 2.23 h = 0.0001 0.004 y[1] (numeric) = -0.0431242361428 0.125961555735 y[1] (closed_form) = -0.0431625100871 0.125949858056 absolute error = 4.002e-05 relative error = 0.03006 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.741 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.754 Order of pole (three term test) = 1.944e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.593 2.234 h = 0.003 0.006 y[1] (numeric) = -0.0432444456782 0.125591891417 y[1] (closed_form) = -0.0432823211191 0.12558072654 absolute error = 3.949e-05 relative error = 0.02973 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.744 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.6 Order of pole (three term test) = 3.842e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.59 2.24 h = 0.0001 0.005 y[1] (numeric) = -0.0436863389391 0.125117430335 y[1] (closed_form) = -0.0437233129471 0.12510540381 absolute error = 3.888e-05 relative error = 0.02934 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.747 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.048 Order of pole (three term test) = 1.471e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5899 2.245 h = 0.0001 0.003 y[1] (numeric) = -0.0438276977857 0.124656925766 y[1] (closed_form) = -0.0438653446817 0.124645342001 absolute error = 3.939e-05 relative error = 0.02981 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.751 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.651 Order of pole (three term test) = 1.121e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5898 2.248 h = 0.001 0.001 y[1] (numeric) = -0.0439153417798 0.124382869069 y[1] (closed_form) = -0.0439532390412 0.124371096642 absolute error = 3.968e-05 relative error = 0.03008 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.753 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.297 Order of pole (three term test) = 6.723e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5888 2.249 h = 0.001 0.003 y[1] (numeric) = -0.0440334138879 0.124316740162 y[1] (closed_form) = -0.0440714647198 0.124304917113 absolute error = 3.985e-05 relative error = 0.03021 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.754 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.157 Order of pole (three term test) = 6.694e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5878 2.252 h = 0.0001 0.004 y[1] (numeric) = -0.0442032606446 0.124065962679 y[1] (closed_form) = -0.0442410031053 0.124054256262 absolute error = 3.952e-05 relative error = 0.03 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.755 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.487 Order of pole (three term test) = 5.218e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5877 2.256 h = 0.003 0.006 y[1] (numeric) = -0.044314415322 0.123700371019 y[1] (closed_form) = -0.0443521090014 0.123688939762 absolute error = 3.939e-05 relative error = 0.02998 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.759 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.625 Order of pole (three term test) = 6.779e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5847 2.262 h = 0.0001 0.005 y[1] (numeric) = -0.0447404521757 0.123225558923 y[1] (closed_form) = -0.0447772431466 0.123213306551 absolute error = 3.878e-05 relative error = 0.02958 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.762 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.059 Order of pole (three term test) = 5.193e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5846 2.267 h = 0.0001 0.003 y[1] (numeric) = -0.044871125685 0.12276998926 y[1] (closed_form) = -0.0449085855937 0.122758153785 absolute error = 3.929e-05 relative error = 0.03005 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.766 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.66 Order of pole (three term test) = 1.029e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5845 2.27 h = 0.001 0.001 y[1] (numeric) = -0.0449523650279 0.122498804127 y[1] (closed_form) = -0.0449900653184 0.12248677806 absolute error = 3.957e-05 relative error = 0.03033 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.768 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.304 Order of pole (three term test) = 1.276e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5835 2.271 h = 0.001 0.003 y[1] (numeric) = -0.0450673145245 0.122431609813 y[1] (closed_form) = -0.04510516383 0.122419530529 absolute error = 3.973e-05 relative error = 0.03045 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.769 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.191 Order of pole (three term test) = 3.918e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5825 2.274 h = 0.0001 0.004 y[1] (numeric) = -0.0452298435479 0.122181837911 y[1] (closed_form) = -0.0452673939926 0.12216988014 absolute error = 3.941e-05 relative error = 0.03025 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.77 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.505 Order of pole (three term test) = 1.650e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5824 2.278 h = 0.003 0.006 y[1] (numeric) = -0.0453325666652 0.121820193296 y[1] (closed_form) = -0.0453700759936 0.121808505871 absolute error = 3.929e-05 relative error = 0.03023 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.774 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.65 Order of pole (three term test) = 5.945e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5794 2.284 h = 0.0001 0.005 y[1] (numeric) = -0.0457430831293 0.121345419797 y[1] (closed_form) = -0.0457796897213 0.121332950727 absolute error = 3.867e-05 relative error = 0.02982 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.777 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.07 Order of pole (three term test) = 6.111e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5793 2.289 h = 0.0001 0.003 y[1] (numeric) = -0.0458634223162 0.120894934113 y[1] (closed_form) = -0.0459006932316 0.1208828569 absolute error = 3.918e-05 relative error = 0.0303 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.781 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.669 Order of pole (three term test) = 2.059e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5792 2.292 h = 0.001 0.001 y[1] (numeric) = -0.0459384650418 0.120626711522 y[1] (closed_form) = -0.0459759665694 0.120614442138 absolute error = 3.946e-05 relative error = 0.03057 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.783 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.311 Order of pole (three term test) = 1.316e-14 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1396.5MB, alloc=44.3MB, time=17.92 x[1] = -1.5782 2.293 h = 0.001 0.003 y[1] (numeric) = -0.0460503343167 0.120558549688 y[1] (closed_form) = -0.0460879803507 0.120546224698 absolute error = 3.961e-05 relative error = 0.03069 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.784 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.224 Order of pole (three term test) = 1.847e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5772 2.296 h = 0.0001 0.004 y[1] (numeric) = -0.046205728877 0.12030993659 y[1] (closed_form) = -0.0462430854467 0.120297737575 absolute error = 3.930e-05 relative error = 0.03049 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.786 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.525 Order of pole (three term test) = 9.930e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5771 2.3 h = 0.003 0.006 y[1] (numeric) = -0.0463002981748 0.119952354476 y[1] (closed_form) = -0.0463376209417 0.119940420899 absolute error = 3.918e-05 relative error = 0.03047 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.789 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.675 Order of pole (three term test) = 6.996e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5741 2.306 h = 0.0001 0.005 y[1] (numeric) = -0.0466956327368 0.119477988587 y[1] (closed_form) = -0.0467320539087 0.119465311762 absolute error = 3.856e-05 relative error = 0.03006 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.792 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.081 Order of pole (three term test) = 8.645e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.574 2.311 h = 0.0001 0.003 y[1] (numeric) = -0.04680598348 0.119032721475 y[1] (closed_form) = -0.0468430637478 0.119020412284 absolute error = 3.907e-05 relative error = 0.03055 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.796 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.678 Order of pole (three term test) = 8.358e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5739 2.314 h = 0.001 0.001 y[1] (numeric) = -0.0468750346568 0.118767543771 y[1] (closed_form) = -0.0469123359866 0.118755041159 absolute error = 3.934e-05 relative error = 0.03081 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.799 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.319 Order of pole (three term test) = 7.784e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5729 2.315 h = 0.001 0.003 y[1] (numeric) = -0.0469838678431 0.118698508387 y[1] (closed_form) = -0.047021309223 0.118685947979 absolute error = 3.949e-05 relative error = 0.03094 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.799 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.258 Order of pole (three term test) = 2.171e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5719 2.318 h = 0.0001 0.004 y[1] (numeric) = -0.047132310754 0.118451197718 y[1] (closed_form) = -0.0471694719416 0.118438767352 absolute error = 3.919e-05 relative error = 0.03074 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.801 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.544 Order of pole (three term test) = 6.339e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5718 2.322 h = 0.003 0.006 y[1] (numeric) = -0.0472189998191 0.11809778222 y[1] (closed_form) = -0.0472561341742 0.1180856123 absolute error = 3.908e-05 relative error = 0.03072 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.804 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.701 Order of pole (three term test) = 1.518e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5688 2.328 h = 0.0001 0.005 y[1] (numeric) = -0.0475994926273 0.117624172934 y[1] (closed_form) = -0.0476357276219 0.117611297084 absolute error = 3.845e-05 relative error = 0.03031 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.807 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.093 Order of pole (three term test) = 8.927e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5687 2.333 h = 0.0001 0.003 y[1] (numeric) = -0.0477001953276 0.117184245166 y[1] (closed_form) = -0.047737083626 0.117171713541 absolute error = 3.896e-05 relative error = 0.03079 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.811 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.687 Order of pole (three term test) = 1.333e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5686 2.336 h = 0.001 0.001 y[1] (numeric) = -0.0477634568519 0.116922186441 y[1] (closed_form) = -0.047800556886 0.116909460458 absolute error = 3.922e-05 relative error = 0.03105 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.814 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.326 Order of pole (three term test) = 9.163e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5676 2.337 h = 0.0001 0.004 y[1] (numeric) = -0.0478692996313 0.116852367626 y[1] (closed_form) = -0.0479065353168 0.116839581845 absolute error = 3.937e-05 relative error = 0.03118 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.814 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.962 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5675 2.341 h = 0.003 0.006 y[1] (numeric) = -0.0479497509869 0.116502441118 y[1] (closed_form) = -0.0479866870133 0.116490173456 absolute error = 3.892e-05 relative error = 0.03089 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.817 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.723 Order of pole (three term test) = 9.497e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5645 2.347 h = 0.0001 0.005 y[1] (numeric) = -0.0483177559093 0.116029918978 y[1] (closed_form) = -0.0483537957451 0.116016976598 absolute error = 3.829e-05 relative error = 0.03047 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.821 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.103 Order of pole (three term test) = 7.281e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5644 2.352 h = 0.0001 0.003 y[1] (numeric) = -0.048410487388 0.115594783286 y[1] (closed_form) = -0.04844717486 0.115582165705 absolute error = 3.880e-05 relative error = 0.03096 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.825 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.695 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5643 2.355 h = 0.001 0.001 y[1] (numeric) = -0.0484689626959 0.115335528343 y[1] (closed_form) = -0.0485058540513 0.115322715941 absolute error = 3.905e-05 relative error = 0.03122 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.827 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.332 Order of pole (three term test) = 3.155e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5633 2.356 h = 0.001 0.003 y[1] (numeric) = -0.0485722611181 0.115265139312 y[1] (closed_form) = -0.0486092843674 0.115252265585 absolute error = 3.920e-05 relative error = 0.03134 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.827 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.322 Order of pole (three term test) = 1.539e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5623 2.359 h = 0.0001 0.004 y[1] (numeric) = -0.04870827144 0.115020680654 y[1] (closed_form) = -0.0487450314234 0.115007943428 absolute error = 3.890e-05 relative error = 0.03115 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.829 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.58 Order of pole (three term test) = 5.445e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5622 2.363 h = 0.003 0.006 y[1] (numeric) = -0.0487810621627 0.114675345028 y[1] (closed_form) = -0.0488178073376 0.114662858723 absolute error = 3.881e-05 relative error = 0.03114 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.833 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.749 Order of pole (three term test) = 1.500e-14 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1443.2MB, alloc=44.3MB, time=18.52 x[1] = -1.5592 2.369 h = 0.0001 0.005 y[1] (numeric) = -0.0491348637658 0.1142041736 y[1] (closed_form) = -0.0491707168133 0.11419104787 absolute error = 3.818e-05 relative error = 0.03071 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.836 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.114 Order of pole (three term test) = 3.834e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5591 2.374 h = 0.0001 0.003 y[1] (numeric) = -0.0492185660998 0.113774563495 y[1] (closed_form) = -0.0492550600731 0.113761740653 absolute error = 3.868e-05 relative error = 0.0312 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.84 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.705 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.559 2.377 h = 0.001 0.001 y[1] (numeric) = -0.0492716190516 0.11351854243 y[1] (closed_form) = -0.0493083080102 0.113505524362 absolute error = 3.893e-05 relative error = 0.03146 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.843 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.339 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.558 2.378 h = 0.001 0.003 y[1] (numeric) = -0.049372016536 0.113447527083 y[1] (closed_form) = -0.0494088331112 0.113434446018 absolute error = 3.907e-05 relative error = 0.03158 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.843 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.357 Order of pole (three term test) = 1.322e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.557 2.381 h = 0.0001 0.004 y[1] (numeric) = -0.0495015942567 0.113204729578 y[1] (closed_form) = -0.0495381564267 0.113191788038 absolute error = 3.878e-05 relative error = 0.03139 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.845 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.6 Order of pole (three term test) = 6.875e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5569 2.385 h = 0.003 0.006 y[1] (numeric) = -0.0495672630917 0.112863797273 y[1] (closed_form) = -0.0496038164881 0.112851101513 absolute error = 3.870e-05 relative error = 0.03139 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.848 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.775 Order of pole (three term test) = 6.301e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5539 2.391 h = 0.0001 0.005 y[1] (numeric) = -0.0499072020746 0.112394271613 y[1] (closed_form) = -0.0499428682977 0.112380970644 absolute error = 3.807e-05 relative error = 0.03095 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.852 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.126 Order of pole (three term test) = 9.077e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5538 2.396 h = 0.0001 0.003 y[1] (numeric) = -0.0499821983107 0.111970271908 y[1] (closed_form) = -0.0500184983127 0.111957252703 absolute error = 3.856e-05 relative error = 0.03145 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.856 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.714 Order of pole (three term test) = 1.537e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5537 2.399 h = 0.001 0.001 y[1] (numeric) = -0.0500300207082 0.11171753733 y[1] (closed_form) = -0.0500665070287 0.111704322756 absolute error = 3.881e-05 relative error = 0.0317 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.858 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.347 Order of pole (three term test) = 1.571e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5527 2.4 h = 0.001 0.003 y[1] (numeric) = -0.0501275663397 0.111645975173 y[1] (closed_form) = -0.050164176069 0.111632696096 absolute error = 3.894e-05 relative error = 0.03182 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.858 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.392 Order of pole (three term test) = 7.371e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5517 2.403 h = 0.0001 0.004 y[1] (numeric) = -0.0502508896177 0.111404948523 y[1] (closed_form) = -0.0502872536459 0.111391811663 absolute error = 3.866e-05 relative error = 0.03164 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.86 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.619 Order of pole (three term test) = 1.634e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5516 2.407 h = 0.003 0.006 y[1] (numeric) = -0.0503096918189 0.111068484673 y[1] (closed_form) = -0.0503460527989 0.111055588424 absolute error = 3.858e-05 relative error = 0.03164 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.864 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.801 Order of pole (three term test) = 1.430e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5486 2.413 h = 0.0001 0.005 y[1] (numeric) = -0.0506361079216 0.110600882166 y[1] (closed_form) = -0.0506715875076 0.110587413849 absolute error = 3.795e-05 relative error = 0.0312 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.867 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.137 Order of pole (three term test) = 6.403e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5485 2.418 h = 0.0001 0.003 y[1] (numeric) = -0.0507027146678 0.110182566262 y[1] (closed_form) = -0.0507388204899 0.110169359363 absolute error = 3.845e-05 relative error = 0.0317 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.871 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.723 Order of pole (three term test) = 1.784e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5484 2.421 h = 0.001 0.001 y[1] (numeric) = -0.0507454945562 0.109933163958 y[1] (closed_form) = -0.0507817782626 0.109919761793 absolute error = 3.868e-05 relative error = 0.03194 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.874 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.354 Order of pole (three term test) = 2.003e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5474 2.422 h = 0.001 0.003 y[1] (numeric) = -0.0508402383113 0.109861130951 y[1] (closed_form) = -0.0508766412915 0.109847662936 absolute error = 3.881e-05 relative error = 0.03206 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.874 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.427 Order of pole (three term test) = 9.928e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5464 2.425 h = 0.0001 0.004 y[1] (numeric) = -0.0509574835185 0.109621976862 y[1] (closed_form) = -0.0509936493391 0.10960865344 absolute error = 3.854e-05 relative error = 0.03188 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.876 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.639 Order of pole (three term test) = 6.290e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5463 2.429 h = 0.003 0.006 y[1] (numeric) = -0.0510096691932 0.109290037677 y[1] (closed_form) = -0.0510458373907 0.109276949676 absolute error = 3.846e-05 relative error = 0.03189 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.879 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.827 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5433 2.435 h = 0.0001 0.005 y[1] (numeric) = -0.0513229006353 0.108824618642 y[1] (closed_form) = -0.0513581939809 0.108810990651 absolute error = 3.783e-05 relative error = 0.03144 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.883 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.149 Order of pole (three term test) = 9.316e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5432 2.44 h = 0.0001 0.003 y[1] (numeric) = -0.0513814278906 0.108412049123 y[1] (closed_form) = -0.0514173395724 0.108398662969 absolute error = 3.833e-05 relative error = 0.03194 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.887 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.733 Order of pole (three term test) = 4.676e-14 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1490.0MB, alloc=44.3MB, time=19.12 x[1] = -1.5431 2.443 h = 0.001 0.001 y[1] (numeric) = -0.0514193494541 0.108166018404 y[1] (closed_form) = -0.0514554308191 0.108152437315 absolute error = 3.855e-05 relative error = 0.03219 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.89 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.361 Order of pole (three term test) = 6.397e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5421 2.444 h = 0.0001 0.004 y[1] (numeric) = -0.0515113420537 0.108093587045 y[1] (closed_form) = -0.0515475386332 0.108079938911 absolute error = 3.868e-05 relative error = 0.03231 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.89 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.176 Order of pole (three term test) = 3.543e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.542 2.448 h = 0.003 0.006 y[1] (numeric) = -0.0515583059134 0.107765393819 y[1] (closed_form) = -0.0515942866805 0.107752238693 absolute error = 3.831e-05 relative error = 0.03207 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.893 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.85 Order of pole (three term test) = 1.922e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.539 2.454 h = 0.0001 0.005 y[1] (numeric) = -0.0518604876572 0.107302201733 y[1] (closed_form) = -0.0518956001332 0.107288533292 absolute error = 3.768e-05 relative error = 0.03162 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.897 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.159 Order of pole (three term test) = 7.230e-15 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5389 2.459 h = 0.0001 0.003 y[1] (numeric) = -0.0519123727195 0.10689471213 y[1] (closed_form) = -0.0519480962529 0.106881269373 absolute error = 3.817e-05 relative error = 0.03212 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.901 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.741 Order of pole (three term test) = 5.038e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5388 2.462 h = 0.001 0.001 y[1] (numeric) = -0.0519462975615 0.106651665305 y[1] (closed_form) = -0.0519821839128 0.106638028167 absolute error = 3.839e-05 relative error = 0.03236 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.903 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.368 Order of pole (three term test) = 7.001e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5378 2.463 h = 0.001 0.003 y[1] (numeric) = -0.0520359595075 0.106578978475 y[1] (closed_form) = -0.0520719576299 0.106565273424 absolute error = 3.852e-05 relative error = 0.03248 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.904 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.493 Order of pole (three term test) = 7.806e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5368 2.466 h = 0.0001 0.004 y[1] (numeric) = -0.0521423821081 0.106343620978 y[1] (closed_form) = -0.0521781585348 0.106330064055 absolute error = 3.826e-05 relative error = 0.0323 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.906 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.677 Order of pole (three term test) = 1.209e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5367 2.47 h = 0.003 0.006 y[1] (numeric) = -0.0521829585899 0.10602029412 y[1] (closed_form) = -0.0522187466592 0.106006962894 absolute error = 3.819e-05 relative error = 0.03232 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.909 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.877 Order of pole (three term test) = 1.110e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5337 2.476 h = 0.0001 0.005 y[1] (numeric) = -0.0524725818877 0.105559722608 y[1] (closed_form) = -0.0525075094565 0.105545908182 absolute error = 3.756e-05 relative error = 0.03186 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.913 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.171 Order of pole (three term test) = 1.205e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5336 2.481 h = 0.0001 0.003 y[1] (numeric) = -0.0525169467109 0.105158065495 y[1] (closed_form) = -0.0525524768782 0.105144458561 absolute error = 3.805e-05 relative error = 0.03237 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.917 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.751 Order of pole (three term test) = 8.451e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5335 2.484 h = 0.001 0.001 y[1] (numeric) = -0.0525463456912 0.104918445246 y[1] (closed_form) = -0.0525820309107 0.104904644649 absolute error = 3.826e-05 relative error = 0.03261 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.919 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.375 Order of pole (three term test) = 5.187e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5325 2.485 h = 0.001 0.003 y[1] (numeric) = -0.0526333531457 0.104845485445 y[1] (closed_form) = -0.0526691462257 0.104831615999 absolute error = 3.839e-05 relative error = 0.03272 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.92 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.528 Order of pole (three term test) = 1.207e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5315 2.488 h = 0.0001 0.004 y[1] (numeric) = -0.0527341915121 0.10461224817 y[1] (closed_form) = -0.0527697709438 0.104598528411 absolute error = 3.813e-05 relative error = 0.03255 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.922 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.697 Order of pole (three term test) = 1.007e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5314 2.492 h = 0.003 0.006 y[1] (numeric) = -0.0527688378461 0.104293558814 y[1] (closed_form) = -0.0528044335378 0.104280059571 absolute error = 3.807e-05 relative error = 0.03257 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.925 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.904 Order of pole (three term test) = 1.308e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5284 2.498 h = 0.0001 0.005 y[1] (numeric) = -0.0530462336846 0.103835822771 y[1] (closed_form) = -0.0530809772643 0.10382186941 absolute error = 3.744e-05 relative error = 0.03211 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.928 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.183 Order of pole (three term test) = 1.003e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5283 2.503 h = 0.0001 0.003 y[1] (numeric) = -0.0530833685692 0.103440032968 y[1] (closed_form) = -0.0531187060316 0.103426269632 absolute error = 3.792e-05 relative error = 0.03262 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.933 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.76 Order of pole (three term test) = 4.735e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5282 2.506 h = 0.001 0.001 y[1] (numeric) = -0.0531084143365 0.103203861974 y[1] (closed_form) = -0.0531438993165 0.103189905882 absolute error = 3.813e-05 relative error = 0.03285 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.935 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.383 Order of pole (three term test) = 6.605e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5272 2.507 h = 0.001 0.003 y[1] (numeric) = -0.0531928193776 0.103130692295 y[1] (closed_form) = -0.0532284083893 0.103116666548 absolute error = 3.825e-05 relative error = 0.03296 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.936 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.564 Order of pole (three term test) = 6.422e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5262 2.51 h = 0.0001 0.004 y[1] (numeric) = -0.0532882411333 0.102899649091 y[1] (closed_form) = -0.0533236243659 0.102885774332 absolute error = 3.801e-05 relative error = 0.0328 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.938 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.717 Order of pole (three term test) = 2.373e-14 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1536.8MB, alloc=44.3MB, time=19.71 x[1] = -1.5261 2.514 h = 0.003 0.006 y[1] (numeric) = -0.0533171864699 0.102585623285 y[1] (closed_form) = -0.0533525903157 0.102571963878 absolute error = 3.795e-05 relative error = 0.03282 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.941 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.931 Order of pole (three term test) = 1.540e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5231 2.52 h = 0.0001 0.005 y[1] (numeric) = -0.0535826825604 0.102130922873 y[1] (closed_form) = -0.053617243228 0.102116837413 absolute error = 3.732e-05 relative error = 0.03236 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.945 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.195 Order of pole (three term test) = 1.182e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.523 2.525 h = 0.0001 0.003 y[1] (numeric) = -0.0536128708047 0.101741026503 y[1] (closed_form) = -0.0536480164136 0.101727114309 absolute error = 3.780e-05 relative error = 0.03287 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.949 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.77 Order of pole (three term test) = 3.944e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5229 2.528 h = 0.001 0.001 y[1] (numeric) = -0.0536337319004 0.101508322226 y[1] (closed_form) = -0.053669017722 0.101494218357 absolute error = 3.800e-05 relative error = 0.0331 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.951 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.39 Order of pole (three term test) = 1.206e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5219 2.529 h = 0.001 0.003 y[1] (numeric) = -0.0537155868643 0.101435002654 y[1] (closed_form) = -0.0537509729719 0.101420828449 absolute error = 3.812e-05 relative error = 0.03321 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.952 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.6 Order of pole (three term test) = 5.349e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5209 2.532 h = 0.0001 0.004 y[1] (numeric) = -0.053805757021 0.101206220894 y[1] (closed_form) = -0.0538409450384 0.101192198733 absolute error = 3.788e-05 relative error = 0.03305 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.954 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.737 Order of pole (three term test) = 1.425e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5208 2.536 h = 0.003 0.006 y[1] (numeric) = -0.0538292249461 0.100896877888 y[1] (closed_form) = -0.0538644376747 0.100883065943 absolute error = 3.782e-05 relative error = 0.03307 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.957 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.958 Order of pole (three term test) = 9.072e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5178 2.542 h = 0.0001 0.005 y[1] (numeric) = -0.0540831453635 0.100445399124 y[1] (closed_form) = -0.0541175243431 0.10043118819 absolute error = 3.720e-05 relative error = 0.03261 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.961 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.207 Order of pole (three term test) = 1.420e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5177 2.547 h = 0.0001 0.003 y[1] (numeric) = -0.0541066632175 0.100061414118 y[1] (closed_form) = -0.0541416180012 0.100047360382 absolute error = 3.767e-05 relative error = 0.03312 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.965 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.78 Order of pole (three term test) = 4.646e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5176 2.55 h = 0.001 0.001 y[1] (numeric) = -0.0541235040449 0.0998321891018 y[1] (closed_form) = -0.054158591964 0.0998179449355 absolute error = 3.787e-05 relative error = 0.03335 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.967 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.398 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5166 2.551 h = 0.0001 0.004 y[1] (numeric) = -0.0542028614192 0.0997587766084 y[1] (closed_form) = -0.0542380459629 0.0997444615399 absolute error = 3.799e-05 relative error = 0.03346 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.968 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.397 Order of pole (three term test) = 3.936e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5165 2.555 h = 0.003 0.006 y[1] (numeric) = -0.0542220193581 0.0994532811579 y[1] (closed_form) = -0.054257057839 0.0994394273539 absolute error = 3.768e-05 relative error = 0.03326 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.971 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.981 Order of pole (three term test) = 6.279e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5135 2.561 h = 0.0001 0.005 y[1] (numeric) = -0.054466273454 0.0990048467747 y[1] (closed_form) = -0.0545004869689 0.0989906163703 absolute error = 3.705e-05 relative error = 0.03279 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.975 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.218 Order of pole (three term test) = 1.607e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5134 2.566 h = 0.0001 0.003 y[1] (numeric) = -0.0544843360345 0.0986260336475 y[1] (closed_form) = -0.0545191171728 0.0986119472657 absolute error = 3.753e-05 relative error = 0.0333 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.979 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.788 Order of pole (three term test) = 5.360e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5133 2.569 h = 0.001 0.001 y[1] (numeric) = -0.0544978863876 0.0983998552711 y[1] (closed_form) = -0.054532794767 0.0983855797293 absolute error = 3.771e-05 relative error = 0.03353 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.982 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.405 Order of pole (three term test) = 5.183e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5123 2.57 h = 0.001 0.003 y[1] (numeric) = -0.0545751357556 0.0983264350827 y[1] (closed_form) = -0.0546101376711 0.0983120882825 absolute error = 3.783e-05 relative error = 0.03364 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.982 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.668 Order of pole (three term test) = 7.269e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5113 2.573 h = 0.0001 0.004 y[1] (numeric) = -0.0546559922171 0.098102077745 y[1] (closed_form) = -0.0546908098703 0.0980878842676 absolute error = 3.760e-05 relative error = 0.03348 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.984 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.776 Order of pole (three term test) = 7.596e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5112 2.577 h = 0.003 0.006 y[1] (numeric) = -0.0546698998906 0.0978015371653 y[1] (closed_form) = -0.0547047491727 0.0977875443944 absolute error = 3.755e-05 relative error = 0.03352 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.987 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.008 Order of pole (three term test) = 1.395e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5082 2.583 h = 0.0001 0.005 y[1] (numeric) = -0.0549031724154 0.0973566311444 y[1] (closed_form) = -0.0549372069464 0.0973422870168 absolute error = 3.693e-05 relative error = 0.03304 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.991 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.23 Order of pole (three term test) = 3.785e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5081 2.588 h = 0.0001 0.003 y[1] (numeric) = -0.0549150598145 0.0969837395117 y[1] (closed_form) = -0.0549496525484 0.0969695245852 absolute error = 3.740e-05 relative error = 0.03356 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.995 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.798 Order of pole (three term test) = 1.263e-13 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1583.5MB, alloc=44.3MB, time=20.31 x[1] = -1.508 2.591 h = 0.001 0.001 y[1] (numeric) = -0.0549248847719 0.0967610497977 y[1] (closed_form) = -0.0549595980879 0.0967466472209 absolute error = 3.758e-05 relative error = 0.03378 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.998 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.412 Order of pole (three term test) = 1.365e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.507 2.592 h = 0.001 0.003 y[1] (numeric) = -0.0549997348849 0.0966876343735 y[1] (closed_form) = -0.0550345382358 0.0966731601718 absolute error = 3.769e-05 relative error = 0.03388 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.998 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.704 Order of pole (three term test) = 1.211e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.506 2.595 h = 0.0001 0.004 y[1] (numeric) = -0.0550757969515 0.0964656962105 y[1] (closed_form) = -0.0551104232028 0.0964513757674 absolute error = 3.747e-05 relative error = 0.03373 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.796 Order of pole (three term test) = 3.325e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5059 2.599 h = 0.003 0.006 y[1] (numeric) = -0.0550848358808 0.0961698570368 y[1] (closed_form) = -0.05511949718 0.0961557322772 absolute error = 3.743e-05 relative error = 0.03377 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.004 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.036 Order of pole (three term test) = 1.350e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5029 2.605 h = 0.0001 0.005 y[1] (numeric) = -0.0553074386734 0.0957286281372 y[1] (closed_form) = -0.0553412958025 0.0957141763162 absolute error = 3.681e-05 relative error = 0.0333 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.007 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.242 Order of pole (three term test) = 3.153e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5028 2.61 h = 0.0001 0.003 y[1] (numeric) = -0.0553134068194 0.0953616552188 y[1] (closed_form) = -0.0553478126106 0.0953473184209 absolute error = 3.727e-05 relative error = 0.03381 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.012 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.808 Order of pole (three term test) = 1.051e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5027 2.613 h = 0.001 0.001 y[1] (numeric) = -0.0553196588354 0.0951424542624 y[1] (closed_form) = -0.0553541787694 0.0951279314518 absolute error = 3.745e-05 relative error = 0.03403 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.014 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.42 Order of pole (three term test) = 1.017e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5017 2.614 h = 0.001 0.003 y[1] (numeric) = -0.0553921620591 0.0950690924721 y[1] (closed_form) = -0.0554267686128 0.0950544977689 absolute error = 3.756e-05 relative error = 0.03413 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.015 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.741 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5007 2.617 h = 0.0001 0.004 y[1] (numeric) = -0.0554635836133 0.0948496185907 y[1] (closed_form) = -0.055498020046 0.0948351778887 absolute error = 3.734e-05 relative error = 0.03398 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.017 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.817 Order of pole (three term test) = 5.269e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5006 2.621 h = 0.003 0.006 y[1] (numeric) = -0.0554679556747 0.094558477511 y[1] (closed_form) = -0.0555024303541 0.0945442275197 absolute error = 3.730e-05 relative error = 0.03403 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.02 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.063 Order of pole (three term test) = 8.548e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4976 2.627 h = 0.0001 0.005 y[1] (numeric) = -0.0556801958638 0.0941210625188 y[1] (closed_form) = -0.0557138772794 0.094106508833 absolute error = 3.669e-05 relative error = 0.03355 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.024 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.254 Order of pole (three term test) = 4.121e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4975 2.632 h = 0.0001 0.003 y[1] (numeric) = -0.0556804936402 0.0937599991328 y[1] (closed_form) = -0.0557147140803 0.0937455469182 absolute error = 3.715e-05 relative error = 0.03406 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.028 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.818 Order of pole (three term test) = 8.756e-15 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4974 2.635 h = 0.001 0.001 y[1] (numeric) = -0.0556833210218 0.0935442831753 y[1] (closed_form) = -0.0557176493817 0.0935296467028 absolute error = 3.732e-05 relative error = 0.03428 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.031 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.428 Order of pole (three term test) = 8.465e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4964 2.636 h = 0.001 0.003 y[1] (numeric) = -0.0557535295303 0.093471021237 y[1] (closed_form) = -0.055787941181 0.0934563126972 absolute error = 3.742e-05 relative error = 0.03438 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.031 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.778 Order of pole (three term test) = 3.562e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4954 2.639 h = 0.0001 0.004 y[1] (numeric) = -0.0558204614026 0.0932540516333 y[1] (closed_form) = -0.055854709727 0.0932394971555 absolute error = 3.721e-05 relative error = 0.03424 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.033 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.838 Order of pole (three term test) = 6.937e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4953 2.643 h = 0.003 0.006 y[1] (numeric) = -0.0558203628929 0.092967600342 y[1] (closed_form) = -0.0558546524512 0.0929532316575 absolute error = 3.718e-05 relative error = 0.03428 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.037 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.091 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4923 2.649 h = 0.0001 0.005 y[1] (numeric) = -0.0560225426893 0.0925341246033 y[1] (closed_form) = -0.0560560501772 0.0925194746829 absolute error = 3.657e-05 relative error = 0.03381 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.04 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.267 Order of pole (three term test) = 5.320e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4922 2.654 h = 0.0001 0.003 y[1] (numeric) = -0.0560174119731 0.0921789555869 y[1] (closed_form) = -0.0560514487725 0.0921643941948 absolute error = 3.702e-05 relative error = 0.03432 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.045 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.827 Order of pole (three term test) = 1.051e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4921 2.657 h = 0.001 0.001 y[1] (numeric) = -0.0560169588998 0.0919667172658 y[1] (closed_form) = -0.056051097609 0.0919519734775 absolute error = 3.719e-05 relative error = 0.03453 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.047 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.436 Order of pole (three term test) = 1.041e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4911 2.658 h = 0.0001 0.004 y[1] (numeric) = -0.0560849246025 0.0918935988385 y[1] (closed_form) = -0.0561191433596 0.0918787828957 absolute error = 3.729e-05 relative error = 0.03463 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.048 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.623 Order of pole (three term test) = 1.019e-13 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1630.3MB, alloc=44.3MB, time=20.90 x[1] = -1.491 2.662 h = 0.003 0.006 y[1] (numeric) = -0.0560813192328 0.0916109800482 y[1] (closed_form) = -0.0561154489121 0.0915965899482 absolute error = 3.704e-05 relative error = 0.03448 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.051 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.115 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.488 2.668 h = 0.0001 0.005 y[1] (numeric) = -0.0562751262454 0.0911811021451 y[1] (closed_form) = -0.0563084839444 0.0911664492927 absolute error = 3.643e-05 relative error = 0.034 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.055 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.277 Order of pole (three term test) = 7.131e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4879 2.673 h = 0.0001 0.003 y[1] (numeric) = -0.0562655811036 0.0908310512678 y[1] (closed_form) = -0.0562994595646 0.0908164763931 absolute error = 3.688e-05 relative error = 0.03452 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.059 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.836 Order of pole (three term test) = 3.566e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4878 2.676 h = 0.001 0.001 y[1] (numeric) = -0.0562624578919 0.0906218347259 y[1] (closed_form) = -0.0562964332804 0.090607079204 absolute error = 3.704e-05 relative error = 0.03472 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.062 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.443 Order of pole (three term test) = 1.172e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4868 2.677 h = 0.001 0.003 y[1] (numeric) = -0.0563285367492 0.0905488987833 y[1] (closed_form) = -0.0563625894634 0.0905340711347 absolute error = 3.714e-05 relative error = 0.03483 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.062 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.847 Order of pole (three term test) = 1.620e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4858 2.68 h = 0.0001 0.004 y[1] (numeric) = -0.0563875358786 0.0903367284551 y[1] (closed_form) = -0.0564214374191 0.0903220544611 absolute error = 3.694e-05 relative error = 0.03469 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.064 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.877 Order of pole (three term test) = 5.956e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4857 2.684 h = 0.003 0.006 y[1] (numeric) = -0.0563796775829 0.0900590139112 y[1] (closed_form) = -0.0564136253251 0.0900445166922 absolute error = 3.691e-05 relative error = 0.03474 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.068 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.143 Order of pole (three term test) = 7.729e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4827 2.69 h = 0.0001 0.005 y[1] (numeric) = -0.0565639740528 0.0896332763699 y[1] (closed_form) = -0.0565971614368 0.0896185372217 absolute error = 3.631e-05 relative error = 0.03426 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.072 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.29 Order of pole (three term test) = 4.198e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4826 2.695 h = 0.0001 0.003 y[1] (numeric) = -0.0565494316987 0.0892890744125 y[1] (closed_form) = -0.0565831300523 0.089274401385 absolute error = 3.675e-05 relative error = 0.03477 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.076 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.846 Order of pole (three term test) = 2.802e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4825 2.698 h = 0.001 0.001 y[1] (numeric) = -0.0565432852537 0.0890833114273 y[1] (closed_form) = -0.0565770749113 0.0890684597852 absolute error = 3.691e-05 relative error = 0.03498 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.078 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.45 Order of pole (three term test) = 1.353e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4815 2.699 h = 0.001 0.003 y[1] (numeric) = -0.0566072174179 0.0890105931272 y[1] (closed_form) = -0.0566410813189 0.0889956694186 absolute error = 3.701e-05 relative error = 0.03508 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.079 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.885 Order of pole (three term test) = 9.110e-15 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4805 2.702 h = 0.0001 0.004 y[1] (numeric) = -0.0566621413635 0.0888010138775 y[1] (closed_form) = -0.0566958603623 0.0887862434281 absolute error = 3.681e-05 relative error = 0.03494 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.081 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.898 Order of pole (three term test) = 4.958e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4804 2.706 h = 0.003 0.006 y[1] (numeric) = -0.0566503433074 0.088527938561 y[1] (closed_form) = -0.0566841109374 0.0885133401524 absolute error = 3.679e-05 relative error = 0.035 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.084 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.171 Order of pole (three term test) = 6.433e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4774 2.712 h = 0.0001 0.005 y[1] (numeric) = -0.0568254163459 0.0881064368888 y[1] (closed_form) = -0.0568584354288 0.0880916165284 absolute error = 3.619e-05 relative error = 0.03452 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.088 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.302 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4773 2.717 h = 0.0001 0.003 y[1] (numeric) = -0.0568060988773 0.0877680538298 y[1] (closed_form) = -0.0568396191168 0.0877532882908 absolute error = 3.663e-05 relative error = 0.03503 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.093 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.856 Order of pole (three term test) = 1.655e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4772 2.72 h = 0.001 0.001 y[1] (numeric) = -0.0567970617141 0.0875657280677 y[1] (closed_form) = -0.0568306678357 0.0875507860272 absolute error = 3.678e-05 relative error = 0.03524 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.095 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.458 Order of pole (three term test) = 3.184e-15 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4762 2.721 h = 0.001 0.003 y[1] (numeric) = -0.0568588979583 0.0874932642532 y[1] (closed_form) = -0.0568925753258 0.0874782502789 absolute error = 3.687e-05 relative error = 0.03533 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.096 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.922 Order of pole (three term test) = 2.234e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4752 2.724 h = 0.0001 0.004 y[1] (numeric) = -0.056909885313 0.0872862987349 y[1] (closed_form) = -0.0569434238703 0.0872714374844 absolute error = 3.668e-05 relative error = 0.0352 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.098 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.92 Order of pole (three term test) = 1.305e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4751 2.728 h = 0.003 0.006 y[1] (numeric) = -0.056894322603 0.0870178380978 y[1] (closed_form) = -0.0569279120416 0.0870031442239 absolute error = 3.666e-05 relative error = 0.03526 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.101 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.199 Order of pole (three term test) = 1.071e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4721 2.734 h = 0.0001 0.005 y[1] (numeric) = -0.0570604538427 0.0866006582945 y[1] (closed_form) = -0.0570933067036 0.0865857616219 absolute error = 3.607e-05 relative error = 0.03478 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.105 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.315 Order of pole (three term test) = 1.300e-13 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1677.0MB, alloc=44.3MB, time=21.50 x[1] = -1.472 2.739 h = 0.0001 0.003 y[1] (numeric) = -0.0570365766132 0.0862680595947 y[1] (closed_form) = -0.057069920814 0.0862532069848 absolute error = 3.650e-05 relative error = 0.03529 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.109 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.866 Order of pole (three term test) = 1.948e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4719 2.742 h = 0.001 0.001 y[1] (numeric) = -0.0570247772661 0.0860691519891 y[1] (closed_form) = -0.0570582021241 0.0860541250627 absolute error = 3.665e-05 relative error = 0.03549 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.112 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.466 Order of pole (three term test) = 1.874e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4709 2.743 h = 0.001 0.003 y[1] (numeric) = -0.0570845678705 0.08599697729 y[1] (closed_form) = -0.0571180610613 0.0859818786304 absolute error = 3.674e-05 relative error = 0.03559 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.112 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.96 Order of pole (three term test) = 3.718e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4699 2.746 h = 0.0001 0.004 y[1] (numeric) = -0.0571317540141 0.0857926442251 y[1] (closed_form) = -0.057165114309 0.0857776976234 absolute error = 3.656e-05 relative error = 0.03546 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.115 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.941 Order of pole (three term test) = 9.713e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4698 2.75 h = 0.003 0.006 y[1] (numeric) = -0.0571125964267 0.0855287702015 y[1] (closed_form) = -0.0571460096811 0.0855139863851 absolute error = 3.654e-05 relative error = 0.03552 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.118 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.228 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4668 2.756 h = 0.0001 0.005 y[1] (numeric) = -0.057270061927 0.0851159892247 y[1] (closed_form) = -0.0573027507034 0.0851010209608 absolute error = 3.595e-05 relative error = 0.03504 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.122 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.327 Order of pole (three term test) = 6.844e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4667 2.761 h = 0.0001 0.003 y[1] (numeric) = -0.0572418336367 0.0847891361664 y[1] (closed_form) = -0.0572750039478 0.0847742017294 absolute error = 3.638e-05 relative error = 0.03556 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.126 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.877 Order of pole (three term test) = 6.843e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4666 2.764 h = 0.001 0.001 y[1] (numeric) = -0.0572273967107 0.0845936251197 y[1] (closed_form) = -0.0572606426468 0.0845785186154 absolute error = 3.652e-05 relative error = 0.03575 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.129 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.474 Order of pole (three term test) = 6.235e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4656 2.765 h = 0.0001 0.004 y[1] (numeric) = -0.0572851914155 0.0845217720384 y[1] (closed_form) = -0.0573185028549 0.0845065940646 absolute error = 3.661e-05 relative error = 0.03585 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.129 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.854 Order of pole (three term test) = 9.660e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4655 2.769 h = 0.003 0.006 y[1] (numeric) = -0.0572632234243 0.0842616311364 y[1] (closed_form) = -0.0572964915369 0.0842468421197 absolute error = 3.641e-05 relative error = 0.03573 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.133 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.252 Order of pole (three term test) = 1.027e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4625 2.775 h = 0.0001 0.005 y[1] (numeric) = -0.0574134999816 0.0838527904334 y[1] (closed_form) = -0.0574460543206 0.0838378319946 absolute error = 3.583e-05 relative error = 0.03525 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.137 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.339 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4624 2.78 h = 0.0001 0.003 y[1] (numeric) = -0.0573817562993 0.0835308976445 y[1] (closed_form) = -0.0574147836396 0.0835159647439 absolute error = 3.625e-05 relative error = 0.03576 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.141 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.885 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4623 2.783 h = 0.001 0.001 y[1] (numeric) = -0.0573651859209 0.0833383206282 y[1] (closed_form) = -0.0573982847334 0.0833232176989 absolute error = 3.638e-05 relative error = 0.03596 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.144 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.481 Order of pole (three term test) = 1.295e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4613 2.784 h = 0.001 0.003 y[1] (numeric) = -0.0574213063292 0.0832667918293 y[1] (closed_form) = -0.0574544682795 0.083251617737 absolute error = 3.647e-05 relative error = 0.03605 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.144 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.031 Order of pole (three term test) = 1.285e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4603 2.787 h = 0.0001 0.004 y[1] (numeric) = -0.0574618003094 0.08306743604 y[1] (closed_form) = -0.0574948398921 0.0830524123851 absolute error = 3.629e-05 relative error = 0.03593 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.146 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.981 Order of pole (three term test) = 4.655e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4602 2.791 h = 0.003 0.006 y[1] (numeric) = -0.057436441113 0.082812049274 y[1] (closed_form) = -0.057469537039 0.0827971800427 absolute error = 3.628e-05 relative error = 0.036 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.15 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.281 Order of pole (three term test) = 1.207e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4572 2.797 h = 0.0001 0.005 y[1] (numeric) = -0.0575785512196 0.082407724937 y[1] (closed_form) = -0.0576109456344 0.0823927032016 absolute error = 3.571e-05 relative error = 0.03552 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.154 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.351 Order of pole (three term test) = 5.566e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4571 2.802 h = 0.0001 0.003 y[1] (numeric) = -0.0575428268874 0.0820914934157 y[1] (closed_form) = -0.0575756845629 0.0820764879094 absolute error = 3.612e-05 relative error = 0.03603 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.158 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.896 Order of pole (three term test) = 1.979e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.457 2.805 h = 0.001 0.001 y[1] (numeric) = -0.0575238402085 0.0819022653101 y[1] (closed_form) = -0.0575567646714 0.0818870921218 absolute error = 3.625e-05 relative error = 0.03622 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.161 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.489 Order of pole (three term test) = 9.445e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.456 2.806 h = 0.001 0.003 y[1] (numeric) = -0.0575780560253 0.0818311126575 y[1] (closed_form) = -0.0576110409498 0.0818158686751 absolute error = 3.634e-05 relative error = 0.03631 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.161 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.069 Order of pole (three term test) = 1.511e-13 0 NO COMPLEX POLE (six term test) for Equation 1 memory used=1723.8MB, alloc=44.3MB, time=22.10 x[1] = -1.455 2.809 h = 0.0001 0.004 y[1] (numeric) = -0.0576151183901 0.0816344216143 y[1] (closed_form) = -0.057647986364 0.0816193270818 absolute error = 3.617e-05 relative error = 0.0362 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.163 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.003 Order of pole (three term test) = 1.095e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4549 2.813 h = 0.003 0.006 y[1] (numeric) = -0.0575866207995 0.0813835222521 y[1] (closed_form) = -0.0576195467461 0.0813685777746 absolute error = 3.616e-05 relative error = 0.03627 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.167 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.31 Order of pole (three term test) = 1.483e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4519 2.819 h = 0.0001 0.005 y[1] (numeric) = -0.0577208241259 0.0809837678806 y[1] (closed_form) = -0.057753060882 0.0809686870792 absolute error = 3.559e-05 relative error = 0.03578 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.171 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.364 Order of pole (three term test) = 1.091e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4518 2.824 h = 0.0001 0.003 y[1] (numeric) = -0.0576813093372 0.0806731487628 y[1] (closed_form) = -0.0577139996628 0.0806580753554 absolute error = 3.600e-05 relative error = 0.0363 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.175 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.906 Order of pole (three term test) = 8.127e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4517 2.827 h = 0.001 0.001 y[1] (numeric) = -0.0576600200228 0.0804872418067 y[1] (closed_form) = -0.0576927726309 0.0804720031078 absolute error = 3.612e-05 relative error = 0.03648 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.178 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.497 Order of pole (three term test) = 9.934e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4507 2.828 h = 0.001 0.003 y[1] (numeric) = -0.0577123792033 0.0804164921831 y[1] (closed_form) = -0.0577451896772 0.0804011831102 absolute error = 3.621e-05 relative error = 0.03658 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.178 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.107 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4497 2.831 h = 0.0001 0.004 y[1] (numeric) = -0.0577461328866 0.0802224714519 y[1] (closed_form) = -0.0577788316584 0.0802073107445 absolute error = 3.604e-05 relative error = 0.03646 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.181 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.024 Order of pole (three term test) = 1.293e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4496 2.835 h = 0.003 0.006 y[1] (numeric) = -0.0577146468085 0.0799760202852 y[1] (closed_form) = -0.0577474050392 0.0799610053444 absolute error = 3.604e-05 relative error = 0.03653 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.184 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.338 Order of pole (three term test) = 1.704e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4466 2.841 h = 0.0001 0.005 y[1] (numeric) = -0.0578411972599 0.0795808820973 y[1] (closed_form) = -0.0578732786569 0.0795657462977 absolute error = 3.547e-05 relative error = 0.03605 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.188 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.377 Order of pole (three term test) = 1.289e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4465 2.846 h = 0.0001 0.003 y[1] (numeric) = -0.0577980759715 0.0792758235031 y[1] (closed_form) = -0.0578306013075 0.0792606867196 absolute error = 3.588e-05 relative error = 0.03656 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.193 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.916 Order of pole (three term test) = 4.273e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4464 2.849 h = 0.001 0.001 y[1] (numeric) = -0.0577745939974 0.0790932080977 y[1] (closed_form) = -0.057807177286 0.0790779084509 absolute error = 3.600e-05 relative error = 0.03675 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.195 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.505 Order of pole (three term test) = 9.232e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4454 2.85 h = 0.001 0.003 y[1] (numeric) = -0.0578251438173 0.0790228865732 y[1] (closed_form) = -0.0578577824553 0.0790075170197 absolute error = 3.608e-05 relative error = 0.03684 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.196 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.146 Order of pole (three term test) = 5.794e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4444 2.853 h = 0.0001 0.004 y[1] (numeric) = -0.0578557085711 0.0788315387785 y[1] (closed_form) = -0.05788824059 0.0788163164166 absolute error = 3.592e-05 relative error = 0.03673 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.198 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.046 Order of pole (three term test) = 1.521e-13 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4443 2.857 h = 0.003 0.006 y[1] (numeric) = -0.0578213789903 0.0785894942557 y[1] (closed_form) = -0.0578539718175 0.0785744134541 absolute error = 3.591e-05 relative error = 0.0368 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.201 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.367 Order of pole (three term test) = 5.888e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4413 2.863 h = 0.0001 0.005 y[1] (numeric) = -0.0579405246919 0.0781990114834 y[1] (closed_form) = -0.0579724530581 0.0781838245946 absolute error = 3.536e-05 relative error = 0.03633 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.205 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.39 Order of pole (three term test) = 6.032e-15 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4412 2.868 h = 0.0001 0.003 y[1] (numeric) = -0.0578939747438 0.0778994587831 y[1] (closed_form) = -0.0579263374895 0.0778842629733 absolute error = 3.575e-05 relative error = 0.03683 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.21 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.927 Order of pole (three term test) = 7.103e-14 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4411 2.871 h = 0.001 0.001 y[1] (numeric) = -0.0578684064655 0.0777201036507 y[1] (closed_form) = -0.0579008230045 0.0777047474376 absolute error = 3.587e-05 relative error = 0.03702 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.212 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.513 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4401 2.872 h = 0.001 0.003 y[1] (numeric) = -0.0579171934945 0.0776502335598 y[1] (closed_form) = -0.0579496629444 0.0776348079511 absolute error = 3.595e-05 relative error = 0.03711 % Correct digits = 3 Radius of convergence (given) for eq 1 = 3.213 Order of pole (given) = 2 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.184 Order of pole (three term test) = 0 0 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = neg ( 2.0 ) / x / x / x ; Iterations = 754 Total Elapsed Time = 22 Seconds Expected Time Remaining = 0 Seconds Optimized Time Remaining = 0 Seconds Expected Total Time = 22 Seconds > quit memory used=1767.6MB, alloc=44.3MB, time=22.65