|\^/| Maple 2016 (X86 64 LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2016 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. #BEGIN OUTFILE1 # before write maple top matter # before write_ats library and user def block #BEGIN ATS LIBRARY BLOCK # Begin Function number 2 > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s\n",str); > fi;# end if 1; > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc # End Function number 2 # Begin Function number 3 > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s",str); > fi;# end if 1; > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc # End Function number 3 # Begin Function number 4 > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > print(label,str); > fi;# end if 1; > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc # End Function number 4 # Begin Function number 5 > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc # End Function number 5 # Begin Function number 6 > omniout_complex := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > if vallen = 4 then > printf("%-30s = %-20.4g %-20g %s \n",prelabel,Re(value), Im(value), postlabel); > else > printf("%-30s = %-20.12g %-20.12g %s \n",prelabel,Re(value),Im(value), postlabel); > fi;# end if 0; > fi;# end if -1; > end; omniout_complex := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-20.4g %-20g %s \n", prelabel, Re(value), Im(value), postlabel) else printf("%-30s = %-20.12g %-20.12g %s \n", prelabel, Re(value), Im(value), postlabel) end if end if end proc # End Function number 6 # Begin Function number 7 > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number -1 > if vallen = 5 then # if number 0 > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi;# end if 0; > fi;# end if -1; > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc # End Function number 7 # Begin Function number 8 > logitem_time := proc(fd,secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > fprintf(fd,""); > if (secs_in >= 0) then # if number -1 > years_int := int_trunc(secs_in / glob_sec_in_year); > sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year); > days_int := int_trunc(sec_temp / glob_sec_in_day) ; > sec_temp := sec_temp mod int_trunc(glob_sec_in_day) ; > hours_int := int_trunc(sec_temp / glob_sec_in_hour); > sec_temp := sec_temp mod int_trunc(glob_sec_in_hour); > minutes_int := int_trunc(sec_temp / glob_sec_in_minute); > sec_int := sec_temp mod int_trunc(glob_sec_in_minute); > if (years_int > 0) then # if number 0 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 1 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 2 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 3 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 3 > else > fprintf(fd," 0.0 Seconds"); > fi;# end if 2 > fprintf(fd,"\n"); > end; logitem_time := proc(fd, secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; fprintf(fd, ""); if 0 <= secs_in then years_int := int_trunc(secs_in/glob_sec_in_year); sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year); days_int := int_trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod int_trunc(glob_sec_in_day); hours_int := int_trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod int_trunc(glob_sec_in_hour); minutes_int := int_trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod int_trunc(glob_sec_in_minute); if 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, " 0.0 Seconds") end if; fprintf(fd, "\n") end proc # End Function number 8 # Begin Function number 9 > omniout_timestr := proc(secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > if (secs_in >= 0) then # if number 2 > years_int := int_trunc(secs_in / glob_sec_in_year); > sec_temp := (int_trunc(secs_in) mod int_trunc(glob_sec_in_year)); > days_int := int_trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod int_trunc(glob_sec_in_day)) ; > hours_int := int_trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod int_trunc(glob_sec_in_hour)); > minutes_int := int_trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod int_trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 3 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 4 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 5 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 6 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 6 > else > printf(" 0.0 Seconds\n"); > fi;# end if 5 > end; omniout_timestr := proc(secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; if 0 <= secs_in then years_int := int_trunc(secs_in/glob_sec_in_year); sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year); days_int := int_trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod int_trunc(glob_sec_in_day); hours_int := int_trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod int_trunc(glob_sec_in_hour); minutes_int := int_trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod int_trunc(glob_sec_in_minute); if 0 < years_int then printf( " = %d Years %d Days %d Hours %d Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" 0.0 Seconds\n") end if end proc # End Function number 9 # Begin Function number 10 > zero_ats_ar := proc(arr_a) > global ATS_MAX_TERMS; > local iii; > iii := 1; > while (iii <= ATS_MAX_TERMS) do # do number 1 > arr_a [iii] := glob__0; > iii := iii + 1; > od;# end do number 1 > end; zero_ats_ar := proc(arr_a) local iii; global ATS_MAX_TERMS; iii := 1; while iii <= ATS_MAX_TERMS do arr_a[iii] := glob__0; iii := iii + 1 end do end proc # End Function number 10 # Begin Function number 11 > ats := proc(mmm_ats,arr_a,arr_b,jjj_ats) > global ATS_MAX_TERMS; > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := glob__0; > if (jjj_ats <= mmm_ats) then # if number 5 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > if ((lll_ats <= ATS_MAX_TERMS and (iii_ats <= ATS_MAX_TERMS) )) then # if number 6 > ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]); > fi;# end if 6; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 5; > ret_ats; > end; ats := proc(mmm_ats, arr_a, arr_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; global ATS_MAX_TERMS; ret_ats := glob__0; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; if lll_ats <= ATS_MAX_TERMS and iii_ats <= ATS_MAX_TERMS then ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]) end if; iii_ats := iii_ats + 1 end do end if; ret_ats end proc # End Function number 11 # Begin Function number 12 > att := proc(mmm_att,arr_aa,arr_bb,jjj_att) > global ATS_MAX_TERMS; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := glob__0; > if (jjj_att < mmm_att) then # if number 5 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while ((iii_att < mmm_att) and (iii_att <= ATS_MAX_TERMS) ) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if ((lll_att <= ATS_MAX_TERMS and (iii_att <= ATS_MAX_TERMS) )) then # if number 6 > ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att); > fi;# end if 6; > iii_att := iii_att + 1; > od;# end do number 1; > ret_att := ret_att / c(mmm_att) ; > fi;# end if 5; > ret_att; > end; att := proc(mmm_att, arr_aa, arr_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global ATS_MAX_TERMS; ret_att := glob__0; if jjj_att < mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att < mmm_att and iii_att <= ATS_MAX_TERMS do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= ATS_MAX_TERMS and iii_att <= ATS_MAX_TERMS then ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])*c(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/c(mmm_att) end if; ret_att end proc # End Function number 12 # Begin Function number 13 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc # End Function number 13 # Begin Function number 14 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc # End Function number 14 # Begin Function number 15 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc # End Function number 15 # Begin Function number 16 > logitem_good_digits := proc(file,rel_error) > global glob_small_float,glob_prec; > local good_digits; > fprintf(file,""); > fprintf(file,"%d",glob_min_good_digits); > fprintf(file,""); > end; logitem_good_digits := proc(file, rel_error) local good_digits; global glob_small_float, glob_prec; fprintf(file, ""); fprintf(file, "%d", glob_min_good_digits); fprintf(file, "") end proc # End Function number 16 # Begin Function number 17 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc # End Function number 17 # Begin Function number 18 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc # End Function number 18 # Begin Function number 19 > logitem_complex := proc(file,x) > fprintf(file,""); > fprintf(file,"%g + %g I",Re(x),Im(x)); > fprintf(file,""); > end; logitem_complex := proc(file, x) fprintf(file, ""); fprintf(file, "%g + %g I", Re(x), Im(x)); fprintf(file, "") end proc # End Function number 19 # Begin Function number 20 > logitem_h_reason := proc(file) > global glob_h_reason; > fprintf(file,""); > if (glob_h_reason = 1) then # if number 5 > fprintf(file,"Max H"); > elif > (glob_h_reason = 2) then # if number 6 > fprintf(file,"Display Interval"); > elif > (glob_h_reason = 3) then # if number 7 > fprintf(file,"Optimal"); > elif > (glob_h_reason = 4) then # if number 8 > fprintf(file,"Pole Accuracy"); > elif > (glob_h_reason = 5) then # if number 9 > fprintf(file,"Min H (Pole)"); > elif > (glob_h_reason = 6) then # if number 10 > fprintf(file,"Pole"); > elif > (glob_h_reason = 7) then # if number 11 > fprintf(file,"Opt Iter"); > else > fprintf(file,"Impossible"); > fi;# end if 11 > fprintf(file,""); > end; logitem_h_reason := proc(file) global glob_h_reason; fprintf(file, ""); if glob_h_reason = 1 then fprintf(file, "Max H") elif glob_h_reason = 2 then fprintf(file, "Display Interval") elif glob_h_reason = 3 then fprintf(file, "Optimal") elif glob_h_reason = 4 then fprintf(file, "Pole Accuracy") elif glob_h_reason = 5 then fprintf(file, "Min H (Pole)") elif glob_h_reason = 6 then fprintf(file, "Pole") elif glob_h_reason = 7 then fprintf(file, "Opt Iter") else fprintf(file, "Impossible") end if; fprintf(file, "") end proc # End Function number 20 # Begin Function number 21 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc # End Function number 21 # Begin Function number 22 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, "\n") end proc # End Function number 22 # Begin Function number 23 > chk_data := proc() > global glob_max_iter,ALWAYS, ATS_MAX_TERMS; > local errflag; > errflag := false; > if (glob_max_iter < 2) then # if number 11 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 11; > if (errflag) then # if number 11 > quit; > fi;# end if 11 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, ATS_MAX_TERMS; errflag := false; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc # End Function number 23 # Begin Function number 24 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := c(clock_sec2); > sub1 := c(t_end2-t_start2); > sub2 := c(t2-t_start2); > if (sub1 = glob__0) then # if number 11 > sec_left := glob__0; > else > if (sub2 > glob__0) then # if number 12 > rrr := (sub1/sub2); > sec_left := rrr * c(ms2) - c(ms2); > else > sec_left := glob__0; > fi;# end if 12 > fi;# end if 11; > sec_left; > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := c(clock_sec2); sub1 := c(t_end2 - t_start2); sub2 := c(t2 - t_start2); if sub1 = glob__0 then sec_left := glob__0 else if glob__0 < sub2 then rrr := sub1/sub2; sec_left := rrr*c(ms2) - c(ms2) else sec_left := glob__0 end if end if; sec_left end proc # End Function number 24 # Begin Function number 25 > comp_percent := proc(t_end2,t_start2, t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub2 > glob_small_float) then # if number 11 > rrr := (glob__100*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 11; > rrr; > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < sub2 then rrr := glob__100*sub2/sub1 else rrr := 0. end if; rrr end proc # End Function number 25 # Begin Function number 26 > comp_rad_from_ratio := proc(term1,term2,last_no) > #TOP TWO TERM RADIUS ANALYSIS > global glob_h,glob_larger_float; > local ret; > if (float_abs(term2) > glob__0) then # if number 11 > ret := float_abs(term1 * glob_h / term2); > else > ret := glob_larger_float; > fi;# end if 11; > ret; > #BOTTOM TWO TERM RADIUS ANALYSIS > end; comp_rad_from_ratio := proc(term1, term2, last_no) local ret; global glob_h, glob_larger_float; if glob__0 < float_abs(term2) then ret := float_abs(term1*glob_h/term2) else ret := glob_larger_float end if; ret end proc # End Function number 26 # Begin Function number 27 > comp_ord_from_ratio := proc(term1,term2,last_no) > #TOP TWO TERM ORDER ANALYSIS > global glob_h,glob_larger_float; > local ret; > if (float_abs(term2) > glob__0) then # if number 11 > ret := glob__1 + float_abs(term2) * c(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(c(last_no)); > else > ret := glob_larger_float; > fi;# end if 11; > ret; > #BOTTOM TWO TERM ORDER ANALYSIS > end; comp_ord_from_ratio := proc(term1, term2, last_no) local ret; global glob_h, glob_larger_float; if glob__0 < float_abs(term2) then ret := glob__1 + float_abs(term2)* c(last_no)*ln(float_abs(term1*glob_h/term2))/ln(c(last_no)) else ret := glob_larger_float end if; ret end proc # End Function number 27 # Begin Function number 28 > c := proc(in_val) > #To Force Conversion when needed > local ret; > ret := evalc(in_val); > ret; > #End Conversion > end; c := proc(in_val) local ret; ret := evalc(in_val); ret end proc # End Function number 28 # Begin Function number 29 > comp_rad_from_three_terms := proc(term1,term2,term3,last_no) > #TOP THREE TERM RADIUS ANALYSIS > global glob_h,glob_larger_float; > local ret,temp; > temp := float_abs(term2*term2*c(last_no)+glob__m2*term2*term2-term1*term3*c(last_no)+term1*term3); > if (float_abs(temp) > glob__0) then # if number 11 > ret := float_abs((term2*glob_h*term1)/(temp)); > else > ret := glob_larger_float; > fi;# end if 11; > ret; > #BOTTOM THREE TERM RADIUS ANALYSIS > end; comp_rad_from_three_terms := proc(term1, term2, term3, last_no) local ret, temp; global glob_h, glob_larger_float; temp := float_abs(term2*term2*c(last_no) + glob__m2*term2*term2 - term1*term3*c(last_no) + term1*term3); if glob__0 < float_abs(temp) then ret := float_abs(term2*glob_h*term1/temp) else ret := glob_larger_float end if; ret end proc # End Function number 29 # Begin Function number 30 > comp_ord_from_three_terms := proc(term1,term2,term3,last_no) > #TOP THREE TERM ORDER ANALYSIS > local ret; > ret := float_abs((glob__4*term1*term3*c(last_no)-glob__3*term1*term3-glob__4*term2*term2*c(last_no)+glob__4*term2*term2+term2*term2*c(last_no*last_no)-term1*term3*c(last_no*last_no))/(term2*term2*c(last_no)-glob__2*term2*term2-term1*term3*c(last_no)+term1*term3)); > ret; > #TOP THREE TERM ORDER ANALYSIS > end; comp_ord_from_three_terms := proc(term1, term2, term3, last_no) local ret; ret := float_abs((glob__4*term1*term3*c(last_no) - glob__3*term1*term3 - glob__4*term2*term2*c(last_no) + glob__4*term2*term2 + term2*term2*c(last_no*last_no) - term1*term3*c(last_no*last_no)) /(term2*term2*c(last_no) - glob__2*term2*term2 - term1*term3*c(last_no) + term1*term3)); ret end proc # End Function number 30 # Begin Function number 31 > comp_rad_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no) > #TOP SIX TERM RADIUS ANALYSIS > global glob_h,glob_larger_float,glob_six_term_ord_save; > local ret,rm0,rm1,rm2,rm3,rm4,nr1,nr2,dr1,dr2,ds2,rad_c,ord_no,ds1,rcs; > if ((term5 <> glob__0) and (term4 <> glob__0) and (term3 <> glob__0) and (term2 <> glob__0) and (term1 <> glob__0)) then # if number 11 > rm0 := term6/term5; > rm1 := term5/term4; > rm2 := term4/term3; > rm3 := term3/term2; > rm4 := term2/term1; > nr1 := c(last_no-1)*rm0 - glob__2*c(last_no-2)*rm1 + c(last_no-3)*rm2; > nr2 := c(last_no-2)*rm1 - glob__2*c(last_no-3)*rm2 + c(last_no-4)*rm3; > dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3; > dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4; > ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3; > ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4; > if ((float_abs(nr1 * dr2 - nr2 * dr1) = glob__0) or (float_abs(dr1) = glob__0)) then # if number 12 > rad_c := glob_larger_float; > ord_no := glob_larger_float; > else > if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0) then # if number 13 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) -c(last_no)/glob__2; > if (float_abs(rcs) <> glob__0) then # if number 14 > if (rcs > glob__0) then # if number 15 > rad_c := float_abs( sqrt(rcs) * float_abs(glob_h)); > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 15 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 14 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 13 > fi;# end if 12 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 11; > glob_six_term_ord_save := ord_no; > rad_c; > #BOTTOM SIX TERM RADIUS ANALYSIS > end; comp_rad_from_six_terms := proc( term1, term2, term3, term4, term5, term6, last_no) local ret, rm0, rm1, rm2, rm3, rm4, nr1, nr2, dr1, dr2, ds2, rad_c, ord_no, ds1, rcs; global glob_h, glob_larger_float, glob_six_term_ord_save; if term5 <> glob__0 and term4 <> glob__0 and term3 <> glob__0 and term2 <> glob__0 and term1 <> glob__0 then rm0 := term6/term5; rm1 := term5/term4; rm2 := term4/term3; rm3 := term3/term2; rm4 := term2/term1; nr1 := c(last_no - 1)*rm0 - glob__2*c(last_no - 2)*rm1 + c(last_no - 3)*rm2; nr2 := c(last_no - 2)*rm1 - glob__2*c(last_no - 3)*rm2 + c(last_no - 4)*rm3; dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3; dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4; ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3; ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4; if float_abs(nr1*dr2 - nr2*dr1) = glob__0 or float_abs(dr1) = glob__0 then rad_c := glob_larger_float; ord_no := glob_larger_float else if glob__0 < float_abs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) - c(last_no)/glob__2; if float_abs(rcs) <> glob__0 then if glob__0 < rcs then rad_c := float_abs(sqrt(rcs)*float_abs(glob_h)) else rad_c := glob_larger_float; ord_no := glob_larger_float end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if; glob_six_term_ord_save := ord_no; rad_c end proc # End Function number 31 # Begin Function number 32 > comp_ord_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no) > global glob_six_term_ord_save; > #TOP SIX TERM ORDER ANALYSIS > #TOP SAVED FROM SIX TERM RADIUS ANALYSIS > glob_six_term_ord_save; > #BOTTOM SIX TERM ORDER ANALYSIS > end; comp_ord_from_six_terms := proc( term1, term2, term3, term4, term5, term6, last_no) global glob_six_term_ord_save; glob_six_term_ord_save end proc # End Function number 32 # Begin Function number 33 > factorial_2 := proc(nnn) > ret := nnn!; > ret;; > end; Warning, `ret` is implicitly declared local to procedure `factorial_2` factorial_2 := proc(nnn) local ret; ret := nnn!; ret end proc # End Function number 33 # Begin Function number 34 > factorial_1 := proc(nnn) > global ATS_MAX_TERMS,array_fact_1; > local ret; > if (nnn <= ATS_MAX_TERMS) then # if number 11 > if (array_fact_1[nnn] = 0) then # if number 12 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 12; > else > ret := factorial_2(nnn); > fi;# end if 11; > ret; > end; factorial_1 := proc(nnn) local ret; global ATS_MAX_TERMS, array_fact_1; if nnn <= ATS_MAX_TERMS then if array_fact_1[nnn] = 0 then ret := factorial_2(nnn); array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := factorial_2(nnn) end if; ret end proc # End Function number 34 # Begin Function number 35 > factorial_3 := proc(mmm,nnn) > global ATS_MAX_TERMS,array_fact_2; > local ret; > if ((nnn <= ATS_MAX_TERMS) and (mmm <= ATS_MAX_TERMS)) then # if number 11 > if (array_fact_2[mmm,nnn] = 0) then # if number 12 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 12; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 11; > ret; > end; factorial_3 := proc(mmm, nnn) local ret; global ATS_MAX_TERMS, array_fact_2; if nnn <= ATS_MAX_TERMS and mmm <= ATS_MAX_TERMS then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := factorial_2(mmm)/factorial_2(nnn) end if; ret end proc # End Function number 35 # Begin Function number 36 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc # End Function number 36 # Begin Function number 37 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc # End Function number 37 # Begin Function number 38 > float_abs := proc(x) > abs(x); > end; float_abs := proc(x) abs(x) end proc # End Function number 38 # Begin Function number 39 > expt := proc(x,y) > x^y; > end; expt := proc(x, y) x^y end proc # End Function number 39 # Begin Function number 40 > neg := proc(x) > -x; > end; neg := proc(x) -x end proc # End Function number 40 # Begin Function number 41 > int_trunc := proc(x) > trunc(x); > end; int_trunc := proc(x) trunc(x) end proc # End Function number 41 # Begin Function number 42 > estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer) > local desired_abs_gbl_error,range,estimated_steps,step_error; > global glob_desired_digits_correct,ALWAYS,ATS_MAX_TERMS; > omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,""); > desired_abs_gbl_error := expt(glob__10,c( -glob_desired_digits_correct)) * c(float_abs(c(estimated_answer))); > omniout_float(ALWAYS,"estimated_h",32,estimated_h,32,""); > omniout_float(ALWAYS,"estimated_answer",32,estimated_answer,32,""); > omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,""); > range := (x_end - x_start); > omniout_float(ALWAYS,"range",32,range,32,""); > estimated_steps := range / estimated_h; > omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,""); > step_error := (c(float_abs(desired_abs_gbl_error) /sqrt(c( estimated_steps))/c(ATS_MAX_TERMS))); > omniout_float(ALWAYS,"step_error",32,step_error,32,""); > (step_error);; > end; estimated_needed_step_error := proc( x_start, x_end, estimated_h, estimated_answer) local desired_abs_gbl_error, range, estimated_steps, step_error; global glob_desired_digits_correct, ALWAYS, ATS_MAX_TERMS; omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""); desired_abs_gbl_error := expt(glob__10, c(-glob_desired_digits_correct))* c(float_abs(c(estimated_answer))); omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, ""); omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, "") ; omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""); range := x_end - x_start; omniout_float(ALWAYS, "range", 32, range, 32, ""); estimated_steps := range/estimated_h; omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, ""); step_error := c(float_abs(desired_abs_gbl_error)/( sqrt(c(estimated_steps))*c(ATS_MAX_TERMS))); omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""); step_error end proc # End Function number 42 #END ATS LIBRARY BLOCK #BEGIN USER FUNCTION BLOCK #BEGIN BLOCK 3 #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > return(cos(sqrt(c(2.0)*c(x)+c(3.0)))+sqrt(c(2.0)*c(x)+c(3.0))*sin(sqrt(c(2.0)*c(x)+c(3.0)))); > end; exact_soln_y := proc(x) return cos(sqrt(c(2.0)*c(x) + c(3.0))) + sqrt(c(2.0)*c(x) + c(3.0))*sin(sqrt(c(2.0)*c(x) + c(3.0))) end proc > next_delta := proc() > global glob_nxt, x_delta; > x_delta := [ 0.001 + 0.00004 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.000 + 0.000 * I ]; > glob_nxt := glob_nxt + 1; > it := x_delta[glob_nxt]; > return it; > end; Warning, `it` is implicitly declared local to procedure `next_delta` next_delta := proc() local it; global glob_nxt, x_delta; x_delta := [0.001 + 0.00004*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 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# 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, > array_const_3D0, #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_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local min_size; > min_size := glob_estimated_size_answer; > if (float_abs(array_y[1]) < min_size) then # if number 3 > min_size := float_abs(array_y[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 3; > if (min_size < glob__1) then # if number 3 > min_size := glob__1; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 3; > min_size; > end; est_size_answer := proc() local min_size; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, 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_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; min_size := glob_estimated_size_answer; if float_abs(array_y[1]) < min_size then min_size := float_abs(array_y[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if min_size < glob__1 then min_size := glob__1; omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; min_size end proc # End Function number 4 # Begin Function number 5 > test_suggested_h := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, #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_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > max_estimated_step_error := glob__small; > no_terms := ATS_MAX_TERMS; > hn_div_ho := glob__0_5; > hn_div_ho_2 := glob__0_25; > hn_div_ho_3 := glob__0_125; > omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""); > omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,""); > omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,""); > est_tmp := float_abs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3); > if (est_tmp >= max_estimated_step_error) then # if number 3 > max_estimated_step_error := est_tmp; > fi;# end if 3; > omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,""); > max_estimated_step_error; > end; test_suggested_h := proc() local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, 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_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; max_estimated_step_error := glob__small; no_terms := ATS_MAX_TERMS; hn_div_ho := glob__0_5; hn_div_ho_2 := glob__0_25; hn_div_ho_3 := glob__0_125; omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""); omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""); omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""); est_tmp := float_abs(array_y[no_terms - 3] + array_y[no_terms - 2]*hn_div_ho + array_y[no_terms - 1]*hn_div_ho_2 + array_y[no_terms]*hn_div_ho_3); if max_estimated_step_error <= est_tmp then max_estimated_step_error := est_tmp end if; omniout_float(ALWAYS, "max_estimated_step_error", 32, max_estimated_step_error, 32, ""); max_estimated_step_error end proc # End Function number 5 # Begin Function number 6 > track_estimated_error := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, #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_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > no_terms := ATS_MAX_TERMS; > hn_div_ho := glob__0_5; > hn_div_ho_2 := glob__0_25; > hn_div_ho_3 := glob__0_125; > est_tmp := c(float_abs(array_y[no_terms-3])) + c(float_abs(array_y[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y[no_terms])) * c(hn_div_ho_3); > if (glob_prec * c(float_abs(array_y[1])) > c(est_tmp)) then # if number 3 > est_tmp := c(glob_prec) * c(float_abs(array_y[1])); > fi;# end if 3; > if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 3 > array_max_est_error[1] := c(est_tmp); > fi;# end if 3 > ; > end; track_estimated_error := proc() local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, 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_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; no_terms := ATS_MAX_TERMS; hn_div_ho := glob__0_5; hn_div_ho_2 := glob__0_25; hn_div_ho_3 := glob__0_125; est_tmp := c(float_abs(array_y[no_terms - 3])) + c(float_abs(array_y[no_terms - 2]))*c(hn_div_ho) + c(float_abs(array_y[no_terms - 1]))*c(hn_div_ho_2) + c(float_abs(array_y[no_terms]))*c(hn_div_ho_3); if c(est_tmp) < glob_prec*c(float_abs(array_y[1])) then est_tmp := c(glob_prec)*c(float_abs(array_y[1])) end if; if c(array_max_est_error[1]) <= c(est_tmp) then array_max_est_error[1] := c(est_tmp) end if end proc # End Function number 6 # Begin Function number 7 > reached_interval := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, #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_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local ret; > if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 3 > ret := true; > else > ret := false; > fi;# end if 3; > return(ret); > end; reached_interval := proc() local ret; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, 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_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; if glob_check_sign*glob_next_display - glob_h/glob__10 <= glob_check_sign*array_x[1] then ret := true else ret := false end if; return ret end proc # End Function number 7 # Begin Function number 8 > display_alot := proc(iter) > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, #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_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err; > #TOP DISPLAY ALOT > ind_var := array_x[1]; > omniout_complex(ALWAYS,"x[1] ",33,ind_var,20," "); > term_no := 1; > numeric_val := array_y[term_no]; > omniout_complex(ALWAYS,"h ",33,glob_h,20," "); > omniout_complex(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > closed_form_val_y := evalf(exact_soln_y(ind_var)); > omniout_complex(ALWAYS,"y[1] (closed_form) ",33,closed_form_val_y,20," "); > abserr := float_abs(numeric_val - closed_form_val_y); > if (float_abs(closed_form_val_y) > 0.0) then # if number 3 > relerr := abserr/float_abs(closed_form_val_y); > if (float_abs(c(relerr)) > 0.0) then # if number 4 > glob_good_digits := round(-log10(relerr)); > else > relerr := 0.0 ; > glob_good_digits := Digits - 2; > fi;# end if 4; > else > ; > relerr := glob__m1 ; > glob_good_digits := -16; > fi;# end if 3; > if (glob_good_digits < glob_min_good_digits) then # if number 3 > glob_min_good_digits := glob_good_digits; > fi;# end if 3; > omniout_float(ALWAYS,"absolute error ",4,abserr,4," "); > omniout_float(ALWAYS,"relative error ",4,relerr * glob__100 ,4,"%"); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > #BOTTOM DISPLAY ALOT > end; display_alot := proc(iter) local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, 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_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; ind_var := array_x[1]; omniout_complex(ALWAYS, "x[1] ", 33, ind_var, 20, " "); term_no := 1; numeric_val := array_y[term_no]; omniout_complex(ALWAYS, "h ", 33, glob_h, 20, " "); omniout_complex(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); closed_form_val_y := evalf(exact_soln_y(ind_var)); omniout_complex(ALWAYS, "y[1] (closed_form) ", 33, closed_form_val_y, 20, " "); abserr := float_abs(numeric_val - closed_form_val_y); if 0. < float_abs(closed_form_val_y) then relerr := abserr/float_abs(closed_form_val_y); if 0. < float_abs(c(relerr)) then glob_good_digits := round(-log10(relerr)) else relerr := 0.; glob_good_digits := Digits - 2 end if else relerr := glob__m1; glob_good_digits := -16 end if; if glob_good_digits < glob_min_good_digits then glob_min_good_digits := glob_good_digits end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 4, " "); omniout_float(ALWAYS, "relative error ", 4, relerr*glob__100, 4, "%"); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " ") end proc # End Function number 8 # Begin Function number 9 > prog_report := proc(x_start,x_end) > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, #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_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := (clock_sec1) - (glob_orig_start_sec); > glob_clock_sec := (clock_sec1) - (glob_clock_start_sec); > left_sec := (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1); > expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h) ,( clock_sec1) - (glob_orig_start_sec)); > opt_clock_sec := ( clock_sec1) - (glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec)); > glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec); > percent_done := comp_percent((x_end),(x_start),(array_x[1]) + (glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr((total_clock_sec)); > if (c(percent_done) < glob__100) then # if number 3 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr((expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr((glob_optimal_expect_sec)); > omniout_str_noeol(INFO,"Expected Total Time "); > omniout_timestr((glob_total_exp_sec)); > fi;# end if 3; > #BOTTOM PROGRESS REPORT > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, 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_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := clock_sec1 - glob_orig_start_sec; glob_clock_sec := clock_sec1 - glob_clock_start_sec; left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1; expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h, clock_sec1 - glob_orig_start_sec); opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec; glob_optimal_expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec) ; glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec); percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(total_clock_sec); if c(percent_done) < glob__100 then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(expect_sec); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(glob_optimal_expect_sec); omniout_str_noeol(INFO, "Expected Total Time "); omniout_timestr(glob_total_exp_sec) end if end proc # End Function number 9 # Begin Function number 10 > check_for_pole := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, #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_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad, last_no; > #TOP CHECK FOR POLE > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,1] := glob_larger_float; > array_ord_test_poles[1,1] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 3 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 3; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 3 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 4 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 5 > found_sing := 0; > fi;# end if 5; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 5 > if (rad_c < array_rad_test_poles[1,1]) then # if number 6 > array_rad_test_poles[1,1] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,1] := rad_c; > array_ord_test_poles[1,1] := tmp_ord; > fi;# end if 6; > fi;# end if 5; > #BOTTOM general radius test1 > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,2] := glob_larger_float; > array_ord_test_poles[1,2] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 5 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 5; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 6 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 7 > found_sing := 0; > fi;# end if 7; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 7 > if (rad_c < array_rad_test_poles[1,2]) then # if number 8 > array_rad_test_poles[1,2] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,2] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 9 > glob_min_pole_est := rad_c; > fi;# end if 9; > array_ord_test_poles[1,2] := tmp_ord; > fi;# end if 8; > fi;# end if 7; > #BOTTOM general radius test1 > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,3] := glob_larger_float; > array_ord_test_poles[1,3] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 7 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 7; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 8 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 9 > found_sing := 0; > fi;# end if 9; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 9 > if (rad_c < array_rad_test_poles[1,3]) then # if number 10 > array_rad_test_poles[1,3] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,3] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 11 > glob_min_pole_est := rad_c; > fi;# end if 11; > array_ord_test_poles[1,3] := tmp_ord; > fi;# end if 10; > fi;# end if 9; > #BOTTOM general radius test1 > ; > if (true) then # if number 9 > display_poles(); > fi;# end if 9 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio, prev_tmp_rad, last_no; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0, array_const_3D0, 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_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 1] := glob_larger_float; array_ord_test_poles[1, 1] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do tmp_rad := comp_rad_from_ratio(array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 1] then array_rad_test_poles[1, 1] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_ratio(array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 1] := rad_c; array_ord_test_poles[1, 1] := tmp_ord end if end if; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 2] := glob_larger_float; array_ord_test_poles[1, 2] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do tmp_rad := comp_rad_from_three_terms( array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 2] then array_rad_test_poles[1, 2] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_three_terms( array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 2] := rad_c; if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c end if; array_ord_test_poles[1, 2] := tmp_ord end if end if; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 3] := glob_larger_float; array_ord_test_poles[1, 3] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do tmp_rad := comp_rad_from_six_terms(array_y_higher[1, last_no - 5], array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3], array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 3] then array_rad_test_poles[1, 3] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_six_terms( array_y_higher[1, last_no - 5], array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3], array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 3] := rad_c; if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c end if; array_ord_test_poles[1, 3] := tmp_ord end if end if; display_poles() end proc # End Function number 10 # Begin Function number 11 > atomall := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_3D0, #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_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > # before write maple main top matter > # before generate constants assign > # before generate globals assign > #END OUTFILE1 > #BEGIN OUTFILE2 > #END OUTFILE2 > #BEGIN ATOMHDR1 > #emit pre mult CONST - LINEAR $eq_no = 1 i = 1 > array_tmp1[1] := array_const_2D0[1] * array_x[1]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 1 > array_tmp2[1] := array_tmp1[1] + array_const_3D0[1]; > #emit pre sqrt 1 $eq_no = 1 > array_tmp3[1] := sqrt(array_tmp2[1]); > array_tmp4_g[1] := sin(array_tmp3[1]); > array_tmp4[1] := cos(array_tmp3[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 mult CONST - LINEAR $eq_no = 1 i = 2 > array_tmp1[2] := array_const_2D0[1] * array_x[2]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre sqrt 2 $eq_no = 1 > array_tmp3[2] := array_tmp2[2] / array_tmp3[1]/glob__2; > #emit pre cos FULL $eq_no = 1 > array_tmp4_g[2] := (att(1,array_tmp4,array_tmp3,1)); > array_tmp4[2] := (neg(att(1,array_tmp4_g,array_tmp3,1))); > #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 > #emit pre sqrt ID_LINEAR iii = 3 $eq_no = 1 > array_tmp3[3] := 0; > array_tmp3[3] := neg(ats(3,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2; > #emit pre cos FULL $eq_no = 1 > array_tmp4_g[3] := (att(2,array_tmp4,array_tmp3,1)); > array_tmp4[3] := (neg(att(2,array_tmp4_g,array_tmp3,1))); > #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 > #emit pre sqrt ID_LINEAR iii = 4 $eq_no = 1 > array_tmp3[4] := 0; > array_tmp3[4] := neg(ats(4,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2; > #emit pre cos FULL $eq_no = 1 > array_tmp4_g[4] := (att(3,array_tmp4,array_tmp3,1)); > array_tmp4[4] := (neg(att(3,array_tmp4_g,array_tmp3,1))); > #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 > #emit pre sqrt ID_LINEAR iii = 5 $eq_no = 1 > array_tmp3[5] := 0; > array_tmp3[5] := neg(ats(5,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2; > #emit pre cos FULL $eq_no = 1 > array_tmp4_g[5] := (att(4,array_tmp4,array_tmp3,1)); > array_tmp4[5] := (neg(att(4,array_tmp4_g,array_tmp3,1))); > #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 sqrt LINEAR $eq_no = 1 > array_tmp3[kkk] := 0; > array_tmp3[kkk] := neg(ats(kkk,array_tmp3,array_tmp3,2)) /array_tmp3[1] / glob__2; > #emit cos FULL $eq_no = 1 > array_tmp4[kkk] := neg(att(kkk-1,array_tmp4_g,array_tmp3,1)); > array_tmp4_g[kkk] := att(kkk-1,array_tmp4,array_tmp3,1); > #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_const_3D0, 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_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; array_tmp1[1] := array_const_2D0[1]*array_x[1]; array_tmp2[1] := array_tmp1[1] + array_const_3D0[1]; array_tmp3[1] := sqrt(array_tmp2[1]); array_tmp4_g[1] := sin(array_tmp3[1]); array_tmp4[1] := cos(array_tmp3[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_tmp1[2] := array_const_2D0[1]*array_x[2]; array_tmp2[2] := array_tmp1[2]; array_tmp3[2] := array_tmp2[2]/(array_tmp3[1]*glob__2); array_tmp4_g[2] := att(1, array_tmp4, array_tmp3, 1); array_tmp4[2] := neg(att(1, array_tmp4_g, array_tmp3, 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_tmp3[3] := 0; array_tmp3[3] := neg(ats(3, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2); array_tmp4_g[3] := att(2, array_tmp4, array_tmp3, 1); array_tmp4[3] := neg(att(2, array_tmp4_g, array_tmp3, 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_tmp3[4] := 0; array_tmp3[4] := neg(ats(4, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2); array_tmp4_g[4] := att(3, array_tmp4, array_tmp3, 1); array_tmp4[4] := neg(att(3, array_tmp4_g, array_tmp3, 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_tmp3[5] := 0; array_tmp3[5] := neg(ats(5, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2); array_tmp4_g[5] := att(4, array_tmp4, array_tmp3, 1); array_tmp4[5] := neg(att(4, array_tmp4_g, array_tmp3, 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_tmp3[kkk] := 0; array_tmp3[kkk] := neg(ats(kkk, array_tmp3, array_tmp3, 2))/( array_tmp3[1]*glob__2); array_tmp4[kkk] := neg(att(kkk - 1, array_tmp4_g, array_tmp3, 1)); array_tmp4_g[kkk] := att(kkk - 1, array_tmp4, array_tmp3, 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, > array_const_3D0, > #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_g, > array_tmp4, > array_tmp5, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > ATS_MAX_TERMS := 30; > # before first input block > #BEGIN FIRST INPUT BLOCK > #BEGIN BLOCK 1 > #BEGIN FIRST INPUT BLOCK > Digits:=32; > max_terms:=30; > #END BLOCK 1 > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > # before generate arrays > array_y_init:= Array(0..(30),[]); > array_norms:= Array(0..(30),[]); > array_fact_1:= Array(0..(30),[]); > array_1st_rel_error:= Array(0..(2),[]); > array_last_rel_error:= Array(0..(2),[]); > array_est_rel_error:= Array(0..(2),[]); > array_max_est_error:= Array(0..(2),[]); > array_type_pole:= Array(0..(2),[]); > array_type_real_pole:= Array(0..(2),[]); > array_type_complex_pole:= Array(0..(2),[]); > array_est_digits:= Array(0..(2),[]); > array_y:= Array(0..(30),[]); > array_x:= Array(0..(30),[]); > array_tmp0:= Array(0..(30),[]); > array_tmp1:= Array(0..(30),[]); > array_tmp2:= Array(0..(30),[]); > array_tmp3:= Array(0..(30),[]); > array_tmp4_g:= Array(0..(30),[]); > array_tmp4:= Array(0..(30),[]); > array_tmp5:= Array(0..(30),[]); > array_m1:= Array(0..(30),[]); > array_y_higher := Array(0..(2) ,(0..30+ 1),[]); > array_y_higher_work := Array(0..(2) ,(0..30+ 1),[]); > array_y_higher_work2 := Array(0..(2) ,(0..30+ 1),[]); > array_y_set_initial := Array(0..(2) ,(0..30+ 1),[]); > array_given_rad_poles := Array(0..(2) ,(0..3+ 1),[]); > array_given_ord_poles := Array(0..(2) ,(0..3+ 1),[]); > array_rad_test_poles := Array(0..(2) ,(0..4+ 1),[]); > array_ord_test_poles := Array(0..(2) ,(0..4+ 1),[]); > array_fact_2 := Array(0..(30) ,(0..30+ 1),[]); > # before generate constants > # before generate globals definition > #Top Generate Globals Definition > #Bottom Generate Globals Deninition > # before generate const definition > # before arrays initialized > term := 1; > while (term <= 30) do # do number 1 > array_y_init[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_norms[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_fact_1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_1st_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_last_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_est_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_max_est_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_real_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_complex_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_est_digits[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_y[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_x[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp0[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp2[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp3[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp4_g[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp4[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_tmp5[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 30) do # do number 1 > array_m1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 30) do # do number 2 > array_y_higher[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 30) do # do number 2 > array_y_higher_work[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 30) do # do number 2 > array_y_higher_work2[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 30) do # do number 2 > array_y_set_initial[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_rad_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_ord_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 4) do # do number 2 > array_rad_test_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 4) do # do number 2 > array_ord_test_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=30) do # do number 1 > term := 1; > while (term <= 30) do # do number 2 > array_fact_2[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > # before symbols initialized > #BEGIN SYMBOLS INITIALIZATED > zero_ats_ar(array_y); > zero_ats_ar(array_x); > zero_ats_ar(array_tmp0); > zero_ats_ar(array_tmp1); > zero_ats_ar(array_tmp2); > zero_ats_ar(array_tmp3); > zero_ats_ar(array_tmp4_g); > zero_ats_ar(array_tmp4); > zero_ats_ar(array_tmp5); > zero_ats_ar(array_m1); > zero_ats_ar(array_const_1); > array_const_1[1] := c(1); > zero_ats_ar(array_const_0D0); > array_const_0D0[1] := c(0.0); > zero_ats_ar(array_const_2D0); > array_const_2D0[1] := c(2.0); > zero_ats_ar(array_const_3D0); > array_const_3D0[1] := c(3.0); > zero_ats_ar(array_m1); > array_m1[1] := glob__m1; > #END SYMBOLS INITIALIZATED > # before generate factorials init > #Initing Factorial Tables > iiif := 0; > while (iiif <= ATS_MAX_TERMS) do # do number 1 > jjjf := 0; > while (jjjf <= ATS_MAX_TERMS) do # do number 2 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 2; > iiif := iiif + 1; > od;# end do number 1; > #Done Initing Factorial Table > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := 5; > glob_yes_pole := 4; > glob_no_pole := 3; > glob_not_given := 0; > glob_no_sing_tests := 4; > glob_ratio_test := 1; > glob_three_term_test := 2; > glob_six_term_test := 3; > glob_log_10 := log(c(10.0)); > MAX_UNCHANGED := 10; > glob__small := c(0.1e-50); > glob_small_float := c(0.1e-50); > glob_smallish_float := c(0.1e-60); > glob_large_float := c(1.0e100); > glob_larger_float := c(1.1e100); > glob__m2 := c(-2); > glob__m1 := c(-1); > glob__0 := c(0); > glob__1 := c(1); > glob__2 := c(2); > glob__3 := c(3); > glob__4 := c(4); > glob__5 := c(5); > glob__8 := c(8); > glob__10 := c(10); > glob__100 := c(100); > glob__pi := c(0.0); > glob__0_5 := c(0.5); > glob__0_8 := c(0.8); > glob__m0_8 := c(-0.8); > glob__0_25 := c(0.25); > glob__0_125 := c(0.125); > glob_h := 0.1; > glob_nxt := 1; > glob_prec := c(1.0e-16); > glob_check_sign := c(1.0); > glob_desired_digits_correct := c(8.0); > glob_max_estimated_step_error := c(0.0); > glob_ratio_of_radius := c(0.1); > glob_percent_done := c(0.0); > glob_total_exp_sec := c(0.1); > glob_optimal_expect_sec := c(0.1); > glob_estimated_size_answer := c(100.0); > glob_almost_1 := c(0.9990); > glob_clock_sec := c(0.0); > glob_clock_start_sec := c(0.0); > glob_disp_incr := c(0.1); > glob_diff_rc_fm := c(0.1); > glob_diff_rc_fmm1 := c(0.1); > glob_diff_rc_fmm2 := c(0.1); > glob_diff_ord_fm := c(0.1); > glob_diff_ord_fmm1 := c(0.1); > glob_diff_ord_fmm2 := c(0.1); > glob_six_term_ord_save := c(0.1); > glob_guess_error_rc := c(0.1); > glob_guess_error_ord := c(0.1); > glob_least_given_sing := c(9.9e200); > glob_least_ratio_sing := c(9.9e200); > glob_least_3_sing := c(9.9e100); > glob_least_6_sing := c(9.9e100); > glob_last_good_h := c(0.1); > glob_max_h := c(0.1); > glob_min_h := c(0.000001); > glob_display_interval := c(0.1); > glob_abserr := c(0.1e-10); > glob_relerr := c(0.1e-10); > glob_min_pole_est := c(0.1e+10); > glob_max_rel_trunc_err := c(0.1e-10); > glob_max_trunc_err := c(0.1e-10); > glob_max_hours := c(0.0); > glob_optimal_clock_start_sec := c(0.0); > glob_optimal_start := c(0.0); > glob_upper_ratio_limit := c(1.0001); > glob_lower_ratio_limit := c(0.9999); > glob_max_sec := c(10000.0); > glob_orig_start_sec := c(0.0); > glob_normmax := c(0.0); > glob_max_minutes := c(0.0); > glob_next_display := c(0.0); > glob_est_digits := 1; > glob_subiter_method := 3; > glob_html_log := true; > glob_min_good_digits := 99999; > glob_good_digits := 0; > glob_min_apfp_est_good_digits := 99999; > glob_apfp_est_good_digits := 0; > glob_max_opt_iter := 10; > glob_dump := false; > glob_djd_debug := true; > glob_display_flag := true; > glob_djd_debug2 := true; > glob_h_reason := 0; > glob_sec_in_minute := 60 ; > glob_min_in_hour := 60; > glob_hours_in_day := 24; > glob_days_in_year := 365; > glob_sec_in_hour := 3600; > glob_sec_in_day := 86400; > glob_sec_in_year := 31536000; > glob_not_yet_finished := true; > glob_initial_pass := true; > glob_not_yet_start_msg := true; > glob_reached_optimal_h := false; > glob_optimal_done := false; > glob_type_given_pole := 0; > glob_optimize := false; > glob_look_poles := false; > glob_dump_closed_form := false; > glob_max_iter := 10000; > glob_no_eqs := 0; > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_start := 0; > glob_iter := 0; > # before generate set diff initial > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > # before generate init omniout const > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > ATS_MAX_TERMS := 30; > glob_iolevel := INFO; > # set default block > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > glob_display_flag := true; > glob_no_eqs := 1; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 10000; > glob_max_hours := (0.0); > glob_max_minutes := (15.0); > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/cos_sqrt_linpostcpx.cpx#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = cos ( sqrt ( 2.0 * x + 3.0 ) ) ; "); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := -1.4 + 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 := 0.0001;"); > omniout_str(ALWAYS,"glob_upper_ratio_limit := c(1.001);"); > omniout_str(ALWAYS,"glob_lower_ratio_limit := c(0.999);"); > 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(-1.5);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_rad_poles[1,2] := c(0.0);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_ord_poles[1,1] := c(0.5);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_ord_poles[1,2] := c(0.0);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_desired_digits_correct:=8;"); > omniout_str(ALWAYS,"glob_max_minutes:=(3.0);"); > omniout_str(ALWAYS,"glob_subiter_method:=3;"); > omniout_str(ALWAYS,"glob_max_iter:=10000;"); > omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);"); > omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);"); > omniout_str(ALWAYS,"glob_look_poles:=true;"); > omniout_str(ALWAYS,"glob_h:=c(0.001);"); > omniout_str(ALWAYS,"glob_display_interval:=c(0.01);"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"return(cos(sqrt(c(2.0)*c(x)+c(3.0)))+sqrt(c(2.0)*c(x)+c(3.0))*sin(sqrt(c(2.0)*c(x)+c(3.0))));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"next_delta := proc()"); > omniout_str(ALWAYS,"global glob_nxt, x_delta;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"x_delta := [ 0.001 + 0.00004 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.000 + 0.000 * I ];"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"glob_nxt := glob_nxt + 1;"); > omniout_str(ALWAYS,"it := x_delta[glob_nxt];"); > omniout_str(ALWAYS,"return it;"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := glob__0; > glob_smallish_float := glob__0; > glob_large_float := c(1.0e100); > glob_larger_float := c( 1.1e100); > glob_almost_1 := c( 0.99); > # before second block > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #BEGIN BLOCK 2 > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := -1.4 + 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 := 0.0001; > glob_upper_ratio_limit := c(1.001); > glob_lower_ratio_limit := c(0.999); > glob_type_given_pole := 1; > array_given_rad_poles[1,1] := c(-1.5); > array_given_rad_poles[1,2] := c(0.0); > array_given_ord_poles[1,1] := c(0.5); > array_given_ord_poles[1,2] := c(0.0); > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=8; > glob_max_minutes:=(3.0); > glob_subiter_method:=3; > glob_max_iter:=10000; > glob_upper_ratio_limit:=c(1.000001); > glob_lower_ratio_limit:=c(0.999999); > glob_look_poles:=true; > glob_h:=c(0.001); > glob_display_interval:=c(0.01); > #END OVERRIDE BLOCK > #END BLOCK 2 > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_sec := (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours); > # after second input block > found_h := true; > glob_h := next_delta(); > #START ADJUST ALL SERIES > if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 9 > h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius; > omniout_str(ALWAYS,"SETTING H FOR POLE"); > glob_h_reason := 6; > if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 10 > omniout_str(ALWAYS,"SETTING H FOR MIN H"); > h_new := glob_min_h; > glob_h_reason := 5; > fi;# end if 10; > term := 1; > ratio := c(1.0); > while (term <= ATS_MAX_TERMS) do # do number 1 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / float_abs(glob_h); > term := term + 1; > od;# end do number 1; > glob_h := h_new; > fi;# end if 9; > #BOTTOM ADJUST ALL SERIES > #END OPTIMIZE CODE > if (glob_html_log) then # if number 9 > html_log_file := fopen("entry.html",WRITE,TEXT); > fi;# end if 9; > #BEGIN SOLUTION CODE > found_h := true; > if (found_h) then # if number 9 > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := c(x_start); > array_x[2] := c(glob_h); > glob_next_display := c(x_start); > glob_min_pole_est := glob_larger_float; > glob_least_given_sing := glob_larger_float; > glob_least_ratio_sing := glob_larger_float; > glob_least_3_sing := glob_larger_float; > glob_least_6_sing := glob_larger_float; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 1 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1)); > term_no := term_no + 1; > od;# end do number 1; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 1 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 2 > it := term_no + r_order - 1; > if (term_no < ATS_MAX_TERMS) then # if number 10 > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1))); > fi;# end if 10; > term_no := term_no + 1; > od;# end do number 2; > r_order := r_order + 1; > od;# end do number 1 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > glob_clock_sec := elapsed_time_seconds(); > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > found_h := true; > glob_h := next_delta(); > #START ADJUST ALL SERIES > if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 10 > h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius; > omniout_str(ALWAYS,"SETTING H FOR POLE"); > glob_h_reason := 6; > if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 11 > omniout_str(ALWAYS,"SETTING H FOR MIN H"); > h_new := glob_min_h; > glob_h_reason := 5; > fi;# end if 11; > term := 1; > ratio := c(1.0); > while (term <= ATS_MAX_TERMS) do # do number 1 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / float_abs(glob_h); > term := term + 1; > od;# end do number 1; > glob_h := h_new; > fi;# end if 10; > #BOTTOM ADJUST ALL SERIES > #END OPTIMIZE CODE > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_iter < glob_max_iter) and ((glob_iter < 10) or ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0))))) do # do number 1 > #left paren 0001C > if (true) then # if number 10 > omniout_str(INFO," "); > fi;# end if 10; > found_h := true; > glob_h := next_delta(); > #START ADJUST ALL SERIES > if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 10 > h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius; > omniout_str(ALWAYS,"SETTING H FOR POLE"); > glob_h_reason := 6; > if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 11 > omniout_str(ALWAYS,"SETTING H FOR MIN H"); > h_new := glob_min_h; > glob_h_reason := 5; > fi;# end if 11; > term := 1; > ratio := c(1.0); > while (term <= ATS_MAX_TERMS) do # do number 2 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / float_abs(glob_h); > term := term + 1; > od;# end do number 2; > glob_h := h_new; > fi;# end if 10; > #BOTTOM ADJUST ALL SERIES > #END OPTIMIZE CODE > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > atomall(); > if ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0))) then # if number 10 > display_alot(current_iter); > fi;# end if 10; > if ((glob_look_poles) and ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0)))) then # if number 10 > check_for_pole(); > fi;# end if 10; > if (true) then # if number 10 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 10; > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := ATS_MAX_TERMS; > while (term_no >= 1) do # do number 2 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 3 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 3; > term_no := term_no - 1; > od;# end do number 2; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > ; > od;# end do number 1;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 10 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 10; > if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec )) then # if number 10 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 10; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = cos ( sqrt ( 2.0 * x + 3.0 ) ) ; "); > 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,"2017-11-26T14:42:02-06:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"cos_sqrt_lin") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = cos ( sqrt ( 2.0 * x + 3.0 ) ) ; ") > ; > 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,"cos_sqrt_lin diffeq.mxt") > ; > logitem_str(html_log_file,"cos_sqrt_lin maple results") > ; > logitem_str(html_log_file,"Poor Accuracy") > ; > 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_const_3D0, 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_g, array_tmp4, array_tmp5, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; ATS_MAX_TERMS := 30; Digits := 32; max_terms := 30; glob_html_log := true; array_y_init := Array(0 .. 30, []); array_norms := Array(0 .. 30, []); array_fact_1 := Array(0 .. 30, []); array_1st_rel_error := Array(0 .. 2, []); array_last_rel_error := Array(0 .. 2, []); array_est_rel_error := Array(0 .. 2, []); array_max_est_error := Array(0 .. 2, []); array_type_pole := Array(0 .. 2, []); array_type_real_pole := Array(0 .. 2, []); array_type_complex_pole := Array(0 .. 2, []); array_est_digits := Array(0 .. 2, []); array_y := Array(0 .. 30, []); array_x := Array(0 .. 30, []); array_tmp0 := Array(0 .. 30, []); array_tmp1 := Array(0 .. 30, []); array_tmp2 := Array(0 .. 30, []); array_tmp3 := Array(0 .. 30, []); array_tmp4_g := Array(0 .. 30, []); array_tmp4 := Array(0 .. 30, []); array_tmp5 := Array(0 .. 30, []); array_m1 := Array(0 .. 30, []); array_y_higher := Array(0 .. 2, 0 .. 31, []); array_y_higher_work := Array(0 .. 2, 0 .. 31, []); array_y_higher_work2 := Array(0 .. 2, 0 .. 31, []); array_y_set_initial := Array(0 .. 2, 0 .. 31, []); array_given_rad_poles := Array(0 .. 2, 0 .. 4, []); array_given_ord_poles := Array(0 .. 2, 0 .. 4, []); array_rad_test_poles := Array(0 .. 2, 0 .. 5, []); array_ord_test_poles := Array(0 .. 2, 0 .. 5, []); array_fact_2 := Array(0 .. 30, 0 .. 31, []); term := 1; while term <= 30 do array_y_init[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_norms[term] := c(0.); term := term + 1 end do ; term := 1; while term <= 30 do array_fact_1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_1st_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_last_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_est_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_max_est_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_type_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_type_real_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_type_complex_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_est_digits[term] := 0; term := term + 1 end do ; term := 1; while term <= 30 do array_y[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_x[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp0[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp2[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp3[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp4_g[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp4[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_tmp5[term] := c(0.); term := term + 1 end do; term := 1; while term <= 30 do array_m1[term] := c(0.); term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 30 do array_y_higher[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 30 do array_y_higher_work[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 30 do array_y_higher_work2[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 30 do array_y_set_initial[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_rad_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_ord_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 4 do array_rad_test_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 4 do array_ord_test_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 30 do term := 1; while term <= 30 do array_fact_2[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; zero_ats_ar(array_y); zero_ats_ar(array_x); zero_ats_ar(array_tmp0); zero_ats_ar(array_tmp1); zero_ats_ar(array_tmp2); zero_ats_ar(array_tmp3); zero_ats_ar(array_tmp4_g); zero_ats_ar(array_tmp4); zero_ats_ar(array_tmp5); zero_ats_ar(array_m1); zero_ats_ar(array_const_1); array_const_1[1] := c(1); zero_ats_ar(array_const_0D0); array_const_0D0[1] := c(0.); zero_ats_ar(array_const_2D0); array_const_2D0[1] := c(2.0); zero_ats_ar(array_const_3D0); array_const_3D0[1] := c(3.0); zero_ats_ar(array_m1); array_m1[1] := glob__m1; iiif := 0; while iiif <= ATS_MAX_TERMS do jjjf := 0; while jjjf <= ATS_MAX_TERMS do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := 5; glob_yes_pole := 4; glob_no_pole := 3; glob_not_given := 0; glob_no_sing_tests := 4; glob_ratio_test := 1; glob_three_term_test := 2; glob_six_term_test := 3; glob_log_10 := log(c(10.0)); MAX_UNCHANGED := 10; glob__small := c(0.1*10^(-50)); glob_small_float := c(0.1*10^(-50)); glob_smallish_float := c(0.1*10^(-60)); glob_large_float := c(0.10*10^101); glob_larger_float := c(0.11*10^101); glob__m2 := c(-2); glob__m1 := c(-1); glob__0 := c(0); glob__1 := c(1); glob__2 := c(2); glob__3 := c(3); glob__4 := c(4); glob__5 := c(5); glob__8 := c(8); glob__10 := c(10); glob__100 := c(100); glob__pi := c(0.); glob__0_5 := c(0.5); glob__0_8 := c(0.8); glob__m0_8 := c(-0.8); glob__0_25 := c(0.25); glob__0_125 := c(0.125); glob_h := 0.1; glob_nxt := 1; glob_prec := c(0.10*10^(-15)); glob_check_sign := c(1.0); glob_desired_digits_correct := c(8.0); glob_max_estimated_step_error := c(0.); glob_ratio_of_radius := c(0.1); glob_percent_done := c(0.); glob_total_exp_sec := c(0.1); glob_optimal_expect_sec := c(0.1); glob_estimated_size_answer := c(100.0); glob_almost_1 := c(0.9990); glob_clock_sec := c(0.); glob_clock_start_sec := c(0.); glob_disp_incr := c(0.1); glob_diff_rc_fm := c(0.1); glob_diff_rc_fmm1 := c(0.1); glob_diff_rc_fmm2 := c(0.1); glob_diff_ord_fm := c(0.1); glob_diff_ord_fmm1 := c(0.1); glob_diff_ord_fmm2 := c(0.1); glob_six_term_ord_save := c(0.1); glob_guess_error_rc := c(0.1); glob_guess_error_ord := c(0.1); glob_least_given_sing := c(0.99*10^201); glob_least_ratio_sing := c(0.99*10^201); glob_least_3_sing := c(0.99*10^101); glob_least_6_sing := c(0.99*10^101); glob_last_good_h := c(0.1); glob_max_h := c(0.1); glob_min_h := c(0.1*10^(-5)); glob_display_interval := c(0.1); glob_abserr := c(0.1*10^(-10)); glob_relerr := c(0.1*10^(-10)); glob_min_pole_est := c(0.1*10^10); glob_max_rel_trunc_err := c(0.1*10^(-10)); glob_max_trunc_err := c(0.1*10^(-10)); glob_max_hours := c(0.); glob_optimal_clock_start_sec := c(0.); glob_optimal_start := c(0.); glob_upper_ratio_limit := c(1.0001); glob_lower_ratio_limit := c(0.9999); glob_max_sec := c(10000.0); glob_orig_start_sec := c(0.); glob_normmax := c(0.); glob_max_minutes := c(0.); glob_next_display := c(0.); glob_est_digits := 1; glob_subiter_method := 3; glob_html_log := true; glob_min_good_digits := 99999; glob_good_digits := 0; glob_min_apfp_est_good_digits := 99999; glob_apfp_est_good_digits := 0; glob_max_opt_iter := 10; glob_dump := false; glob_djd_debug := true; glob_display_flag := true; glob_djd_debug2 := true; glob_h_reason := 0; glob_sec_in_minute := 60; glob_min_in_hour := 60; glob_hours_in_day := 24; glob_days_in_year := 365; glob_sec_in_hour := 3600; glob_sec_in_day := 86400; glob_sec_in_year := 31536000; glob_not_yet_finished := true; glob_initial_pass := true; glob_not_yet_start_msg := true; glob_reached_optimal_h := false; glob_optimal_done := false; glob_type_given_pole := 0; glob_optimize := false; glob_look_poles := false; glob_dump_closed_form := false; glob_max_iter := 10000; glob_no_eqs := 0; glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_start := 0; glob_iter := 0; array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 30] := false; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; ATS_MAX_TERMS := 30; glob_iolevel := INFO; glob_orig_start_sec := elapsed_time_seconds(); glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 10000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/cos_sqrt_linpostcpx.cpx#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = cos ( sqrt ( 2.0 \ * x + 3.0 ) ) ; "); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := -1.4 + 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 := 0.0001;"); omniout_str(ALWAYS, "glob_upper_ratio_limit := c(1.001);"); omniout_str(ALWAYS, "glob_lower_ratio_limit := c(0.999);"); 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(-1.5);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_rad_poles[1,2] := c(0.0);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_ord_poles[1,1] := c(0.5);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_ord_poles[1,2] := c(0.0);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_desired_digits_correct:=8;"); omniout_str(ALWAYS, "glob_max_minutes:=(3.0);"); omniout_str(ALWAYS, "glob_subiter_method:=3;"); omniout_str(ALWAYS, "glob_max_iter:=10000;"); omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);"); omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);"); omniout_str(ALWAYS, "glob_look_poles:=true;"); omniout_str(ALWAYS, "glob_h:=c(0.001);"); omniout_str(ALWAYS, "glob_display_interval:=c(0.01);"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "return(cos(sqrt(c(2.0)*c(x)+c(3.0)))+sqrt(c(2.0)\ *c(x)+c(3.0))*sin(sqrt(c(2.0)*c(x)+c(3.0))));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "next_delta := proc()"); omniout_str(ALWAYS, "global glob_nxt, x_delta;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "x_delta := [ 0.001 + 0.00004 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); 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omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 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(0.10*10^101); glob_larger_float := c(0.11*10^101); glob_almost_1 := c(0.99); x_start := -1.4 + 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 := 0.0001; glob_upper_ratio_limit := c(1.001); glob_lower_ratio_limit := c(0.999); glob_type_given_pole := 1; array_given_rad_poles[1, 1] := c(-1.5); array_given_rad_poles[1, 2] := c(0.); array_given_ord_poles[1, 1] := c(0.5); array_given_ord_poles[1, 2] := c(0.); glob_desired_digits_correct := 8; glob_max_minutes := 3.0; glob_subiter_method := 3; glob_max_iter := 10000; glob_upper_ratio_limit := c(1.000001); glob_lower_ratio_limit := c(0.999999); glob_look_poles := true; glob_h := c(0.001); glob_display_interval := c(0.01); glob_last_good_h := glob_h; glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours; found_h := true; glob_h := next_delta(); if float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h) then h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius; omniout_str(ALWAYS, "SETTING H FOR POLE"); glob_h_reason := 6; if glob_check_sign*h_new < glob_check_sign*glob_min_h then omniout_str(ALWAYS, "SETTING H FOR MIN H"); h_new := glob_min_h; glob_h_reason := 5 end if; term := 1; ratio := c(1.0); while term <= ATS_MAX_TERMS do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/float_abs(glob_h); term := term + 1 end do; glob_h := h_new end if; if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT) end if; found_h := true; if found_h then omniout_str(ALWAYS, "START of Soultion"); array_x[1] := c(x_start); array_x[2] := c(glob_h); glob_next_display := c(x_start); glob_min_pole_est := glob_larger_float; glob_least_given_sing := glob_larger_float; glob_least_ratio_sing := glob_larger_float; glob_least_3_sing := glob_larger_float; glob_least_6_sing := glob_larger_float; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1)); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; if term_no < ATS_MAX_TERMS then array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, c(term_no - 1))/ c(factorial_1(term_no - 1)) end if; term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); glob_clock_sec := elapsed_time_seconds(); glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; found_h := true; glob_h := next_delta(); if float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h) then h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius ; omniout_str(ALWAYS, "SETTING H FOR POLE"); glob_h_reason := 6; if glob_check_sign*h_new < glob_check_sign*glob_min_h then omniout_str(ALWAYS, "SETTING H FOR MIN H"); h_new := glob_min_h; glob_h_reason := 5 end if; term := 1; ratio := c(1.0); while term <= ATS_MAX_TERMS do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/float_abs(glob_h); term := term + 1 end do; glob_h := h_new end if; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_iter < glob_max_iter and (glob_iter < 10 or not (Re(glob_h) = 0. and Im(glob_h) = 0.)) do omniout_str(INFO, " "); found_h := true; glob_h := next_delta(); if float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h) then h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius; omniout_str(ALWAYS, "SETTING H FOR POLE"); glob_h_reason := 6; if glob_check_sign*h_new < glob_check_sign*glob_min_h then omniout_str(ALWAYS, "SETTING H FOR MIN H"); h_new := glob_min_h; glob_h_reason := 5 end if; term := 1; ratio := c(1.0); while term <= ATS_MAX_TERMS do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/float_abs(glob_h); term := term + 1 end do; glob_h := h_new end if; glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); atomall(); if not (Re(glob_h) = 0. and Im(glob_h) = 0.) then display_alot(current_iter) end if; if glob_look_poles and not (Re(glob_h) = 0. and Im(glob_h) = 0.) then check_for_pole() end if; glob_next_display := glob_next_display + glob_display_interval; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 2; ord := 2; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_higher[2, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 2; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); term_no := ATS_MAX_TERMS; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if glob_max_sec <= elapsed_time_seconds() - glob_orig_start_sec then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y , x , 1 ) = cos ( sqrt ( 2.\ 0 * x + 3.0 ) ) ; "); 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, "2017-11-26T14:42:02-06:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "cos_sqrt_lin"); logitem_str(html_log_file, "diff ( y , x , 1 ) = co\ s ( sqrt ( 2.0 * x + 3.0 ) ) ; "); 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, "cos_sqrt_lin diffeq.mxt"); logitem_str(html_log_file, "cos_sqrt_lin maple results"); logitem_str(html_log_file, "Poor Accuracy"); 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/cos_sqrt_linpostcpx.cpx################# diff ( y , x , 1 ) = cos ( sqrt ( 2.0 * x + 3.0 ) ) ; ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := -1.4 + 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 := 0.0001; glob_upper_ratio_limit := c(1.001); glob_lower_ratio_limit := c(0.999); glob_type_given_pole := 1; array_given_rad_poles[1,1] := c(-1.5); array_given_rad_poles[1,2] := c(0.0); array_given_ord_poles[1,1] := c(0.5); array_given_ord_poles[1,2] := c(0.0); #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=8; glob_max_minutes:=(3.0); glob_subiter_method:=3; glob_max_iter:=10000; glob_upper_ratio_limit:=c(1.000001); glob_lower_ratio_limit:=c(0.999999); glob_look_poles:=true; glob_h:=c(0.001); glob_display_interval:=c(0.01); #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) return(cos(sqrt(c(2.0)*c(x)+c(3.0)))+sqrt(c(2.0)*c(x)+c(3.0))*sin(sqrt(c(2.0)*c(x)+c(3.0)))); end; next_delta := proc() global glob_nxt, x_delta; x_delta := [ 0.001 + 0.00004 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.000 + 0.000 * I ]; glob_nxt := glob_nxt + 1; it := x_delta[glob_nxt]; return it; end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = -1.4 0.1 h = 0.0001 0.005 y[1] (numeric) = 1.09988999683 0.0901111079483 y[1] (closed_form) = 1.09988999683 0.0901111079483 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 0.1414 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3999 0.105 h = 0.0001 0.003 y[1] (numeric) = 1.1004634081 0.094601521103 y[1] (closed_form) = 1.10047550513 0.094600651045 absolute error = 1.213e-05 relative error = 0.001098 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.1451 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=30.8MB, alloc=40.3MB, time=0.44 x[1] = -1.3998 0.108 h = 0.001 0.001 y[1] (numeric) = 1.10085790704 0.0972906183304 y[1] (closed_form) = 1.10087437151 0.0972893274481 absolute error = 1.652e-05 relative error = 0.001494 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.1473 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3988 0.109 h = 0.001 0.003 y[1] (numeric) = 1.10186187209 0.0980857612963 y[1] (closed_form) = 1.10187830804 0.0980835029701 absolute error = 1.659e-05 relative error = 0.0015 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.1487 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3978 0.112 h = 0.0001 0.004 y[1] (numeric) = 1.10307646365 0.100676083871 y[1] (closed_form) = 1.10309665752 0.100670780385 absolute error = 2.088e-05 relative error = 0.001885 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.1516 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3977 0.116 h = 0.003 0.006 y[1] (numeric) = 1.10359902245 0.104255185665 y[1] (closed_form) = 1.10362694456 0.104249200593 absolute error = 2.856e-05 relative error = 0.002576 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.1547 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3947 0.122 h = 0.0001 0.005 y[1] (numeric) = 1.1069630791 0.109302385791 y[1] (closed_form) = 1.10700339631 0.109278511355 absolute error = 4.686e-05 relative error = 0.004212 % Correct digits = 4 Radius of convergence (given) for eq 1 = 0.1612 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=76.4MB, alloc=52.3MB, time=1.05 x[1] = -1.3946 0.127 h = 0.0001 0.003 y[1] (numeric) = 1.10764109733 0.11376117394 y[1] (closed_form) = 1.10769355533 0.113736282244 absolute error = 5.806e-05 relative error = 0.005214 % Correct digits = 4 Radius of convergence (given) for eq 1 = 0.165 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3945 0.13 h = 0.001 0.001 y[1] (numeric) = 1.10809813477 0.116430318362 y[1] (closed_form) = 1.10815494707 0.116404969063 absolute error = 6.221e-05 relative error = 0.005583 % Correct digits = 4 Radius of convergence (given) for eq 1 = 0.1674 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3935 0.131 h = 0.001 0.003 y[1] (numeric) = 1.10911716558 0.117198451878 y[1] (closed_form) = 1.10917394129 0.117172136724 absolute error = 6.258e-05 relative error = 0.005611 % Correct digits = 4 Radius of convergence (given) for eq 1 = 0.1688 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3925 0.134 h = 0.0001 0.004 y[1] (numeric) = 1.11038886458 0.119749812795 y[1] (closed_form) = 1.11044936882 0.119720429947 absolute error = 6.726e-05 relative error = 0.006022 % Correct digits = 4 Radius of convergence (given) for eq 1 = 0.1718 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3924 0.138 h = 0.003 0.006 y[1] (numeric) = 1.1109948878 0.123302825609 y[1] (closed_form) = 1.11106309966 0.123272703505 absolute error = 7.457e-05 relative error = 0.00667 % Correct digits = 4 Radius of convergence (given) for eq 1 = 0.175 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=121.9MB, alloc=52.3MB, time=1.64 x[1] = -1.3894 0.144 h = 0.0001 0.005 y[1] (numeric) = 1.11446691609 0.128250855544 y[1] (closed_form) = 1.11454736281 0.128202777957 absolute error = 9.372e-05 relative error = 0.008354 % Correct digits = 4 Radius of convergence (given) for eq 1 = 0.1816 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3893 0.149 h = 0.0001 0.003 y[1] (numeric) = 1.11524921273 0.132677235782 y[1] (closed_form) = 1.11534175878 0.132628050361 absolute error = 0.0001048 relative error = 0.009331 % Correct digits = 4 Radius of convergence (given) for eq 1 = 0.1856 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3892 0.152 h = 0.001 0.001 y[1] (numeric) = 1.11576853427 0.135325993553 y[1] (closed_form) = 1.11586542138 0.135276315233 absolute error = 0.0001089 relative error = 0.009687 % Correct digits = 4 Radius of convergence (given) for eq 1 = 0.1881 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3882 0.153 h = 0.001 0.003 y[1] (numeric) = 1.11680240392 0.136067050685 y[1] (closed_form) = 1.11689924658 0.13601640828 absolute error = 0.0001093 relative error = 0.009713 % Correct digits = 4 Radius of convergence (given) for eq 1 = 0.1895 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3872 0.156 h = 0.0001 0.004 y[1] (numeric) = 1.11813082357 0.138579089825 y[1] (closed_form) = 1.11823136541 0.13852535731 absolute error = 0.000114 relative error = 0.01012 % Correct digits = 4 Radius of convergence (given) for eq 1 = 0.1925 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=167.4MB, alloc=52.3MB, time=2.22 x[1] = -1.3871 0.16 h = 0.003 0.006 y[1] (numeric) = 1.11881997585 0.142105434595 y[1] (closed_form) = 1.11892820487 0.142050905814 absolute error = 0.0001212 relative error = 0.01074 % Correct digits = 4 Radius of convergence (given) for eq 1 = 0.1958 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3841 0.166 h = 0.0001 0.005 y[1] (numeric) = 1.12239905406 0.146953654034 y[1] (closed_form) = 1.12251935851 0.146881105825 absolute error = 0.0001405 relative error = 0.01241 % Correct digits = 4 Radius of convergence (given) for eq 1 = 0.2025 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.384 0.171 h = 0.0001 0.003 y[1] (numeric) = 1.12328521026 0.151346900834 y[1] (closed_form) = 1.12341757487 0.151273156054 absolute error = 0.0001515 relative error = 0.01337 % Correct digits = 4 Radius of convergence (given) for eq 1 = 0.2066 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3839 0.174 h = 0.001 0.001 y[1] (numeric) = 1.12386655969 0.153974840121 y[1] (closed_form) = 1.1240032522 0.153900568192 absolute error = 0.0001556 relative error = 0.01371 % Correct digits = 4 Radius of convergence (given) for eq 1 = 0.2092 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3829 0.175 h = 0.001 0.003 y[1] (numeric) = 1.12491504124 0.154688755073 y[1] (closed_form) = 1.1250516816 0.154613520947 absolute error = 0.000156 relative error = 0.01374 % Correct digits = 4 Radius of convergence (given) for eq 1 = 0.2106 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=213.0MB, alloc=52.3MB, time=2.80 x[1] = -1.3819 0.178 h = 0.0001 0.004 y[1] (numeric) = 1.12629979358 0.157161114407 y[1] (closed_form) = 1.12644010375 0.157082767873 absolute error = 0.0001607 relative error = 0.01413 % Correct digits = 4 Radius of convergence (given) for eq 1 = 0.2136 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3818 0.182 h = 0.003 0.006 y[1] (numeric) = 1.12707173744 0.160660214353 y[1] (closed_form) = 1.12721971448 0.160581015003 absolute error = 0.0001678 relative error = 0.01474 % Correct digits = 4 Radius of convergence (given) for eq 1 = 0.217 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3788 0.188 h = 0.0001 0.005 y[1] (numeric) = 1.13075694208 0.16540798825 y[1] (closed_form) = 1.13091683581 0.165310707184 absolute error = 0.0001872 relative error = 0.01638 % Correct digits = 4 Radius of convergence (given) for eq 1 = 0.2237 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3787 0.193 h = 0.0001 0.003 y[1] (numeric) = 1.13174653681 0.169767379402 y[1] (closed_form) = 1.13191845322 0.169668814145 absolute error = 0.0001982 relative error = 0.01731 % Correct digits = 4 Radius of convergence (given) for eq 1 = 0.228 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3786 0.196 h = 0.001 0.001 y[1] (numeric) = 1.13238965624 0.172374070241 y[1] (closed_form) = 1.1325658875 0.172274944344 absolute error = 0.0002022 relative error = 0.01765 % Correct digits = 4 Radius of convergence (given) for eq 1 = 0.2306 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=258.6MB, alloc=52.3MB, time=3.38 x[1] = -1.3776 0.197 h = 0.0001 0.004 y[1] (numeric) = 1.13345252273 0.17306077833 y[1] (closed_form) = 1.13362869425 0.172960692204 absolute error = 0.0002026 relative error = 0.01767 % Correct digits = 4 Radius of convergence (given) for eq 1 = 0.2319 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3775 0.201 h = 0.003 0.006 y[1] (numeric) = 1.13429580505 0.176536947356 y[1] (closed_form) = 1.1344796144 0.176435959777 absolute error = 0.0002097 relative error = 0.01827 % Correct digits = 4 Radius of convergence (given) for eq 1 = 0.2354 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3745 0.207 h = 0.0001 0.005 y[1] (numeric) = 1.13807282569 0.181199005591 y[1] (closed_form) = 1.13826841624 0.181079881885 absolute error = 0.000229 relative error = 0.01987 % Correct digits = 4 Radius of convergence (given) for eq 1 = 0.2421 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3744 0.212 h = 0.0001 0.003 y[1] (numeric) = 1.13915153287 0.185529904194 y[1] (closed_form) = 1.13935911588 0.18540942103 absolute error = 0.00024 relative error = 0.02079 % Correct digits = 4 Radius of convergence (given) for eq 1 = 0.2464 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3743 0.215 h = 0.001 0.001 y[1] (numeric) = 1.13984787415 0.188118693729 y[1] (closed_form) = 1.14005976125 0.187997621399 absolute error = 0.000244 relative error = 0.02112 % Correct digits = 4 Radius of convergence (given) for eq 1 = 0.249 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=304.2MB, alloc=52.3MB, time=3.96 x[1] = -1.3733 0.216 h = 0.001 0.003 y[1] (numeric) = 1.14092326607 0.188782099767 y[1] (closed_form) = 1.14113508696 0.18866006886 absolute error = 0.0002445 relative error = 0.02114 % Correct digits = 4 Radius of convergence (given) for eq 1 = 0.2504 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3723 0.219 h = 0.0001 0.004 y[1] (numeric) = 1.14241228649 0.191180338551 y[1] (closed_form) = 1.14262772276 0.191055153717 absolute error = 0.0002492 relative error = 0.02151 % Correct digits = 4 Radius of convergence (given) for eq 1 = 0.2535 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3722 0.223 h = 0.003 0.006 y[1] (numeric) = 1.14333772122 0.194628191273 y[1] (closed_form) = 1.14356078733 0.19450204901 absolute error = 0.0002563 relative error = 0.02209 % Correct digits = 4 Radius of convergence (given) for eq 1 = 0.257 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3692 0.229 h = 0.0001 0.005 y[1] (numeric) = 1.14721915275 0.19918862462 y[1] (closed_form) = 1.14745384225 0.199044286291 absolute error = 0.0002755 relative error = 0.02366 % Correct digits = 4 Radius of convergence (given) for eq 1 = 0.2637 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3691 0.234 h = 0.0001 0.003 y[1] (numeric) = 1.14840051731 0.203484326504 y[1] (closed_form) = 1.1486471638 0.203338542244 absolute error = 0.0002865 relative error = 0.02456 % Correct digits = 4 Radius of convergence (given) for eq 1 = 0.2681 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.369 0.237 h = 0.001 0.001 y[1] (numeric) = 1.14915814947 0.206051069103 y[1] (closed_form) = 1.14940908717 0.205904663129 absolute error = 0.0002905 relative error = 0.02488 % Correct digits = 4 memory used=349.8MB, alloc=52.3MB, time=4.54 Radius of convergence (given) for eq 1 = 0.2708 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.368 0.238 h = 0.001 0.003 y[1] (numeric) = 1.15024750467 0.206687148115 y[1] (closed_form) = 1.15049836873 0.206539785631 absolute error = 0.0002909 relative error = 0.02489 % Correct digits = 4 Radius of convergence (given) for eq 1 = 0.2722 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.367 0.241 h = 0.0001 0.004 y[1] (numeric) = 1.15179174567 0.209044689717 y[1] (closed_form) = 1.15204619567 0.208894151363 absolute error = 0.0002956 relative error = 0.02525 % Correct digits = 4 Radius of convergence (given) for eq 1 = 0.2753 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3669 0.245 h = 0.003 0.006 y[1] (numeric) = 1.15279900144 0.212463655552 y[1] (closed_form) = 1.15306106099 0.212312104029 absolute error = 0.0003027 relative error = 0.02582 % Correct digits = 4 Radius of convergence (given) for eq 1 = 0.2788 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3639 0.251 h = 0.0001 0.005 y[1] (numeric) = 1.15678391542 0.216921843149 y[1] (closed_form) = 1.15705744085 0.216752036658 absolute error = 0.0003219 relative error = 0.02735 % Correct digits = 4 Radius of convergence (given) for eq 1 = 0.2855 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3638 0.256 h = 0.0001 0.003 y[1] (numeric) = 1.15806750944 0.221181634294 y[1] (closed_form) = 1.15835295706 0.221010295757 absolute error = 0.0003329 relative error = 0.02823 % Correct digits = 4 Radius of convergence (given) for eq 1 = 0.29 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=395.4MB, alloc=52.3MB, time=5.12 x[1] = -1.3637 0.259 h = 0.001 0.001 y[1] (numeric) = 1.15888616995 0.223725904924 y[1] (closed_form) = 1.15917589595 0.22355391248 absolute error = 0.0003369 relative error = 0.02854 % Correct digits = 4 Radius of convergence (given) for eq 1 = 0.2927 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3627 0.26 h = 0.001 0.003 y[1] (numeric) = 1.15998926136 0.224334595331 y[1] (closed_form) = 1.16027890638 0.224161648486 absolute error = 0.0003373 relative error = 0.02855 % Correct digits = 4 Radius of convergence (given) for eq 1 = 0.294 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3617 0.263 h = 0.0001 0.004 y[1] (numeric) = 1.16158833048 0.226651089775 y[1] (closed_form) = 1.16188153193 0.226474945249 absolute error = 0.000342 relative error = 0.02889 % Correct digits = 4 Radius of convergence (given) for eq 1 = 0.2971 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3616 0.267 h = 0.003 0.006 y[1] (numeric) = 1.1626770615 0.230040600281 y[1] (closed_form) = 1.16297785212 0.229863387046 absolute error = 0.0003491 relative error = 0.02945 % Correct digits = 4 Radius of convergence (given) for eq 1 = 0.3007 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3586 0.273 h = 0.0001 0.005 y[1] (numeric) = 1.16676452771 0.234395926107 y[1] (closed_form) = 1.16707662699 0.234200399949 absolute error = 0.0003683 relative error = 0.03094 % Correct digits = 4 Radius of convergence (given) for eq 1 = 0.3074 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=441.0MB, alloc=52.3MB, time=5.70 x[1] = -1.3585 0.278 h = 0.0001 0.003 y[1] (numeric) = 1.16814992075 0.238619095196 y[1] (closed_form) = 1.16847390787 0.238421951157 absolute error = 0.0003793 relative error = 0.0318 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.3119 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3584 0.281 h = 0.001 0.001 y[1] (numeric) = 1.1690293455 0.241140470487 y[1] (closed_form) = 1.1693575982 0.240942640637 absolute error = 0.0003833 relative error = 0.0321 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.3147 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3574 0.282 h = 0.001 0.003 y[1] (numeric) = 1.17014594602 0.24172171179 y[1] (closed_form) = 1.17047411045 0.241522929679 absolute error = 0.0003837 relative error = 0.0321 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.316 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3564 0.285 h = 0.0001 0.004 y[1] (numeric) = 1.17179944964 0.243996811193 y[1] (closed_form) = 1.17213114094 0.243794809729 absolute error = 0.0003884 relative error = 0.03244 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.3191 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3563 0.289 h = 0.003 0.006 y[1] (numeric) = 1.17296930796 0.247356300059 y[1] (closed_form) = 1.17330856795 0.247153174528 absolute error = 0.0003954 relative error = 0.03298 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.3228 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=486.6MB, alloc=52.3MB, time=6.28 x[1] = -1.3533 0.295 h = 0.0001 0.005 y[1] (numeric) = 1.17715839448 0.251608152907 y[1] (closed_form) = 1.17750880612 0.251386657389 absolute error = 0.0004145 relative error = 0.03443 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.3295 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3532 0.3 h = 0.0001 0.003 y[1] (numeric) = 1.17864515352 0.255793991301 y[1] (closed_form) = 1.17900741893 0.255570792296 absolute error = 0.0004255 relative error = 0.03527 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.334 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3531 0.303 h = 0.001 0.001 y[1] (numeric) = 1.17958507679 0.258292049532 y[1] (closed_form) = 1.17995159499 0.258068133052 absolute error = 0.0004295 relative error = 0.03556 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.3367 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3521 0.304 h = 0.0001 0.004 y[1] (numeric) = 1.18071495929 0.258845782301 y[1] (closed_form) = 1.18108138199 0.258620915733 absolute error = 0.0004299 relative error = 0.03556 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.3381 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.352 0.308 h = 0.003 0.006 y[1] (numeric) = 1.18195474407 0.262179937223 y[1] (closed_form) = 1.1823287101 0.261953899991 absolute error = 0.000437 relative error = 0.03608 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.3417 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=532.2MB, alloc=52.3MB, time=6.87 x[1] = -1.349 0.314 h = 0.0001 0.005 y[1] (numeric) = 1.18623179677 0.266343433565 y[1] (closed_form) = 1.18661678008 0.266098976042 absolute error = 0.000456 relative error = 0.0375 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.3484 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3489 0.319 h = 0.0001 0.003 y[1] (numeric) = 1.18780591568 0.270497773919 y[1] (closed_form) = 1.1882027246 0.270251538983 absolute error = 0.000467 relative error = 0.03832 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.353 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3488 0.322 h = 0.001 0.001 y[1] (numeric) = 1.18879798462 0.272976141469 y[1] (closed_form) = 1.1891990357 0.272729161817 absolute error = 0.000471 relative error = 0.0386 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.3557 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3478 0.323 h = 0.001 0.003 y[1] (numeric) = 1.18993944653 0.273506303572 y[1] (closed_form) = 1.19034039589 0.273258375641 absolute error = 0.0004714 relative error = 0.0386 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.3571 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3468 0.326 h = 0.0001 0.004 y[1] (numeric) = 1.19169369127 0.275704095052 y[1] (closed_form) = 1.19209811259 0.275452907459 absolute error = 0.0004761 relative error = 0.03891 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.3602 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=577.8MB, alloc=52.3MB, time=7.44 x[1] = -1.3467 0.33 h = 0.003 0.006 y[1] (numeric) = 1.1930139486 0.279007177189 y[1] (closed_form) = 1.19342590081 0.278754762718 absolute error = 0.0004831 relative error = 0.03942 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.3639 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3437 0.336 h = 0.0001 0.005 y[1] (numeric) = 1.19739089006 0.283066064848 y[1] (closed_form) = 1.19781370277 0.282795174582 absolute error = 0.0005021 relative error = 0.0408 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.3706 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3436 0.341 h = 0.0001 0.003 y[1] (numeric) = 1.19906557068 0.287181757747 y[1] (closed_form) = 1.19950017518 0.28690900483 absolute error = 0.0005131 relative error = 0.0416 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.3752 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3435 0.344 h = 0.001 0.001 y[1] (numeric) = 1.20011764445 0.28963602466 y[1] (closed_form) = 1.20055647829 0.289362495726 absolute error = 0.0005171 relative error = 0.04187 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.3779 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3425 0.345 h = 0.001 0.003 y[1] (numeric) = 1.2012719663 0.290138567793 y[1] (closed_form) = 1.20171069127 0.289864092808 absolute error = 0.0005175 relative error = 0.04186 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.3793 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=623.5MB, alloc=52.3MB, time=8.02 x[1] = -1.3415 0.348 h = 0.0001 0.004 y[1] (numeric) = 1.20307951723 0.292293975885 y[1] (closed_form) = 1.20352168443 0.292016219968 absolute error = 0.0005222 relative error = 0.04216 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.3824 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3414 0.352 h = 0.003 0.006 y[1] (numeric) = 1.20447990129 0.295565423833 y[1] (closed_form) = 1.2049295785 0.295286386146 absolute error = 0.0005292 relative error = 0.04266 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.3861 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3384 0.358 h = 0.0001 0.005 y[1] (numeric) = 1.20895579461 0.299519105282 y[1] (closed_form) = 1.20941617563 0.299221537102 absolute error = 0.0005482 relative error = 0.044 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.3928 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3383 0.363 h = 0.0001 0.003 y[1] (numeric) = 1.21073059643 0.303595449664 y[1] (closed_form) = 1.21120273543 0.303295933774 absolute error = 0.0005591 relative error = 0.04478 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.3974 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3382 0.366 h = 0.001 0.001 y[1] (numeric) = 1.21184240476 0.306025198876 y[1] (closed_form) = 1.21231876024 0.305724875832 absolute error = 0.0005631 relative error = 0.04504 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.4002 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=669.1MB, alloc=52.3MB, time=8.60 x[1] = -1.3372 0.367 h = 0.001 0.003 y[1] (numeric) = 1.21300935933 0.306500066672 y[1] (closed_form) = 1.21348559881 0.306198799834 absolute error = 0.0005635 relative error = 0.04503 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.4015 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3362 0.37 h = 0.0001 0.004 y[1] (numeric) = 1.21486981841 0.308612751595 y[1] (closed_form) = 1.21534947033 0.308308182701 absolute error = 0.0005682 relative error = 0.04531 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.4046 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3361 0.374 h = 0.003 0.006 y[1] (numeric) = 1.21634997298 0.311852007252 y[1] (closed_form) = 1.21683711387 0.311546101847 absolute error = 0.0005752 relative error = 0.0458 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.4083 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3331 0.38 h = 0.0001 0.005 y[1] (numeric) = 1.22092387952 0.315699889742 y[1] (closed_form) = 1.2214215676 0.315375399935 absolute error = 0.0005941 relative error = 0.0471 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.415 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.333 0.385 h = 0.0001 0.003 y[1] (numeric) = 1.2227983594 0.319736187202 y[1] (closed_form) = 1.22330777161 0.319409664805 absolute error = 0.0006051 relative error = 0.04786 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.4197 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=715.0MB, alloc=52.3MB, time=9.18 x[1] = -1.3329 0.388 h = 0.001 0.001 y[1] (numeric) = 1.22396963044 0.322141003279 y[1] (closed_form) = 1.22448324623 0.321813642742 absolute error = 0.0006091 relative error = 0.04811 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.4225 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3319 0.389 h = 0.001 0.003 y[1] (numeric) = 1.22514899048 0.32258814044 y[1] (closed_form) = 1.22566248319 0.322259838394 absolute error = 0.0006095 relative error = 0.04809 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.4238 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3309 0.392 h = 0.0001 0.004 y[1] (numeric) = 1.22706195855 0.324657764522 y[1] (closed_form) = 1.22757883385 0.32432613944 absolute error = 0.0006141 relative error = 0.04837 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.4269 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3308 0.396 h = 0.003 0.006 y[1] (numeric) = 1.22862152527 0.327864271923 y[1] (closed_form) = 1.22914586831 0.327531255742 absolute error = 0.0006212 relative error = 0.04883 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.4306 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3278 0.402 h = 0.0001 0.005 y[1] (numeric) = 1.23329250474 0.331605767482 y[1] (closed_form) = 1.23382723838 0.331254113768 absolute error = 0.00064 relative error = 0.0501 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.4373 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=760.7MB, alloc=52.3MB, time=9.76 x[1] = -1.3277 0.407 h = 0.0001 0.003 y[1] (numeric) = 1.2352662169 0.335601322276 y[1] (closed_form) = 1.23581264073 0.33524755127 absolute error = 0.0006509 relative error = 0.05084 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.442 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3276 0.41 h = 0.001 0.001 y[1] (numeric) = 1.23649667723 0.337980791418 y[1] (closed_form) = 1.23704729167 0.337626151424 absolute error = 0.0006549 relative error = 0.05108 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.4448 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3266 0.411 h = 0.0001 0.004 y[1] (numeric) = 1.23768821546 0.338400143714 y[1] (closed_form) = 1.23823869978 0.338044564521 absolute error = 0.0006553 relative error = 0.05106 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.4461 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3265 0.415 h = 0.003 0.006 y[1] (numeric) = 1.23931625415 0.341578957617 y[1] (closed_form) = 1.2398741823 0.341221941638 absolute error = 0.0006624 relative error = 0.05151 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.4498 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3235 0.421 h = 0.0001 0.005 y[1] (numeric) = 1.24407131321 0.345229552724 y[1] (closed_form) = 1.24463949783 0.34485385223 absolute error = 0.0006812 relative error = 0.05274 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.4565 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=806.4MB, alloc=52.3MB, time=10.35 x[1] = -1.3234 0.426 h = 0.0001 0.003 y[1] (numeric) = 1.2461305788 0.349190657271 y[1] (closed_form) = 1.24671042529 0.348812766314 absolute error = 0.0006921 relative error = 0.05346 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.4612 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3233 0.429 h = 0.001 0.001 y[1] (numeric) = 1.24741207574 0.351548679101 y[1] (closed_form) = 1.24799610201 0.35116989255 absolute error = 0.0006961 relative error = 0.05369 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.464 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3223 0.43 h = 0.001 0.003 y[1] (numeric) = 1.2486142464 0.351944213881 y[1] (closed_form) = 1.24919813645 0.35156449006 absolute error = 0.0006965 relative error = 0.05367 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.4653 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3213 0.433 h = 0.0001 0.004 y[1] (numeric) = 1.25062437761 0.35393343449 y[1] (closed_form) = 1.25121159479 0.353550348631 absolute error = 0.0007011 relative error = 0.05392 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.4684 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3212 0.437 h = 0.003 0.006 y[1] (numeric) = 1.25233115641 0.357078468439 y[1] (closed_form) = 1.25292580201 0.356693890044 absolute error = 0.0007082 relative error = 0.05436 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.4722 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3182 0.443 h = 0.0001 0.005 y[1] (numeric) = 1.25718154109 0.360621583997 y[1] (closed_form) = 1.2577862866 0.360218269386 absolute error = 0.0007269 relative error = 0.05556 % Correct digits = 3 memory used=852.2MB, alloc=52.3MB, time=10.93 Radius of convergence (given) for eq 1 = 0.4789 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3181 0.448 h = 0.0001 0.003 y[1] (numeric) = 1.25933921071 0.364540652981 y[1] (closed_form) = 1.25995558389 0.364135063538 absolute error = 0.0007378 relative error = 0.05626 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.4835 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.318 0.451 h = 0.001 0.001 y[1] (numeric) = 1.26067938886 0.366872558932 y[1] (closed_form) = 1.26129992872 0.366466043281 absolute error = 0.0007418 relative error = 0.05648 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.4863 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.317 0.452 h = 0.001 0.003 y[1] (numeric) = 1.26189331539 0.367240208068 y[1] (closed_form) = 1.26251371204 0.366832757508 absolute error = 0.0007422 relative error = 0.05646 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.4876 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.316 0.455 h = 0.0001 0.004 y[1] (numeric) = 1.26395481152 0.369185408688 y[1] (closed_form) = 1.26457850525 0.368774575534 absolute error = 0.0007468 relative error = 0.0567 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.4908 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3159 0.459 h = 0.003 0.006 y[1] (numeric) = 1.26573997214 0.372296111406 y[1] (closed_form) = 1.26637107255 0.371883731552 absolute error = 0.0007539 relative error = 0.05712 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.4945 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=897.9MB, alloc=52.3MB, time=11.51 x[1] = -1.3129 0.465 h = 0.0001 0.005 y[1] (numeric) = 1.2706847373 0.375731173088 y[1] (closed_form) = 1.27132578107 0.375300006073 absolute error = 0.0007726 relative error = 0.05828 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.5012 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3128 0.47 h = 0.0001 0.003 y[1] (numeric) = 1.27294035764 0.379607518377 y[1] (closed_form) = 1.27359299469 0.379173992347 absolute error = 0.0007835 relative error = 0.05896 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.5059 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3127 0.473 h = 0.001 0.001 y[1] (numeric) = 1.27433893907 0.381912899305 y[1] (closed_form) = 1.27499572964 0.381478416571 absolute error = 0.0007875 relative error = 0.05917 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.5087 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3117 0.474 h = 0.001 0.003 y[1] (numeric) = 1.27556439416 0.382252611614 y[1] (closed_form) = 1.27622103453 0.381817196359 absolute error = 0.0007879 relative error = 0.05915 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.51 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3107 0.477 h = 0.0001 0.004 y[1] (numeric) = 1.27767685175 0.384153462717 y[1] (closed_form) = 1.27833675913 0.383714644462 absolute error = 0.0007925 relative error = 0.05938 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.5132 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=943.6MB, alloc=52.3MB, time=12.08 x[1] = -1.3106 0.481 h = 0.003 0.006 y[1] (numeric) = 1.27954002767 0.387229286522 y[1] (closed_form) = 1.28020731978 0.38678886755 absolute error = 0.0007995 relative error = 0.05978 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.5169 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3076 0.487 h = 0.0001 0.005 y[1] (numeric) = 1.28457822652 0.390555724773 y[1] (closed_form) = 1.28525530543 0.390096468453 absolute error = 0.0008181 relative error = 0.06091 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.5236 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3075 0.492 h = 0.0001 0.003 y[1] (numeric) = 1.28693134165 0.39438866092 y[1] (closed_form) = 1.28761997925 0.393926961589 absolute error = 0.0008291 relative error = 0.06157 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.5283 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3074 0.495 h = 0.001 0.001 y[1] (numeric) = 1.28838804689 0.39666710932 y[1] (closed_form) = 1.28908082475 0.3962044229 absolute error = 0.0008331 relative error = 0.06177 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.5311 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3064 0.496 h = 0.001 0.003 y[1] (numeric) = 1.28962480319 0.396978834685 y[1] (closed_form) = 1.29031742391 0.396515218161 absolute error = 0.0008335 relative error = 0.06174 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.5324 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=989.4MB, alloc=52.3MB, time=12.67 x[1] = -1.3054 0.499 h = 0.0001 0.004 y[1] (numeric) = 1.29178781773 0.39883500886 y[1] (closed_form) = 1.2924836753 0.398367969078 absolute error = 0.0008381 relative error = 0.06196 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.5356 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3053 0.503 h = 0.003 0.006 y[1] (numeric) = 1.29372864033 0.401875408231 y[1] (closed_form) = 1.2944318605 0.401406713864 absolute error = 0.0008451 relative error = 0.06236 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.5394 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3023 0.509 h = 0.0001 0.005 y[1] (numeric) = 1.29885932445 0.405092658276 y[1] (closed_form) = 1.29957217486 0.404605077129 absolute error = 0.0008636 relative error = 0.06345 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.546 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3022 0.514 h = 0.0001 0.003 y[1] (numeric) = 1.30130947583 0.408881502524 y[1] (closed_form) = 1.30203385011 0.40839139456 absolute error = 0.0008746 relative error = 0.06409 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.5507 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3021 0.517 h = 0.001 0.001 y[1] (numeric) = 1.30282402385 0.411132612532 y[1] (closed_form) = 1.30355252506 0.410641487203 absolute error = 0.0008786 relative error = 0.06429 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.5536 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1035.2MB, alloc=52.3MB, time=13.26 x[1] = -1.3011 0.518 h = 0.0001 0.004 y[1] (numeric) = 1.30407185402 0.411416301901 y[1] (closed_form) = 1.30480019116 0.41092424891 absolute error = 0.000879 relative error = 0.06425 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.5549 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.301 0.522 h = 0.003 0.006 y[1] (numeric) = 1.30607965113 0.414426691344 y[1] (closed_form) = 1.30681532747 0.413932938738 absolute error = 0.000886 relative error = 0.06463 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.5586 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.298 0.528 h = 0.0001 0.005 y[1] (numeric) = 1.31129049249 0.417550593494 y[1] (closed_form) = 1.31203566488 0.417037910291 absolute error = 0.0009045 relative error = 0.0657 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.5653 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2979 0.533 h = 0.0001 0.003 y[1] (numeric) = 1.31382433651 0.421302088642 y[1] (closed_form) = 1.31458100361 0.420786806223 absolute error = 0.0009155 relative error = 0.06632 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.57 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2978 0.536 h = 0.001 0.001 y[1] (numeric) = 1.31538877964 0.423530027363 y[1] (closed_form) = 1.31614956248 0.423013701444 absolute error = 0.0009194 relative error = 0.06651 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.5729 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1080.9MB, alloc=52.3MB, time=13.84 x[1] = -1.2968 0.537 h = 0.001 0.003 y[1] (numeric) = 1.31664629453 0.423789674038 y[1] (closed_form) = 1.31740690733 0.423272422499 absolute error = 0.0009198 relative error = 0.06647 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.5742 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2958 0.54 h = 0.0001 0.004 y[1] (numeric) = 1.31890284471 0.425562441523 y[1] (closed_form) = 1.31966663832 0.425041729074 absolute error = 0.0009244 relative error = 0.06668 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.5773 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2957 0.544 h = 0.003 0.006 y[1] (numeric) = 1.32098759866 0.428536394258 y[1] (closed_form) = 1.32175871378 0.428013927115 absolute error = 0.0009314 relative error = 0.06704 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.5811 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2927 0.55 h = 0.0001 0.005 y[1] (numeric) = 1.32628916282 0.431550058665 y[1] (closed_form) = 1.32706961737 0.431008612887 absolute error = 0.0009499 relative error = 0.06808 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.5878 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2926 0.555 h = 0.0001 0.003 y[1] (numeric) = 1.328919191 0.435256193108 y[1] (closed_form) = 1.32971110501 0.43471206467 absolute error = 0.0009608 relative error = 0.06868 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.5925 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1126.6MB, alloc=52.3MB, time=14.42 x[1] = -1.2925 0.558 h = 0.001 0.001 y[1] (numeric) = 1.33054095466 0.437456039209 y[1] (closed_form) = 1.3313369709 0.43691083719 absolute error = 0.0009648 relative error = 0.06886 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.5953 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2915 0.559 h = 0.001 0.003 y[1] (numeric) = 1.33180912094 0.437687558731 y[1] (closed_form) = 1.33260496026 0.437141433585 absolute error = 0.0009652 relative error = 0.06882 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.5966 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2905 0.562 h = 0.0001 0.004 y[1] (numeric) = 1.33411506871 0.439414719491 y[1] (closed_form) = 1.33491405852 0.438865113611 absolute error = 0.0009698 relative error = 0.06901 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.5998 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2904 0.566 h = 0.003 0.006 y[1] (numeric) = 1.33627640973 0.442351694704 y[1] (closed_form) = 1.33708269834 0.441800280683 absolute error = 0.0009768 relative error = 0.06937 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.6036 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2874 0.572 h = 0.0001 0.005 y[1] (numeric) = 1.34166774364 0.44525457025 y[1] (closed_form) = 1.34248321505 0.444684130303 absolute error = 0.0009952 relative error = 0.07037 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.6102 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1172.4MB, alloc=52.3MB, time=15.01 x[1] = -1.2873 0.577 h = 0.0001 0.003 y[1] (numeric) = 1.34439348999 0.448914668928 y[1] (closed_form) = 1.34522038534 0.44834146308 absolute error = 0.001006 relative error = 0.07096 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.615 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2872 0.58 h = 0.001 0.001 y[1] (numeric) = 1.34607228873 0.451086021243 y[1] (closed_form) = 1.34690327271 0.450511711833 absolute error = 0.00101 relative error = 0.07112 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.6178 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2862 0.581 h = 0.001 0.003 y[1] (numeric) = 1.34735087906 0.451289367598 y[1] (closed_form) = 1.34818167925 0.450714137581 absolute error = 0.001011 relative error = 0.07109 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.6191 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2852 0.584 h = 0.0001 0.004 y[1] (numeric) = 1.34970581576 0.452970602404 y[1] (closed_form) = 1.35053973604 0.452391871979 absolute error = 0.001015 relative error = 0.07127 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.6222 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2851 0.588 h = 0.003 0.006 y[1] (numeric) = 1.3519433672 0.455870062947 y[1] (closed_form) = 1.35278456338 0.455289471087 absolute error = 0.001022 relative error = 0.07161 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.626 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1218.1MB, alloc=52.3MB, time=15.59 x[1] = -1.2821 0.594 h = 0.0001 0.005 y[1] (numeric) = 1.35742351623 0.458661603295 y[1] (closed_form) = 1.35827373855 0.458061938964 absolute error = 0.00104 relative error = 0.07258 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.6327 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.282 0.599 h = 0.0001 0.003 y[1] (numeric) = 1.36024451218 0.462274993868 y[1] (closed_form) = 1.36110612267 0.461672480596 absolute error = 0.001051 relative error = 0.07315 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.6374 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2819 0.602 h = 0.001 0.001 y[1] (numeric) = 1.36198005903 0.464417452883 y[1] (closed_form) = 1.36284574445 0.463813806171 absolute error = 0.001055 relative error = 0.07331 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.6403 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2809 0.603 h = 0.001 0.003 y[1] (numeric) = 1.36326884606 0.464592581117 y[1] (closed_form) = 1.36413434085 0.463988016344 absolute error = 0.001056 relative error = 0.07327 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.6416 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2799 0.606 h = 0.0001 0.004 y[1] (numeric) = 1.36567236196 0.466227572867 y[1] (closed_form) = 1.3665409464 0.465619488166 absolute error = 0.00106 relative error = 0.07344 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.6447 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1263.8MB, alloc=52.3MB, time=16.18 x[1] = -1.2798 0.61 h = 0.003 0.006 y[1] (numeric) = 1.36798574514 0.469088983781 y[1] (closed_form) = 1.36886158234 0.468478984499 absolute error = 0.001067 relative error = 0.07377 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.6485 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2768 0.616 h = 0.0001 0.005 y[1] (numeric) = 1.37355375311 0.471768647381 y[1] (closed_form) = 1.37443845979 0.471139529827 absolute error = 0.001086 relative error = 0.07472 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.6552 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2767 0.621 h = 0.0001 0.003 y[1] (numeric) = 1.37646952753 0.475334660225 y[1] (closed_form) = 1.37736558632 0.474702610898 absolute error = 0.001097 relative error = 0.07527 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.6599 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2766 0.624 h = 0.001 0.001 y[1] (numeric) = 1.37826153399 0.477447828085 y[1] (closed_form) = 1.3791616539 0.476814615539 absolute error = 0.001101 relative error = 0.07542 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.6628 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2756 0.625 h = 0.0001 0.004 y[1] (numeric) = 1.37956029038 0.477594694305 y[1] (closed_form) = 1.38046021285 0.476960566272 absolute error = 0.001101 relative error = 0.07538 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.6641 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2755 0.629 h = 0.003 0.006 y[1] (numeric) = 1.38193910797 0.480423822319 y[1] (closed_form) = 1.38284625985 0.479787735269 absolute error = 0.001108 relative error = 0.07569 % Correct digits = 3 memory used=1309.6MB, alloc=52.3MB, time=16.76 Radius of convergence (given) for eq 1 = 0.6679 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2725 0.635 h = 0.0001 0.005 y[1] (numeric) = 1.3875833165 0.483007787183 y[1] (closed_form) = 1.3884992035 0.482352541167 absolute error = 0.001126 relative error = 0.07661 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.6745 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2724 0.64 h = 0.0001 0.003 y[1] (numeric) = 1.39058086901 0.486533606041 y[1] (closed_form) = 1.39150807785 0.485875356686 absolute error = 0.001137 relative error = 0.07715 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.6793 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2723 0.643 h = 0.001 0.001 y[1] (numeric) = 1.39242159717 0.488621911568 y[1] (closed_form) = 1.39335285553 0.487962473274 absolute error = 0.001141 relative error = 0.07729 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.6821 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2713 0.644 h = 0.001 0.003 y[1] (numeric) = 1.39372909017 0.488744531519 y[1] (closed_form) = 1.3946601452 0.488084179893 absolute error = 0.001141 relative error = 0.07725 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.6834 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2703 0.647 h = 0.0001 0.004 y[1] (numeric) = 1.39622246626 0.490293206153 y[1] (closed_form) = 1.39715655436 0.489629298317 absolute error = 0.001146 relative error = 0.07741 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.6866 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1355.3MB, alloc=52.3MB, time=17.33 x[1] = -1.2702 0.651 h = 0.003 0.006 y[1] (numeric) = 1.39867640785 0.493083291841 y[1] (closed_form) = 1.39961770578 0.492417370653 absolute error = 0.001153 relative error = 0.07771 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.6904 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2672 0.657 h = 0.0001 0.005 y[1] (numeric) = 1.40440669835 0.49555437356 y[1] (closed_form) = 1.40535657465 0.494869248989 absolute error = 0.001171 relative error = 0.07861 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.697 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2671 0.662 h = 0.0001 0.003 y[1] (numeric) = 1.40749815375 0.499031570262 y[1] (closed_form) = 1.40845931532 0.498343359908 absolute error = 0.001182 relative error = 0.07912 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.7018 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.267 0.665 h = 0.001 0.001 y[1] (numeric) = 1.40939480535 0.501089845263 y[1] (closed_form) = 1.41036000245 0.50040041637 absolute error = 0.001186 relative error = 0.07926 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.7046 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.266 0.666 h = 0.001 0.003 y[1] (numeric) = 1.41071184522 0.501184121635 y[1] (closed_form) = 1.41167683222 0.500493782035 absolute error = 0.001186 relative error = 0.07922 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.7059 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1401.2MB, alloc=52.3MB, time=17.91 x[1] = -1.265 0.669 h = 0.0001 0.004 y[1] (numeric) = 1.41325262639 0.502685652903 y[1] (closed_form) = 1.41422061583 0.501991738009 absolute error = 0.001191 relative error = 0.07937 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.7091 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2649 0.673 h = 0.003 0.006 y[1] (numeric) = 1.41578131135 0.505436166096 y[1] (closed_form) = 1.41675648693 0.504740185135 absolute error = 0.001198 relative error = 0.07966 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.7129 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2619 0.679 h = 0.0001 0.005 y[1] (numeric) = 1.42159672322 0.507793836796 y[1] (closed_form) = 1.4225803204 0.507078608777 absolute error = 0.001216 relative error = 0.08053 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.7195 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2618 0.684 h = 0.0001 0.003 y[1] (numeric) = 1.42478160305 0.511221749509 y[1] (closed_form) = 1.42577644862 0.510503353478 absolute error = 0.001227 relative error = 0.08103 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.7243 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2617 0.687 h = 0.001 0.001 y[1] (numeric) = 1.42673388526 0.513249600873 y[1] (closed_form) = 1.42773275228 0.5125299568 absolute error = 0.001231 relative error = 0.08116 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.7272 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1447.0MB, alloc=52.3MB, time=18.49 x[1] = -1.2607 0.688 h = 0.001 0.003 y[1] (numeric) = 1.4280602447 0.513315492801 y[1] (closed_form) = 1.42905889485 0.512594940673 absolute error = 0.001231 relative error = 0.08111 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.7284 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2597 0.691 h = 0.0001 0.004 y[1] (numeric) = 1.43064801723 0.51476957182 y[1] (closed_form) = 1.43164963915 0.514045425465 absolute error = 0.001236 relative error = 0.08125 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.7316 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2596 0.695 h = 0.003 0.006 y[1] (numeric) = 1.43325105899 0.517479986026 y[1] (closed_form) = 1.43425984313 0.516753721041 absolute error = 0.001243 relative error = 0.08154 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.7354 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2566 0.701 h = 0.0001 0.005 y[1] (numeric) = 1.43915063014 0.519723722622 y[1] (closed_form) = 1.44016767908 0.518978167646 absolute error = 0.001261 relative error = 0.08238 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.7421 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2565 0.706 h = 0.0001 0.003 y[1] (numeric) = 1.44242845341 0.523101692261 y[1] (closed_form) = 1.44345671359 0.52235288726 absolute error = 0.001272 relative error = 0.08286 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.7468 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1492.9MB, alloc=52.3MB, time=19.08 x[1] = -1.2564 0.709 h = 0.001 0.001 y[1] (numeric) = 1.44443607189 0.525098728546 y[1] (closed_form) = 1.44546833932 0.524348646098 absolute error = 0.001276 relative error = 0.08299 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.7497 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2554 0.71 h = 0.001 0.003 y[1] (numeric) = 1.44577152362 0.525136196223 y[1] (closed_form) = 1.44680356744 0.524385208397 absolute error = 0.001276 relative error = 0.08294 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.751 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2544 0.713 h = 0.0001 0.004 y[1] (numeric) = 1.44840587278 0.526542516246 y[1] (closed_form) = 1.44944085763 0.525787915416 absolute error = 0.001281 relative error = 0.08307 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.7541 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2543 0.717 h = 0.003 0.006 y[1] (numeric) = 1.45108288274 0.529212307182 y[1] (closed_form) = 1.45212500571 0.528455535311 absolute error = 0.001288 relative error = 0.08334 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.7579 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2513 0.723 h = 0.0001 0.005 y[1] (numeric) = 1.45706564962 0.53134159138 y[1] (closed_form) = 1.45811588055 0.530565487326 absolute error = 0.001306 relative error = 0.08416 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.7646 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1538.7MB, alloc=52.3MB, time=19.66 x[1] = -1.2512 0.728 h = 0.0001 0.003 y[1] (numeric) = 1.46043593281 0.534668961611 y[1] (closed_form) = 1.46149733753 0.533889525739 absolute error = 0.001317 relative error = 0.08463 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.7693 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2511 0.731 h = 0.001 0.001 y[1] (numeric) = 1.46249859174 0.536634793052 y[1] (closed_form) = 1.46356398941 0.535854050422 absolute error = 0.001321 relative error = 0.08475 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.7722 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2501 0.732 h = 0.0001 0.004 y[1] (numeric) = 1.4638429085 0.536643797727 y[1] (closed_form) = 1.46490807585 0.535862152423 absolute error = 0.001321 relative error = 0.0847 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.7735 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.25 0.736 h = 0.003 0.006 y[1] (numeric) = 1.46658377078 0.539279076709 y[1] (closed_form) = 1.46765605264 0.538495216514 absolute error = 0.001328 relative error = 0.08496 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.7773 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.247 0.742 h = 0.0001 0.005 y[1] (numeric) = 1.47263874872 0.5413104081 y[1] (closed_form) = 1.47371900403 0.54050717813 absolute error = 0.001346 relative error = 0.08576 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.7839 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1584.6MB, alloc=52.3MB, time=20.25 x[1] = -1.2469 0.747 h = 0.0001 0.003 y[1] (numeric) = 1.47608884254 0.544594794076 y[1] (closed_form) = 1.47718024013 0.543788161608 absolute error = 0.001357 relative error = 0.08622 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.7887 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2468 0.75 h = 0.001 0.001 y[1] (numeric) = 1.47819901844 0.546534105412 y[1] (closed_form) = 1.47929439692 0.545726140861 absolute error = 0.001361 relative error = 0.08632 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.7916 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2458 0.751 h = 0.001 0.003 y[1] (numeric) = 1.47955112363 0.546518681774 y[1] (closed_form) = 1.480646266 0.54570981682 absolute error = 0.001361 relative error = 0.08628 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.7929 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2448 0.754 h = 0.0001 0.004 y[1] (numeric) = 1.48227161119 0.547835867465 y[1] (closed_form) = 1.48336963748 0.547023354607 absolute error = 0.001366 relative error = 0.0864 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.796 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2447 0.758 h = 0.0001 0.004 y[1] (numeric) = 1.48508571617 0.550429550258 y[1] (closed_form) = 1.48619083575 0.549614768952 absolute error = 0.001373 relative error = 0.08665 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.7998 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1630.4MB, alloc=52.3MB, time=20.83 x[1] = -1.2446 0.762 h = 0.003 0.006 y[1] (numeric) = 1.48791399758 0.553018695118 y[1] (closed_form) = 1.48902621114 0.552201637583 absolute error = 0.00138 relative error = 0.0869 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.8037 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2416 0.768 h = 0.0001 0.005 y[1] (numeric) = 1.49406865116 0.554917603162 y[1] (closed_form) = 1.49518865565 0.554081122236 absolute error = 0.001398 relative error = 0.08767 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.8103 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2415 0.773 h = 0.0001 0.003 y[1] (numeric) = 1.49762802485 0.558144531049 y[1] (closed_form) = 1.49875913003 0.557304550776 absolute error = 0.001409 relative error = 0.08811 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.8151 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2414 0.776 h = 0.001 0.001 y[1] (numeric) = 1.49980327582 0.560048368731 y[1] (closed_form) = 1.50093834595 0.559207021671 absolute error = 0.001413 relative error = 0.08821 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.818 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2404 0.777 h = 0.001 0.003 y[1] (numeric) = 1.50116632002 0.559999780907 y[1] (closed_form) = 1.50230114609 0.55915753643 absolute error = 0.001413 relative error = 0.08816 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.8192 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1676.1MB, alloc=52.3MB, time=21.42 x[1] = -1.2394 0.78 h = 0.0001 0.004 y[1] (numeric) = 1.50394181215 0.561261573284 y[1] (closed_form) = 1.50507948657 0.560415658262 absolute error = 0.001418 relative error = 0.08827 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.8224 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2393 0.784 h = 0.003 0.006 y[1] (numeric) = 1.50684289901 0.563808500702 y[1] (closed_form) = 1.50798763966 0.562960255368 absolute error = 0.001425 relative error = 0.08851 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.8262 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2363 0.79 h = 0.0001 0.005 y[1] (numeric) = 1.51307784092 0.56559136587 y[1] (closed_form) = 1.51423021554 0.564723657199 absolute error = 0.001443 relative error = 0.08926 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.8328 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2362 0.795 h = 0.0001 0.003 y[1] (numeric) = 1.51672822408 0.568765696034 y[1] (closed_form) = 1.51789166101 0.567894406883 absolute error = 0.001454 relative error = 0.08969 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.8376 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2361 0.798 h = 0.001 0.001 y[1] (numeric) = 1.51895762782 0.570637141983 y[1] (closed_form) = 1.52012501508 0.569764457018 absolute error = 0.001458 relative error = 0.08978 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.8405 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1721.9MB, alloc=52.3MB, time=22.00 x[1] = -1.2351 0.799 h = 0.001 0.003 y[1] (numeric) = 1.52032884956 0.570559968918 y[1] (closed_form) = 1.5214959861 0.569686389323 absolute error = 0.001458 relative error = 0.08973 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.8418 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2341 0.802 h = 0.0001 0.004 y[1] (numeric) = 1.52314924987 0.571772766163 y[1] (closed_form) = 1.52431920381 0.570895497863 absolute error = 0.001462 relative error = 0.08984 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.8449 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.234 0.806 h = 0.003 0.006 y[1] (numeric) = 1.52612274246 0.574276958597 y[1] (closed_form) = 1.52729973765 0.573397308189 absolute error = 0.001469 relative error = 0.09007 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.8488 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.231 0.812 h = 0.0001 0.005 y[1] (numeric) = 1.53243700309 0.575943281867 y[1] (closed_form) = 1.53362147528 0.575044128912 absolute error = 0.001487 relative error = 0.09079 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.8554 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2309 0.817 h = 0.0001 0.003 y[1] (numeric) = 1.53617790201 0.579064369016 y[1] (closed_form) = 1.53737339783 0.578161554677 absolute error = 0.001498 relative error = 0.09121 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.8602 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2308 0.82 h = 0.001 0.001 y[1] (numeric) = 1.53846115666 0.580903040185 y[1] (closed_form) = 1.53966058808 0.579998801099 absolute error = 0.001502 relative error = 0.0913 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.8631 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1767.8MB, alloc=52.3MB, time=22.58 x[1] = -1.2298 0.821 h = 0.001 0.003 y[1] (numeric) = 1.53984032876 0.580797247382 y[1] (closed_form) = 1.54103950283 0.579892116479 absolute error = 0.001502 relative error = 0.09125 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.8643 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2288 0.824 h = 0.0001 0.004 y[1] (numeric) = 1.54270521745 0.58196075348 y[1] (closed_form) = 1.54390717789 0.581051915868 absolute error = 0.001507 relative error = 0.09135 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.8675 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2287 0.828 h = 0.003 0.006 y[1] (numeric) = 1.54575071705 0.584421697756 y[1] (closed_form) = 1.54695969358 0.583510426393 absolute error = 0.001514 relative error = 0.09157 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.8713 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2257 0.834 h = 0.0001 0.005 y[1] (numeric) = 1.55214332542 0.585970984902 y[1] (closed_form) = 1.55335962194 0.585040172524 absolute error = 0.001532 relative error = 0.09227 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.878 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2256 0.839 h = 0.0001 0.003 y[1] (numeric) = 1.5559742439 0.589038186528 y[1] (closed_form) = 1.55720152508 0.588103632091 absolute error = 0.001543 relative error = 0.09267 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.8827 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1813.5MB, alloc=52.3MB, time=23.17 x[1] = -1.2255 0.842 h = 0.001 0.001 y[1] (numeric) = 1.55831104615 0.590843701563 y[1] (closed_form) = 1.55954224807 0.589907693539 absolute error = 0.001547 relative error = 0.09276 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.8856 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2245 0.843 h = 0.001 0.003 y[1] (numeric) = 1.55969794149 0.590709255576 y[1] (closed_form) = 1.56092887944 0.589772358576 absolute error = 0.001547 relative error = 0.09271 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.8869 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2235 0.846 h = 0.0001 0.004 y[1] (numeric) = 1.56260689777 0.59182317666 y[1] (closed_form) = 1.56384059102 0.590882555099 absolute error = 0.001551 relative error = 0.0928 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.89 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2234 0.85 h = 0.003 0.006 y[1] (numeric) = 1.56572400371 0.594240361843 y[1] (closed_form) = 1.56696468769 0.593297255047 absolute error = 0.001558 relative error = 0.09301 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.8939 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2204 0.856 h = 0.0001 0.005 y[1] (numeric) = 1.57219398745 0.595672123438 y[1] (closed_form) = 1.57344183439 0.594709437897 absolute error = 0.001576 relative error = 0.0937 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.9005 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1859.2MB, alloc=52.3MB, time=23.76 x[1] = -1.2203 0.861 h = 0.0001 0.003 y[1] (numeric) = 1.57611442684 0.598684799825 y[1] (closed_form) = 1.57737321915 0.59771829178 absolute error = 0.001587 relative error = 0.09408 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.9053 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2202 0.864 h = 0.001 0.001 y[1] (numeric) = 1.57850447191 0.600456779067 y[1] (closed_form) = 1.57976717001 0.59948878869 absolute error = 0.001591 relative error = 0.09416 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.9082 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2192 0.865 h = 0.0001 0.004 y[1] (numeric) = 1.57989886341 0.600293647502 y[1] (closed_form) = 1.58116129095 0.599324771017 absolute error = 0.001591 relative error = 0.09411 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.9094 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2191 0.869 h = 0.003 0.006 y[1] (numeric) = 1.58307781557 0.602673603951 y[1] (closed_form) = 1.58434720974 0.601702199115 absolute error = 0.001598 relative error = 0.09432 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.9133 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2161 0.875 h = 0.0001 0.005 y[1] (numeric) = 1.58961502957 0.604004721125 y[1] (closed_form) = 1.59089145196 0.603013703785 absolute error = 0.001616 relative error = 0.09498 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.9199 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1905.0MB, alloc=52.3MB, time=24.35 x[1] = -1.216 0.88 h = 0.0001 0.003 y[1] (numeric) = 1.59361278421 0.606971012112 y[1] (closed_form) = 1.59490011886 0.605976102737 absolute error = 0.001627 relative error = 0.09536 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.9247 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2159 0.883 h = 0.001 0.001 y[1] (numeric) = 1.59604881937 0.608714451397 y[1] (closed_form) = 1.59734004719 0.607718034845 absolute error = 0.001631 relative error = 0.09543 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.9276 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2149 0.884 h = 0.001 0.003 y[1] (numeric) = 1.59744982373 0.608526688721 y[1] (closed_form) = 1.59874077528 0.607529388471 absolute error = 0.001631 relative error = 0.09538 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.9288 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2139 0.887 h = 0.0001 0.004 y[1] (numeric) = 1.60044025511 0.609548081935 y[1] (closed_form) = 1.60173390421 0.608547023947 absolute error = 0.001636 relative error = 0.09547 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.932 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2138 0.891 h = 0.003 0.006 y[1] (numeric) = 1.6036900662 0.611883331092 y[1] (closed_form) = 1.60499065888 0.61087969218 absolute error = 0.001643 relative error = 0.09566 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.9358 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1950.7MB, alloc=52.3MB, time=24.93 x[1] = -1.2108 0.897 h = 0.0001 0.005 y[1] (numeric) = 1.61030284829 0.613096013165 y[1] (closed_form) = 1.61161031211 0.612072725391 absolute error = 0.00166 relative error = 0.09631 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.9425 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2107 0.902 h = 0.0001 0.003 y[1] (numeric) = 1.61438919699 0.616006589985 y[1] (closed_form) = 1.61570753322 0.614979330161 absolute error = 0.001671 relative error = 0.09668 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.9473 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2106 0.905 h = 0.001 0.001 y[1] (numeric) = 1.61687790849 0.617715787873 y[1] (closed_form) = 1.61820012272 0.616686992302 absolute error = 0.001675 relative error = 0.09674 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.9501 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2096 0.906 h = 0.001 0.003 y[1] (numeric) = 1.61828598696 0.617499279435 y[1] (closed_form) = 1.61960791836 0.616469603083 absolute error = 0.001676 relative error = 0.09669 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.9514 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2086 0.909 h = 0.0001 0.004 y[1] (numeric) = 1.62131928031 0.618470253767 y[1] (closed_form) = 1.62264387803 0.617436802268 absolute error = 0.00168 relative error = 0.09677 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.9546 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1996.2MB, alloc=52.3MB, time=25.52 x[1] = -1.2085 0.913 h = 0.003 0.006 y[1] (numeric) = 1.62463954676 0.620760289731 y[1] (closed_form) = 1.6259710621 0.619724206272 absolute error = 0.001687 relative error = 0.09696 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.9584 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2055 0.919 h = 0.0001 0.005 y[1] (numeric) = 1.63132692065 0.621854060998 y[1] (closed_form) = 1.63266515004 0.620798293057 absolute error = 0.001705 relative error = 0.09759 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.965 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2054 0.924 h = 0.0001 0.003 y[1] (numeric) = 1.63550135776 0.624708291919 y[1] (closed_form) = 1.63685041938 0.623648472147 absolute error = 0.001716 relative error = 0.09794 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.9698 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2053 0.927 h = 0.001 0.001 y[1] (numeric) = 1.63804243667 0.626382873605 y[1] (closed_form) = 1.63939536103 0.625321489611 absolute error = 0.00172 relative error = 0.098 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.9727 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2043 0.928 h = 0.001 0.003 y[1] (numeric) = 1.6394573623 0.626137590015 y[1] (closed_form) = 1.6408099973 0.625075328184 absolute error = 0.00172 relative error = 0.09795 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.974 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2041.8MB, alloc=52.3MB, time=26.10 x[1] = -1.2033 0.931 h = 0.0001 0.004 y[1] (numeric) = 1.64253309315 0.627057859889 y[1] (closed_form) = 1.64388836318 0.625991805655 absolute error = 0.001724 relative error = 0.09803 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.9771 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2032 0.935 h = 0.003 0.006 y[1] (numeric) = 1.64592340677 0.629302180397 y[1] (closed_form) = 1.64728556826 0.628233443326 absolute error = 0.001731 relative error = 0.09821 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.981 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2002 0.941 h = 0.0001 0.005 y[1] (numeric) = 1.65268439487 0.630276569956 y[1] (closed_form) = 1.6540531133 0.62918811352 absolute error = 0.001749 relative error = 0.09882 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.9876 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2001 0.946 h = 0.0001 0.003 y[1] (numeric) = 1.65694641228 0.633073826057 y[1] (closed_form) = 1.65832592246 0.631981238248 absolute error = 0.00176 relative error = 0.09916 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.9924 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2 0.949 h = 0.001 0.001 y[1] (numeric) = 1.65953954827 0.634713418444 y[1] (closed_form) = 1.66092290581 0.633619238032 absolute error = 0.001764 relative error = 0.09922 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.9953 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2087.4MB, alloc=52.3MB, time=26.68 x[1] = -1.199 0.95 h = 0.001 0.003 y[1] (numeric) = 1.66096109419 0.634439331361 y[1] (closed_form) = 1.66234415584 0.633344276081 absolute error = 0.001764 relative error = 0.09917 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.9965 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.198 0.953 h = 0.0001 0.004 y[1] (numeric) = 1.66407883713 0.635308613355 y[1] (closed_form) = 1.66546450249 0.634209748574 absolute error = 0.001768 relative error = 0.09923 % Correct digits = 3 Radius of convergence (given) for eq 1 = 0.9997 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1979 0.957 h = 0.003 0.006 y[1] (numeric) = 1.66753878781 0.637506718408 y[1] (closed_form) = 1.66893131826 0.636405120072 absolute error = 0.001776 relative error = 0.09941 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.004 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1949 0.963 h = 0.0001 0.005 y[1] (numeric) = 1.6743724112 0.638361260161 y[1] (closed_form) = 1.67577134146 0.637239908313 absolute error = 0.001793 relative error = 0.1 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.01 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1948 0.968 h = 0.0001 0.003 y[1] (numeric) = 1.67872149843 0.641100915343 y[1] (closed_form) = 1.68013117965 0.639975352816 absolute error = 0.001804 relative error = 0.1003 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.015 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2132.8MB, alloc=52.3MB, time=27.26 x[1] = -1.1947 0.971 h = 0.001 0.001 y[1] (numeric) = 1.68136637971 0.642705147047 y[1] (closed_form) = 1.68277989281 0.641577963632 absolute error = 0.001808 relative error = 0.1004 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.018 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1937 0.972 h = 0.0001 0.004 y[1] (numeric) = 1.6827943191 0.642402229176 y[1] (closed_form) = 1.6842075298 0.64127417389 absolute error = 0.001808 relative error = 0.1003 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.019 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1936 0.976 h = 0.003 0.006 y[1] (numeric) = 1.68631444209 0.644560976347 y[1] (closed_form) = 1.68773449328 0.643430144996 absolute error = 0.001815 relative error = 0.1005 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.023 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1906 0.982 h = 0.0001 0.005 y[1] (numeric) = 1.69321123775 0.645312836876 y[1] (closed_form) = 1.69463755388 0.644162221336 absolute error = 0.001833 relative error = 0.1011 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.03 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1905 0.987 h = 0.0001 0.003 y[1] (numeric) = 1.69763555738 0.648003440751 y[1] (closed_form) = 1.69907259006 0.646848545971 absolute error = 0.001844 relative error = 0.1014 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.034 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2178.3MB, alloc=52.3MB, time=27.85 x[1] = -1.1904 0.99 h = 0.001 0.001 y[1] (numeric) = 1.70032515576 0.649577550383 y[1] (closed_form) = 1.70176600724 0.648421010257 absolute error = 0.001848 relative error = 0.1015 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.037 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1894 0.991 h = 0.001 0.003 y[1] (numeric) = 1.7017587607 0.649249867357 y[1] (closed_form) = 1.70319930416 0.648092457882 absolute error = 0.001848 relative error = 0.1014 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.039 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1884 0.994 h = 0.0001 0.004 y[1] (numeric) = 1.7049541582 0.650024014295 y[1] (closed_form) = 1.70639724713 0.648862763539 absolute error = 0.001852 relative error = 0.1015 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.042 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1883 0.998 h = 0.003 0.006 y[1] (numeric) = 1.70854315358 0.652135618063 y[1] (closed_form) = 1.7099930586 0.650971539487 absolute error = 0.001859 relative error = 0.1016 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.046 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1853 1.004 h = 0.0001 0.005 y[1] (numeric) = 1.71551076504 0.652766764583 y[1] (closed_form) = 1.71696677782 0.65158286904 absolute error = 0.001877 relative error = 0.1022 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.052 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2223.8MB, alloc=52.3MB, time=28.42 x[1] = -1.1852 1.009 h = 0.0001 0.003 y[1] (numeric) = 1.72002120557 0.655398603884 y[1] (closed_form) = 1.72148789354 0.65421035024 absolute error = 0.001888 relative error = 0.1025 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.057 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1851 1.012 h = 0.001 0.001 y[1] (numeric) = 1.72276196972 0.65693666259 y[1] (closed_form) = 1.7242324608 0.655746735489 absolute error = 0.001892 relative error = 0.1025 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.06 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1841 1.013 h = 0.001 0.003 y[1] (numeric) = 1.72420154654 0.656580098072 y[1] (closed_form) = 1.72567172314 0.655389304667 absolute error = 0.001892 relative error = 0.1025 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.061 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1831 1.016 h = 0.0001 0.004 y[1] (numeric) = 1.72743773738 0.657302453137 y[1] (closed_form) = 1.72891042796 0.656107801795 absolute error = 0.001896 relative error = 0.1025 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.064 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.183 1.02 h = 0.003 0.006 y[1] (numeric) = 1.7310951919 0.659366418645 y[1] (closed_form) = 1.73257467163 0.658168889224 absolute error = 0.001903 relative error = 0.1027 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.068 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2269.4MB, alloc=52.3MB, time=28.98 x[1] = -1.18 1.026 h = 0.0001 0.005 y[1] (numeric) = 1.73813263655 0.659876398794 y[1] (closed_form) = 1.73961806686 0.658659020362 absolute error = 0.001921 relative error = 0.1032 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.075 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1799 1.031 h = 0.0001 0.003 y[1] (numeric) = 1.74272868061 0.662448855488 y[1] (closed_form) = 1.74422474443 0.661227040335 absolute error = 0.001932 relative error = 0.1036 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.08 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1798 1.034 h = 0.001 0.001 y[1] (numeric) = 1.74552029472 0.663950496785 y[1] (closed_form) = 1.74702014585 0.66272698016 absolute error = 0.001936 relative error = 0.1036 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.082 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1788 1.035 h = 0.001 0.003 y[1] (numeric) = 1.74696561677 0.663565026472 y[1] (closed_form) = 1.74846514698 0.662340646615 absolute error = 0.001936 relative error = 0.1035 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.084 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1778 1.038 h = 0.0001 0.004 y[1] (numeric) = 1.75024217199 0.664235314565 y[1] (closed_form) = 1.75174418466 0.663007060271 absolute error = 0.00194 relative error = 0.1036 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.087 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1777 1.042 h = 0.003 0.006 y[1] (numeric) = 1.75396766819 0.666251150573 y[1] (closed_form) = 1.75547644284 0.6650199681 absolute error = 0.001947 relative error = 0.1037 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.091 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2315.0MB, alloc=52.3MB, time=29.55 x[1] = -1.1747 1.048 h = 0.0001 0.005 y[1] (numeric) = 1.76107396218 0.666639516798 y[1] (closed_form) = 1.76258853024 0.665388454006 absolute error = 0.001964 relative error = 0.1043 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.097 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1746 1.053 h = 0.0001 0.003 y[1] (numeric) = 1.76575509004 0.669151975692 y[1] (closed_form) = 1.76728024962 0.667896397803 absolute error = 0.001975 relative error = 0.1046 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.102 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1745 1.056 h = 0.001 0.001 y[1] (numeric) = 1.76859723688 0.670616834822 y[1] (closed_form) = 1.77012616786 0.669359527542 absolute error = 0.00198 relative error = 0.1046 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.105 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1735 1.057 h = 0.001 0.003 y[1] (numeric) = 1.7700480776 0.670202435455 y[1] (closed_form) = 1.77157668123 0.668944268041 absolute error = 0.00198 relative error = 0.1045 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.106 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1725 1.06 h = 0.0001 0.004 y[1] (numeric) = 1.77336456737 0.670820383639 y[1] (closed_form) = 1.77489562189 0.669558325442 absolute error = 0.001984 relative error = 0.1046 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.109 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2360.5MB, alloc=52.3MB, time=30.12 x[1] = -1.1724 1.064 h = 0.003 0.006 y[1] (numeric) = 1.77715768587 0.672787601191 y[1] (closed_form) = 1.77869547501 0.67152256488 absolute error = 0.001991 relative error = 0.1047 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.113 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1694 1.07 h = 0.0001 0.005 y[1] (numeric) = 1.78433184415 0.673053910746 y[1] (closed_form) = 1.7858752695 0.671768963542 absolute error = 0.002008 relative error = 0.1053 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.12 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1693 1.075 h = 0.0001 0.003 y[1] (numeric) = 1.78909753372 0.675505759495 y[1] (closed_form) = 1.7906515083 0.674216219063 absolute error = 0.002019 relative error = 0.1055 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.125 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1692 1.078 h = 0.001 0.001 y[1] (numeric) = 1.79198989467 0.676933473431 y[1] (closed_form) = 1.79354762464 0.675642175782 absolute error = 0.002023 relative error = 0.1056 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.128 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1682 1.079 h = 0.0001 0.004 y[1] (numeric) = 1.79344602757 0.676490122793 y[1] (closed_form) = 1.79500342378 0.675197968135 absolute error = 0.002024 relative error = 0.1055 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.129 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2405.9MB, alloc=52.3MB, time=30.84 x[1] = -1.1681 1.083 h = 0.003 0.006 y[1] (numeric) = 1.79729760493 0.678415898794 y[1] (closed_form) = 1.7988617106 0.677120724134 absolute error = 0.002031 relative error = 0.1057 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.133 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1651 1.089 h = 0.0001 0.005 y[1] (numeric) = 1.80453084983 0.67857758758 y[1] (closed_form) = 1.80610045674 0.677262474424 absolute error = 0.002048 relative error = 0.1062 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.139 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.165 1.094 h = 0.0001 0.003 y[1] (numeric) = 1.80936963927 0.680977775755 y[1] (closed_form) = 1.81094975969 0.679658001807 absolute error = 0.002059 relative error = 0.1064 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.144 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1649 1.097 h = 0.001 0.001 y[1] (numeric) = 1.81230541498 0.682373819923 y[1] (closed_form) = 1.81388927725 0.681052264693 absolute error = 0.002063 relative error = 0.1065 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.147 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1639 1.098 h = 0.001 0.003 y[1] (numeric) = 1.81376626713 0.681905591373 y[1] (closed_form) = 1.8153497901 0.680583181767 absolute error = 0.002063 relative error = 0.1064 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.148 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2451.5MB, alloc=52.3MB, time=31.45 x[1] = -1.1629 1.101 h = 0.0001 0.004 y[1] (numeric) = 1.81715654973 0.682425891747 y[1] (closed_form) = 1.81874246489 0.68109956098 absolute error = 0.002067 relative error = 0.1065 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.151 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1628 1.105 h = 0.003 0.006 y[1] (numeric) = 1.8210749678 0.684302141806 y[1] (closed_form) = 1.82266756674 0.682972740108 absolute error = 0.002075 relative error = 0.1066 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.155 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1598 1.111 h = 0.0001 0.005 y[1] (numeric) = 1.82837424595 0.684340951111 y[1] (closed_form) = 1.82997218892 0.68299158171 absolute error = 0.002091 relative error = 0.1071 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.162 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1597 1.116 h = 0.0001 0.003 y[1] (numeric) = 1.83329662657 0.686679391021 y[1] (closed_form) = 1.83490504018 0.685325283151 absolute error = 0.002103 relative error = 0.1073 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.167 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1596 1.119 h = 0.001 0.001 y[1] (numeric) = 1.83628202412 0.688037615261 y[1] (closed_form) = 1.83789416335 0.686681698461 absolute error = 0.002107 relative error = 0.1074 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.17 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2497.2MB, alloc=52.3MB, time=32.22 x[1] = -1.1586 1.12 h = 0.001 0.003 y[1] (numeric) = 1.83774774747 0.687540394178 y[1] (closed_form) = 1.83935954104 0.686183626174 absolute error = 0.002107 relative error = 0.1073 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.171 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1576 1.123 h = 0.0001 0.004 y[1] (numeric) = 1.84117673323 0.688007580629 y[1] (closed_form) = 1.84279088727 0.686646875564 absolute error = 0.002111 relative error = 0.1074 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.174 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1575 1.127 h = 0.003 0.006 y[1] (numeric) = 1.84516156933 0.689833821038 y[1] (closed_form) = 1.84678237922 0.688469995572 absolute error = 0.002118 relative error = 0.1075 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.178 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1545 1.133 h = 0.0001 0.005 y[1] (numeric) = 1.85252589221 0.689749321865 y[1] (closed_form) = 1.85415188892 0.68836550022 absolute error = 0.002135 relative error = 0.108 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.185 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1544 1.138 h = 0.0001 0.003 y[1] (numeric) = 1.85753133519 0.692025409313 y[1] (closed_form) = 1.85916775935 0.69063677177 absolute error = 0.002146 relative error = 0.1082 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.189 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2542.7MB, alloc=52.3MB, time=32.82 x[1] = -1.1543 1.141 h = 0.001 0.001 y[1] (numeric) = 1.860566032 0.693345455544 y[1] (closed_form) = 1.86220616546 0.69195498152 absolute error = 0.00215 relative error = 0.1082 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.192 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1533 1.142 h = 0.001 0.003 y[1] (numeric) = 1.86203640029 0.69281922269 y[1] (closed_form) = 1.86367618173 0.691427900662 absolute error = 0.002151 relative error = 0.1082 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.193 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1523 1.145 h = 0.0001 0.004 y[1] (numeric) = 1.86550365595 0.693233030632 y[1] (closed_form) = 1.86714576611 0.691837755797 absolute error = 0.002155 relative error = 0.1082 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.197 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1522 1.149 h = 0.003 0.006 y[1] (numeric) = 1.86955448352 0.69500878128 y[1] (closed_form) = 1.87120322139 0.693610336738 absolute error = 0.002162 relative error = 0.1083 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.2 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1492 1.155 h = 0.0001 0.005 y[1] (numeric) = 1.87698286144 0.694800549442 y[1] (closed_form) = 1.87863662891 0.693382080979 absolute error = 0.002179 relative error = 0.1088 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.207 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2588.2MB, alloc=52.3MB, time=33.40 x[1] = -1.1491 1.16 h = 0.0001 0.003 y[1] (numeric) = 1.88207083565 0.697013683099 y[1] (closed_form) = 1.88373498709 0.695590321559 absolute error = 0.00219 relative error = 0.1091 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.212 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.149 1.163 h = 0.001 0.001 y[1] (numeric) = 1.88515450776 0.698295194981 y[1] (closed_form) = 1.88682235206 0.696869969505 absolute error = 0.002194 relative error = 0.1091 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.215 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.148 1.164 h = 0.001 0.003 y[1] (numeric) = 1.88662929483 0.69773993216 y[1] (closed_form) = 1.88829678078 0.696313861904 absolute error = 0.002194 relative error = 0.109 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.216 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.147 1.167 h = 0.0001 0.004 y[1] (numeric) = 1.89013438629 0.698100099173 y[1] (closed_form) = 1.89180416914 0.696670060521 absolute error = 0.002198 relative error = 0.109 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.219 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1469 1.171 h = 0.003 0.006 y[1] (numeric) = 1.89425077692 0.699824882256 y[1] (closed_form) = 1.89592715916 0.698391624757 absolute error = 0.002206 relative error = 0.1092 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.223 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2633.8MB, alloc=52.3MB, time=33.99 x[1] = -1.1439 1.177 h = 0.0001 0.005 y[1] (numeric) = 1.90174221903 0.699492498381 y[1] (closed_form) = 1.90342347366 0.69803918995 absolute error = 0.002222 relative error = 0.1096 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.23 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1438 1.182 h = 0.0001 0.003 y[1] (numeric) = 1.90691219103 0.701642079793 y[1] (closed_form) = 1.90860378583 0.700183801356 absolute error = 0.002233 relative error = 0.1099 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.235 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1437 1.185 h = 0.001 0.001 y[1] (numeric) = 1.91004451313 0.702884702732 y[1] (closed_form) = 1.91173978425 0.701424533 absolute error = 0.002237 relative error = 0.1099 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.237 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1427 1.186 h = 0.0001 0.004 y[1] (numeric) = 1.91152349291 0.702300392782 y[1] (closed_form) = 1.91321839937 0.700839381522 absolute error = 0.002238 relative error = 0.1098 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.239 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1426 1.19 h = 0.003 0.006 y[1] (numeric) = 1.91569659022 0.70398169659 y[1] (closed_form) = 1.91739807029 0.702517425231 absolute error = 0.002245 relative error = 0.1099 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.243 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2679.3MB, alloc=52.3MB, time=34.58 x[1] = -1.1396 1.196 h = 0.0001 0.005 y[1] (numeric) = 1.9232430072 0.703542849769 y[1] (closed_form) = 1.92494922465 0.702058502942 absolute error = 0.002262 relative error = 0.1104 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.249 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1395 1.201 h = 0.0001 0.003 y[1] (numeric) = 1.92848389791 0.705638218566 y[1] (closed_form) = 1.9302004185 0.704148835191 absolute error = 0.002273 relative error = 0.1106 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.254 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1394 1.204 h = 0.001 0.001 y[1] (numeric) = 1.93165830374 0.706847658803 y[1] (closed_form) = 1.93337848664 0.705356360462 absolute error = 0.002277 relative error = 0.1106 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.257 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1384 1.205 h = 0.001 0.003 y[1] (numeric) = 1.93314105776 0.706238379386 y[1] (closed_form) = 1.93486087055 0.70474624226 absolute error = 0.002277 relative error = 0.1106 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.258 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1374 1.208 h = 0.0001 0.004 y[1] (numeric) = 1.93671604074 0.706498480594 y[1] (closed_form) = 1.93843809131 0.705002346099 absolute error = 0.002281 relative error = 0.1106 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.261 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2724.9MB, alloc=52.3MB, time=35.15 x[1] = -1.1373 1.212 h = 0.003 0.006 y[1] (numeric) = 1.9409539029 0.708127930014 y[1] (closed_form) = 1.94268250019 0.70662848533 absolute error = 0.002288 relative error = 0.1107 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.265 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1343 1.218 h = 0.0001 0.005 y[1] (numeric) = 1.94856154224 0.707564151775 y[1] (closed_form) = 1.95029471968 0.706044605974 absolute error = 0.002305 relative error = 0.1111 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.272 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1342 1.223 h = 0.0001 0.003 y[1] (numeric) = 1.95388343906 0.709594855993 y[1] (closed_form) = 1.95562687529 0.708070197181 absolute error = 0.002316 relative error = 0.1114 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.277 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1341 1.226 h = 0.001 0.001 y[1] (numeric) = 1.95710589013 0.71076474821 y[1] (closed_form) = 1.95885297192 0.709238147253 absolute error = 0.00232 relative error = 0.1114 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.279 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1331 1.227 h = 0.001 0.003 y[1] (numeric) = 1.95859241663 0.710126389805 y[1] (closed_form) = 1.96033912203 0.708598953362 absolute error = 0.00232 relative error = 0.1113 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.281 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2770.3MB, alloc=52.3MB, time=35.72 x[1] = -1.1321 1.23 h = 0.0001 0.004 y[1] (numeric) = 1.96220399189 0.71033210615 y[1] (closed_form) = 1.96395290313 0.708800657193 absolute error = 0.002325 relative error = 0.1113 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.284 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.132 1.234 h = 0.003 0.006 y[1] (numeric) = 1.96650618706 0.711909228726 y[1] (closed_form) = 1.96826161612 0.710374420913 absolute error = 0.002332 relative error = 0.1114 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.288 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.129 1.24 h = 0.0001 0.005 y[1] (numeric) = 1.97417405467 0.711220113452 y[1] (closed_form) = 1.97593390668 0.709665179604 absolute error = 0.002348 relative error = 0.1119 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.294 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1289 1.245 h = 0.0001 0.003 y[1] (numeric) = 1.97957641759 0.713185562862 y[1] (closed_form) = 1.9813464837 0.711625439794 absolute error = 0.002359 relative error = 0.1121 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.299 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1288 1.248 h = 0.001 0.001 y[1] (numeric) = 1.98284658471 0.71431555746 y[1] (closed_form) = 1.98462027953 0.712753465163 absolute error = 0.002363 relative error = 0.1121 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.302 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2815.8MB, alloc=52.3MB, time=36.30 x[1] = -1.1278 1.249 h = 0.001 0.003 y[1] (numeric) = 1.98433665788 0.713648105872 y[1] (closed_form) = 1.98610997007 0.712085181414 absolute error = 0.002364 relative error = 0.112 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.303 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1268 1.252 h = 0.0001 0.004 y[1] (numeric) = 1.98798438805 0.713799183309 y[1] (closed_form) = 1.98975987409 0.71223223135 absolute error = 0.002368 relative error = 0.1121 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.306 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1267 1.256 h = 0.003 0.006 y[1] (numeric) = 1.99235048078 0.715323510167 y[1] (closed_form) = 1.99413245553 0.713753150851 absolute error = 0.002375 relative error = 0.1121 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.31 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1237 1.262 h = 0.0001 0.005 y[1] (numeric) = 2.00007758149 0.714508657055 y[1] (closed_form) = 2.00186382201 0.712918147517 absolute error = 0.002392 relative error = 0.1126 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.317 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1236 1.267 h = 0.0001 0.003 y[1] (numeric) = 2.00555986822 0.716408264326 y[1] (closed_form) = 2.00735627786 0.714812489613 absolute error = 0.002403 relative error = 0.1128 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.322 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2861.3MB, alloc=52.3MB, time=36.88 x[1] = -1.1235 1.27 h = 0.001 0.001 y[1] (numeric) = 2.00887742087 0.717498013458 y[1] (closed_form) = 2.01067744226 0.715900242531 absolute error = 0.002407 relative error = 0.1128 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.325 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1225 1.271 h = 0.001 0.003 y[1] (numeric) = 2.01037081503 0.71680145553 y[1] (closed_form) = 2.01217044755 0.715202855791 absolute error = 0.002407 relative error = 0.1127 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.326 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1215 1.274 h = 0.0001 0.004 y[1] (numeric) = 2.0140542619 0.716897642192 y[1] (closed_form) = 2.01585603625 0.715295000121 absolute error = 0.002411 relative error = 0.1127 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.329 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1214 1.278 h = 0.003 0.006 y[1] (numeric) = 2.01848381494 0.718368706783 y[1] (closed_form) = 2.0202920487 0.716762609022 absolute error = 0.002419 relative error = 0.1128 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.333 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1184 1.284 h = 0.0001 0.005 y[1] (numeric) = 2.02626915253 0.717427719845 y[1] (closed_form) = 2.02808149487 0.715801448406 absolute error = 0.002435 relative error = 0.1132 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.34 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2906.8MB, alloc=52.3MB, time=37.47 x[1] = -1.1183 1.289 h = 0.0001 0.003 y[1] (numeric) = 2.03183081853 0.719260900546 y[1] (closed_form) = 2.03365328472 0.717629288233 absolute error = 0.002446 relative error = 0.1134 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.344 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1182 1.292 h = 0.001 0.001 y[1] (numeric) = 2.03519542486 0.720310058129 y[1] (closed_form) = 2.03702148573 0.718676422714 absolute error = 0.00245 relative error = 0.1134 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.347 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1172 1.293 h = 0.0001 0.004 y[1] (numeric) = 2.03669191441 0.719584381733 y[1] (closed_form) = 2.0385175802 0.717949920882 absolute error = 0.00245 relative error = 0.1134 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.348 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1171 1.297 h = 0.003 0.006 y[1] (numeric) = 2.04117638405 0.721009975721 y[1] (closed_form) = 2.04300848285 0.719372018579 absolute error = 0.002458 relative error = 0.1135 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.352 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1141 1.303 h = 0.0001 0.005 y[1] (numeric) = 2.04901256028 0.71996078112 y[1] (closed_form) = 2.05084863263 0.71830262882 absolute error = 0.002474 relative error = 0.1139 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.359 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.114 1.308 h = 0.0001 0.003 y[1] (numeric) = 2.05464291624 0.721737254961 y[1] (closed_form) = 2.05648907411 0.720073696289 absolute error = 0.002485 relative error = 0.1141 % Correct digits = 3 memory used=2952.3MB, alloc=52.3MB, time=38.06 Radius of convergence (given) for eq 1 = 1.364 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1139 1.311 h = 0.001 0.001 y[1] (numeric) = 2.05804824716 0.722751752002 y[1] (closed_form) = 2.05989798525 0.721086146958 absolute error = 0.002489 relative error = 0.1141 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.367 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1129 1.312 h = 0.001 0.003 y[1] (numeric) = 2.0595475676 0.722001035697 y[1] (closed_form) = 2.06139690525 0.720334608068 absolute error = 0.002489 relative error = 0.114 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.368 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1119 1.315 h = 0.0001 0.004 y[1] (numeric) = 2.06329696672 0.721994833629 y[1] (closed_form) = 2.06514838664 0.720324336103 absolute error = 0.002494 relative error = 0.114 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.371 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1118 1.319 h = 0.003 0.006 y[1] (numeric) = 2.06784408217 0.723366299387 y[1] (closed_form) = 2.06970190705 0.72169225633 absolute error = 0.002501 relative error = 0.1141 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.375 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1088 1.325 h = 0.0001 0.005 y[1] (numeric) = 2.07573664332 0.722190235039 y[1] (closed_form) = 2.07759828459 0.720495974725 absolute error = 0.002517 relative error = 0.1145 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.382 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2997.9MB, alloc=52.3MB, time=38.64 x[1] = -1.1087 1.33 h = 0.0001 0.003 y[1] (numeric) = 2.0814453662 0.72389919601 y[1] (closed_form) = 2.08331704714 0.722199454099 absolute error = 0.002528 relative error = 0.1147 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.386 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1086 1.333 h = 0.001 0.001 y[1] (numeric) = 2.08489713385 0.724872458226 y[1] (closed_form) = 2.08677237774 0.723170643236 absolute error = 0.002532 relative error = 0.1147 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.389 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1076 1.334 h = 0.001 0.003 y[1] (numeric) = 2.08639913036 0.724092600953 y[1] (closed_form) = 2.08827396763 0.722389966802 absolute error = 0.002533 relative error = 0.1146 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.391 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1066 1.337 h = 0.0001 0.004 y[1] (numeric) = 2.09018299104 0.724030794345 y[1] (closed_form) = 2.09205987844 0.722324075911 absolute error = 0.002537 relative error = 0.1146 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.394 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1065 1.341 h = 0.003 0.006 y[1] (numeric) = 2.09479231155 0.725347670772 y[1] (closed_form) = 2.09667557404 0.723637358955 absolute error = 0.002544 relative error = 0.1147 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.398 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3043.4MB, alloc=52.3MB, time=39.23 x[1] = -1.1035 1.347 h = 0.0001 0.005 y[1] (numeric) = 2.10274025837 0.724044354452 y[1] (closed_form) = 2.10462718011 0.722313804008 absolute error = 0.00256 relative error = 0.1151 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.404 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1034 1.352 h = 0.0001 0.003 y[1] (numeric) = 2.10852679721 0.725685226424 y[1] (closed_form) = 2.11042371246 0.723949119417 absolute error = 0.002571 relative error = 0.1153 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.409 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1033 1.355 h = 0.001 0.001 y[1] (numeric) = 2.11202466595 0.726616912769 y[1] (closed_form) = 2.11392512679 0.724878706074 absolute error = 0.002575 relative error = 0.1152 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.412 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1023 1.356 h = 0.001 0.003 y[1] (numeric) = 2.11352911326 0.725807905355 y[1] (closed_form) = 2.11542916131 0.724068882948 absolute error = 0.002576 relative error = 0.1152 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.413 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1013 1.359 h = 0.0001 0.004 y[1] (numeric) = 2.11734699419 0.725690250739 y[1] (closed_form) = 2.11924906017 0.72394712982 absolute error = 0.00258 relative error = 0.1152 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.416 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3089.0MB, alloc=52.3MB, time=39.81 x[1] = -1.1012 1.363 h = 0.003 0.006 y[1] (numeric) = 2.12201807561 0.726952080295 y[1] (closed_form) = 2.12392648665 0.725205318312 absolute error = 0.002587 relative error = 0.1153 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.42 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0982 1.369 h = 0.0001 0.005 y[1] (numeric) = 2.13002040784 0.725521134595 y[1] (closed_form) = 2.131932321 0.723754113341 absolute error = 0.002603 relative error = 0.1156 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.427 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0981 1.374 h = 0.0001 0.003 y[1] (numeric) = 2.13588420945 0.727093344361 y[1] (closed_form) = 2.13780606967 0.725320691839 absolute error = 0.002615 relative error = 0.1158 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.432 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.098 1.377 h = 0.001 0.001 y[1] (numeric) = 2.13942784235 0.72798311556 y[1] (closed_form) = 2.14135323066 0.72620833684 absolute error = 0.002619 relative error = 0.1158 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.434 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.097 1.378 h = 0.001 0.003 y[1] (numeric) = 2.14093451531 0.727144949862 y[1] (closed_form) = 2.14285948471 0.725369358903 absolute error = 0.002619 relative error = 0.1158 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.436 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3134.6MB, alloc=52.3MB, time=40.41 x[1] = -1.096 1.381 h = 0.0001 0.004 y[1] (numeric) = 2.14478597438 0.72697120595 y[1] (closed_form) = 2.14671292948 0.725191502406 absolute error = 0.002623 relative error = 0.1158 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.439 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0959 1.385 h = 0.003 0.006 y[1] (numeric) = 2.14951837083 0.728177533447 y[1] (closed_form) = 2.15145164073 0.726394141328 absolute error = 0.00263 relative error = 0.1158 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.443 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0929 1.391 h = 0.0001 0.005 y[1] (numeric) = 2.15757408723 0.726618585775 y[1] (closed_form) = 2.15951070215 0.72481491447 absolute error = 0.002646 relative error = 0.1162 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.449 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0928 1.396 h = 0.0001 0.003 y[1] (numeric) = 2.16351459623 0.728121563055 y[1] (closed_form) = 2.16546111145 0.726312186036 absolute error = 0.002658 relative error = 0.1164 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.454 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0927 1.399 h = 0.001 0.001 y[1] (numeric) = 2.16710365503 0.728969081609 y[1] (closed_form) = 2.16905368076 0.727157551982 absolute error = 0.002662 relative error = 0.1163 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.457 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3180.1MB, alloc=52.3MB, time=41.00 x[1] = -1.0917 1.4 h = 0.003 0.006 y[1] (numeric) = 2.16861232863 0.728101750511 y[1] (closed_form) = 2.17056192933 0.726289412143 absolute error = 0.002662 relative error = 0.1163 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.458 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0887 1.406 h = 0.0001 0.005 y[1] (numeric) = 2.17670095503 0.726453220355 y[1] (closed_form) = 2.17865378756 0.7246205966 absolute error = 0.002678 relative error = 0.1166 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.465 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0886 1.411 h = 0.0001 0.003 y[1] (numeric) = 2.18269214565 0.727906328512 y[1] (closed_form) = 2.18465484428 0.726067949173 absolute error = 0.002689 relative error = 0.1168 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.47 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0885 1.414 h = 0.001 0.001 y[1] (numeric) = 2.18631118098 0.728723452971 y[1] (closed_form) = 2.1882773773 0.726882903358 absolute error = 0.002693 relative error = 0.1168 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.473 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0875 1.415 h = 0.001 0.003 y[1] (numeric) = 2.18782036542 0.727836012112 y[1] (closed_form) = 2.18978613261 0.725994656334 absolute error = 0.002693 relative error = 0.1168 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.474 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3225.7MB, alloc=52.3MB, time=41.58 x[1] = -1.0865 1.418 h = 0.0001 0.004 y[1] (numeric) = 2.19172606964 0.727566233203 y[1] (closed_form) = 2.19369376767 0.725720742256 absolute error = 0.002698 relative error = 0.1168 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.477 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0864 1.422 h = 0.003 0.006 y[1] (numeric) = 2.19655951969 0.728676333793 y[1] (closed_form) = 2.19853347985 0.726827075237 absolute error = 0.002705 relative error = 0.1168 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.481 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0834 1.428 h = 0.0001 0.005 y[1] (numeric) = 2.2046998243 0.726899212089 y[1] (closed_form) = 2.2066768639 0.725029646339 absolute error = 0.002721 relative error = 0.1171 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.488 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0833 1.433 h = 0.0001 0.003 y[1] (numeric) = 2.21076676571 0.728282145957 y[1] (closed_form) = 2.21275362415 0.726406750626 absolute error = 0.002732 relative error = 0.1173 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.492 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0832 1.436 h = 0.001 0.001 y[1] (numeric) = 2.2144306447 0.729056460739 y[1] (closed_form) = 2.21642098307 0.727178868893 absolute error = 0.002736 relative error = 0.1173 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.495 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3271.2MB, alloc=52.3MB, time=42.17 x[1] = -1.0822 1.437 h = 0.001 0.003 y[1] (numeric) = 2.21594145015 0.728139850461 y[1] (closed_form) = 2.21793135331 0.726261455991 absolute error = 0.002736 relative error = 0.1173 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.497 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0812 1.44 h = 0.0001 0.004 y[1] (numeric) = 2.21987953443 0.72781335572 y[1] (closed_form) = 2.2218713361 0.725930812431 absolute error = 0.002741 relative error = 0.1173 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.5 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0811 1.444 h = 0.003 0.006 y[1] (numeric) = 2.22477308109 0.7288667538 y[1] (closed_form) = 2.22677111412 0.726980395855 absolute error = 0.002748 relative error = 0.1173 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.504 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0781 1.45 h = 0.0001 0.005 y[1] (numeric) = 2.23296406486 0.726960677807 y[1] (closed_form) = 2.23496502032 0.725053994707 absolute error = 0.002764 relative error = 0.1176 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.51 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.078 1.455 h = 0.0001 0.003 y[1] (numeric) = 2.23910619588 0.728272875054 y[1] (closed_form) = 2.24111692262 0.72636028864 absolute error = 0.002775 relative error = 0.1178 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.515 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3316.7MB, alloc=52.3MB, time=42.75 x[1] = -1.0779 1.458 h = 0.001 0.001 y[1] (numeric) = 2.24281457688 0.729004047479 y[1] (closed_form) = 2.24482876568 0.727089238409 absolute error = 0.002779 relative error = 0.1178 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.518 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0769 1.459 h = 0.001 0.003 y[1] (numeric) = 2.24432677869 0.728058263423 y[1] (closed_form) = 2.24634052624 0.726142655293 absolute error = 0.002779 relative error = 0.1177 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.519 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0759 1.462 h = 0.0001 0.004 y[1] (numeric) = 2.24829679817 0.727674819636 y[1] (closed_form) = 2.25031241183 0.725755049193 absolute error = 0.002784 relative error = 0.1177 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.522 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0758 1.466 h = 0.003 0.006 y[1] (numeric) = 2.2532499892 0.728671068758 y[1] (closed_form) = 2.25527180329 0.726747436787 absolute error = 0.002791 relative error = 0.1178 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.526 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0728 1.472 h = 0.0001 0.005 y[1] (numeric) = 2.2614906475 0.72663568367 y[1] (closed_form) = 2.26351522703 0.724691709306 absolute error = 0.002807 relative error = 0.1181 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.533 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3362.2MB, alloc=52.3MB, time=43.34 x[1] = -1.0727 1.477 h = 0.0001 0.003 y[1] (numeric) = 2.26770740478 0.72787658491 y[1] (closed_form) = 2.26974170775 0.725926633764 absolute error = 0.002818 relative error = 0.1183 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.538 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0726 1.48 h = 0.001 0.001 y[1] (numeric) = 2.27145994486 0.728564284086 y[1] (closed_form) = 2.27349769191 0.726612084241 absolute error = 0.002822 relative error = 0.1182 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.54 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0716 1.481 h = 0.0001 0.004 y[1] (numeric) = 2.27297331855 0.727589322916 y[1] (closed_form) = 2.2750106183 0.725636327602 absolute error = 0.002822 relative error = 0.1182 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.542 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0715 1.485 h = 0.003 0.006 y[1] (numeric) = 2.27797817531 0.728536726384 y[1] (closed_form) = 2.28002164791 0.726579830124 absolute error = 0.002829 relative error = 0.1182 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.546 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0685 1.491 h = 0.0001 0.005 y[1] (numeric) = 2.28626233259 0.726390331315 y[1] (closed_form) = 2.28830843574 0.724413076538 absolute error = 0.002845 relative error = 0.1185 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.552 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3407.7MB, alloc=52.3MB, time=43.92 x[1] = -1.0684 1.496 h = 0.0001 0.003 y[1] (numeric) = 2.29254373121 0.727570297416 y[1] (closed_form) = 2.29459951723 0.725587002255 absolute error = 0.002857 relative error = 0.1187 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.557 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0683 1.499 h = 0.001 0.001 y[1] (numeric) = 2.29633452956 0.728220833104 y[1] (closed_form) = 2.29839374443 0.726235266693 absolute error = 0.002861 relative error = 0.1187 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.56 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0673 1.5 h = 0.001 0.003 y[1] (numeric) = 2.29784907988 0.727220765681 y[1] (closed_form) = 2.29990784223 0.72523440684 absolute error = 0.002861 relative error = 0.1186 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.561 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0663 1.503 h = 0.0001 0.004 y[1] (numeric) = 2.30187802148 0.726731107651 y[1] (closed_form) = 2.30393858975 0.724740561415 absolute error = 0.002865 relative error = 0.1186 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.564 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0662 1.507 h = 0.003 0.006 y[1] (numeric) = 2.30694168049 0.727620533462 y[1] (closed_form) = 2.30900839163 0.725626038564 absolute error = 0.002872 relative error = 0.1187 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.568 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3453.3MB, alloc=52.3MB, time=44.50 x[1] = -1.0632 1.513 h = 0.0001 0.005 y[1] (numeric) = 2.31527364458 0.725344169911 y[1] (closed_form) = 2.31734282934 0.723329300609 absolute error = 0.002888 relative error = 0.119 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.575 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0631 1.518 h = 0.0001 0.003 y[1] (numeric) = 2.32162862208 0.726451800205 y[1] (closed_form) = 2.3237074413 0.724430817541 absolute error = 0.002899 relative error = 0.1191 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.58 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.063 1.521 h = 0.001 0.001 y[1] (numeric) = 2.32546294192 0.727058247574 y[1] (closed_form) = 2.32754517182 0.725034967803 absolute error = 0.002903 relative error = 0.1191 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.583 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.062 1.522 h = 0.001 0.003 y[1] (numeric) = 2.32697824676 0.726028996885 y[1] (closed_form) = 2.32906001814 0.72400492832 absolute error = 0.002904 relative error = 0.119 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.584 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.061 1.525 h = 0.0001 0.004 y[1] (numeric) = 2.33103784942 0.725481729382 y[1] (closed_form) = 2.33312139422 0.723453460376 absolute error = 0.002908 relative error = 0.119 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.587 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3498.9MB, alloc=52.3MB, time=45.08 x[1] = -1.0609 1.529 h = 0.003 0.006 y[1] (numeric) = 2.33615985486 0.726312736693 y[1] (closed_form) = 2.33824951104 0.724280472645 absolute error = 0.002915 relative error = 0.1191 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.591 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0579 1.535 h = 0.0001 0.005 y[1] (numeric) = 2.34453861851 0.723906063619 y[1] (closed_form) = 2.34663059141 0.721853410005 absolute error = 0.002931 relative error = 0.1194 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.597 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0578 1.54 h = 0.0001 0.003 y[1] (numeric) = 2.35096660537 0.724940807153 y[1] (closed_form) = 2.35306816404 0.722881967465 absolute error = 0.002942 relative error = 0.1195 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.602 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0577 1.543 h = 0.001 0.001 y[1] (numeric) = 2.35484410015 0.725502840422 y[1] (closed_form) = 2.35694905123 0.72344167787 absolute error = 0.002946 relative error = 0.1195 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.605 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0567 1.544 h = 0.001 0.003 y[1] (numeric) = 2.35635993541 0.724444406058 y[1] (closed_form) = 2.35846442198 0.722382458374 absolute error = 0.002946 relative error = 0.1194 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.606 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3544.4MB, alloc=52.3MB, time=45.67 x[1] = -1.0557 1.547 h = 0.0001 0.004 y[1] (numeric) = 2.36044975136 0.723839304304 y[1] (closed_form) = 2.36255597882 0.721773143287 absolute error = 0.00295 relative error = 0.1194 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.61 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0556 1.551 h = 0.003 0.006 y[1] (numeric) = 2.36562964439 0.724611455812 y[1] (closed_form) = 2.36774195155 0.722541253549 absolute error = 0.002958 relative error = 0.1195 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.613 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0526 1.557 h = 0.0001 0.005 y[1] (numeric) = 2.37405419948 0.722074136993 y[1] (closed_form) = 2.37616866651 0.719983530725 absolute error = 0.002973 relative error = 0.1198 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.62 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0525 1.562 h = 0.0001 0.003 y[1] (numeric) = 2.38055462407 0.723035445776 y[1] (closed_form) = 2.38267862786 0.720938580991 absolute error = 0.002985 relative error = 0.1199 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.625 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0524 1.565 h = 0.001 0.001 y[1] (numeric) = 2.38447494599 0.723552740962 y[1] (closed_form) = 2.38660232381 0.721453527657 absolute error = 0.002989 relative error = 0.1199 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.628 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0514 1.566 h = 0.001 0.003 y[1] (numeric) = 2.3859910877 0.722465123536 y[1] (closed_form) = 2.38811799507 0.720365128784 absolute error = 0.002989 relative error = 0.1198 % Correct digits = 3 memory used=3590.0MB, alloc=52.3MB, time=46.26 Radius of convergence (given) for eq 1 = 1.629 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0504 1.569 h = 0.0001 0.004 y[1] (numeric) = 2.39011066846 0.721801964943 y[1] (closed_form) = 2.39223928416 0.719697744125 absolute error = 0.002993 relative error = 0.1198 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.632 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0503 1.573 h = 0.003 0.006 y[1] (numeric) = 2.39534798858 0.722514825732 y[1] (closed_form) = 2.3974826521 0.720406517637 absolute error = 0.003 relative error = 0.1198 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.636 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0473 1.579 h = 0.0001 0.005 y[1] (numeric) = 2.40381732611 0.71984652976 y[1] (closed_form) = 2.40595399269 0.717717803944 absolute error = 0.003016 relative error = 0.1201 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.643 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0472 1.584 h = 0.0001 0.003 y[1] (numeric) = 2.41038961471 0.720733858773 y[1] (closed_form) = 2.41253576875 0.718598802265 absolute error = 0.003027 relative error = 0.1203 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.647 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0471 1.587 h = 0.001 0.001 y[1] (numeric) = 2.4143524147 0.721206093693 y[1] (closed_form) = 2.41650192431 0.719068663111 absolute error = 0.003031 relative error = 0.1202 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.65 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3635.5MB, alloc=52.3MB, time=46.85 x[1] = -1.0461 1.588 h = 0.0001 0.004 y[1] (numeric) = 2.41586863908 0.720089294837 y[1] (closed_form) = 2.41801767229 0.717951086518 absolute error = 0.003032 relative error = 0.1202 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.652 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.046 1.592 h = 0.003 0.006 y[1] (numeric) = 2.42115573495 0.720751449143 y[1] (closed_form) = 2.42331078774 0.718609114817 absolute error = 0.003039 relative error = 0.1202 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.655 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.043 1.598 h = 0.0001 0.005 y[1] (numeric) = 2.4296643766 0.717970667776 y[1] (closed_form) = 2.43182129766 0.715807902636 absolute error = 0.003054 relative error = 0.1205 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.662 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0429 1.603 h = 0.0001 0.003 y[1] (numeric) = 2.4362989523 0.718794730009 y[1] (closed_form) = 2.43846531902 0.716625571674 absolute error = 0.003066 relative error = 0.1206 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.667 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0428 1.606 h = 0.001 0.001 y[1] (numeric) = 2.44029857751 0.719228422254 y[1] (closed_form) = 2.44246828411 0.717056867707 absolute error = 0.00307 relative error = 0.1206 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.67 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3681.1MB, alloc=52.3MB, time=47.44 x[1] = -1.0418 1.607 h = 0.001 0.003 y[1] (numeric) = 2.44181504151 0.718086504439 y[1] (closed_form) = 2.44398426658 0.715914175299 absolute error = 0.00307 relative error = 0.1205 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.671 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0408 1.61 h = 0.0001 0.004 y[1] (numeric) = 2.44598950927 0.717315072608 y[1] (closed_form) = 2.44816038212 0.715138493735 absolute error = 0.003074 relative error = 0.1205 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.674 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0407 1.614 h = 0.003 0.006 y[1] (numeric) = 2.45133317479 0.717917128872 y[1] (closed_form) = 2.45351003619 0.715736377152 absolute error = 0.003081 relative error = 0.1206 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.678 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0377 1.62 h = 0.0001 0.005 y[1] (numeric) = 2.45988472301 0.715004754455 y[1] (closed_form) = 2.46206329594 0.71280355955 absolute error = 0.003097 relative error = 0.1208 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.685 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0376 1.625 h = 0.0001 0.003 y[1] (numeric) = 2.46659009594 0.715753823796 y[1] (closed_form) = 2.46877806469 0.71354616402 absolute error = 0.003108 relative error = 0.121 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.69 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3726.6MB, alloc=52.3MB, time=48.01 x[1] = -1.0375 1.628 h = 0.001 0.001 y[1] (numeric) = 2.47063155024 0.71614185688 y[1] (closed_form) = 2.4728228402 0.713931775524 absolute error = 0.003112 relative error = 0.1209 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.692 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0365 1.629 h = 0.001 0.003 y[1] (numeric) = 2.47214768084 0.714970760718 y[1] (closed_form) = 2.47433848336 0.712759908525 absolute error = 0.003112 relative error = 0.1209 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.694 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0355 1.632 h = 0.0001 0.004 y[1] (numeric) = 2.47635062905 0.71414064201 y[1] (closed_form) = 2.47854304668 0.711925527797 absolute error = 0.003117 relative error = 0.1209 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.697 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0354 1.636 h = 0.003 0.006 y[1] (numeric) = 2.48175040011 0.714682171002 y[1] (closed_form) = 2.48394877388 0.712462838414 absolute error = 0.003124 relative error = 0.1209 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.701 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0324 1.642 h = 0.0001 0.005 y[1] (numeric) = 2.49034384352 0.711637885894 y[1] (closed_form) = 2.49254377214 0.709398098472 absolute error = 0.003139 relative error = 0.1211 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.707 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3772.2MB, alloc=52.3MB, time=48.60 x[1] = -1.0323 1.647 h = 0.0001 0.003 y[1] (numeric) = 2.49711943391 0.712311425826 y[1] (closed_form) = 2.49932870821 0.710065102126 absolute error = 0.003151 relative error = 0.1213 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.712 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0322 1.65 h = 0.001 0.001 y[1] (numeric) = 2.50120236472 0.71265348272 y[1] (closed_form) = 2.50341494146 0.710404712174 absolute error = 0.003155 relative error = 0.1212 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.715 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0312 1.651 h = 0.001 0.003 y[1] (numeric) = 2.50271793855 0.711453212754 y[1] (closed_form) = 2.50493002198 0.709203675152 absolute error = 0.003155 relative error = 0.1212 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.716 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0302 1.654 h = 0.0001 0.004 y[1] (numeric) = 2.50694891599 0.710564193037 y[1] (closed_form) = 2.50916258182 0.708310381286 absolute error = 0.003159 relative error = 0.1212 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.719 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0301 1.658 h = 0.003 0.006 y[1] (numeric) = 2.51240432564 0.711044769059 y[1] (closed_form) = 2.51462391502 0.70878669358 absolute error = 0.003166 relative error = 0.1212 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.723 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3817.7MB, alloc=52.3MB, time=49.16 x[1] = -1.0271 1.664 h = 0.0001 0.005 y[1] (numeric) = 2.52103865206 0.707868260434 y[1] (closed_form) = 2.52325963965 0.705589719193 absolute error = 0.003182 relative error = 0.1214 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.73 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.027 1.669 h = 0.0001 0.003 y[1] (numeric) = 2.5278838781 0.708465737429 y[1] (closed_form) = 2.53011416094 0.706180588777 absolute error = 0.003193 relative error = 0.1216 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.735 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0269 1.672 h = 0.001 0.001 y[1] (numeric) = 2.53200793161 0.708761502916 y[1] (closed_form) = 2.53424149802 0.706473882254 absolute error = 0.003197 relative error = 0.1215 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.738 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0259 1.673 h = 0.001 0.003 y[1] (numeric) = 2.53352272548 0.707532064704 y[1] (closed_form) = 2.53575579273 0.705243680791 absolute error = 0.003197 relative error = 0.1215 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.739 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0249 1.676 h = 0.0001 0.004 y[1] (numeric) = 2.53778128024 0.706583932041 y[1] (closed_form) = 2.54001589715 0.704291262007 absolute error = 0.003202 relative error = 0.1215 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.742 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3863.3MB, alloc=52.3MB, time=49.73 x[1] = -1.0248 1.68 h = 0.003 0.006 y[1] (numeric) = 2.54329185989 0.7070031318 y[1] (closed_form) = 2.54553236756 0.704706152862 absolute error = 0.003209 relative error = 0.1215 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.746 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0218 1.686 h = 0.0001 0.005 y[1] (numeric) = 2.55196605638 0.703694091647 y[1] (closed_form) = 2.55420780567 0.701376636739 absolute error = 0.003224 relative error = 0.1217 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.753 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0217 1.691 h = 0.0001 0.003 y[1] (numeric) = 2.55888033416 0.704214975172 y[1] (closed_form) = 2.561131328 0.701890841992 absolute error = 0.003236 relative error = 0.1218 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.757 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0216 1.694 h = 0.001 0.001 y[1] (numeric) = 2.56304515537 0.704464135849 y[1] (closed_form) = 2.56529941379 0.702137505598 absolute error = 0.00324 relative error = 0.1218 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.76 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0206 1.695 h = 0.0001 0.004 y[1] (numeric) = 2.56455894626 0.703205535964 y[1] (closed_form) = 2.56681269969 0.70087814629 absolute error = 0.00324 relative error = 0.1218 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.761 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3908.9MB, alloc=52.3MB, time=50.30 x[1] = -1.0205 1.699 h = 0.003 0.006 y[1] (numeric) = 2.57011737693 0.703572216405 y[1] (closed_form) = 2.57237699221 0.701240479799 absolute error = 0.003247 relative error = 0.1218 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.765 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0175 1.705 h = 0.0001 0.005 y[1] (numeric) = 2.57882666413 0.700149313059 y[1] (closed_form) = 2.5810873864 0.697797090408 absolute error = 0.003262 relative error = 0.122 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.772 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0174 1.71 h = 0.0001 0.003 y[1] (numeric) = 2.58580083116 0.700604657972 y[1] (closed_form) = 2.58807075494 0.698245695665 absolute error = 0.003274 relative error = 0.1221 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.777 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0173 1.713 h = 0.001 0.001 y[1] (numeric) = 2.59000101884 0.700813933053 y[1] (closed_form) = 2.59227419108 0.698452451956 absolute error = 0.003278 relative error = 0.1221 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.78 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0163 1.714 h = 0.001 0.003 y[1] (numeric) = 2.59151411518 0.699530222248 y[1] (closed_form) = 2.59378677738 0.697167984975 absolute error = 0.003278 relative error = 0.122 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.781 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3954.4MB, alloc=52.3MB, time=50.88 x[1] = -1.0153 1.717 h = 0.0001 0.004 y[1] (numeric) = 2.59582348982 0.698471853391 y[1] (closed_form) = 2.59809764082 0.696105307745 absolute error = 0.003282 relative error = 0.122 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.784 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0152 1.721 h = 0.003 0.006 y[1] (numeric) = 2.60143621812 0.698776371804 y[1] (closed_form) = 2.60371619892 0.696405433272 absolute error = 0.003289 relative error = 0.122 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.788 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0122 1.727 h = 0.0001 0.005 y[1] (numeric) = 2.61018349205 0.695220364518 y[1] (closed_form) = 2.61246442334 0.692828931075 absolute error = 0.003305 relative error = 0.1223 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.795 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0121 1.732 h = 0.0001 0.003 y[1] (numeric) = 2.61722562516 0.695598129738 y[1] (closed_form) = 2.6195157067 0.693199886284 absolute error = 0.003316 relative error = 0.1224 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.799 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.012 1.735 h = 0.001 0.001 y[1] (numeric) = 2.62146592041 0.695760217418 y[1] (closed_form) = 2.62375923126 0.693359430301 absolute error = 0.00332 relative error = 0.1223 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.802 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4000.0MB, alloc=52.3MB, time=51.45 x[1] = -1.011 1.736 h = 0.001 0.003 y[1] (numeric) = 2.62297759913 0.694447357212 y[1] (closed_form) = 2.62527039413 0.692045817792 absolute error = 0.00332 relative error = 0.1223 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.804 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.01 1.739 h = 0.0001 0.004 y[1] (numeric) = 2.62731325701 0.693329275827 y[1] (closed_form) = 2.62960750798 0.69092341651 absolute error = 0.003324 relative error = 0.1223 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.807 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0099 1.743 h = 0.003 0.006 y[1] (numeric) = 2.63297981075 0.693571214685 y[1] (closed_form) = 2.6352798582 0.691160917816 absolute error = 0.003332 relative error = 0.1223 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.811 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0069 1.749 h = 0.0001 0.005 y[1] (numeric) = 2.64176405627 0.689881809212 y[1] (closed_form) = 2.64406489778 0.687451009282 absolute error = 0.003347 relative error = 0.1225 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.817 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0068 1.754 h = 0.0001 0.003 y[1] (numeric) = 2.64887356571 0.690181472776 y[1] (closed_form) = 2.65118350593 0.687743792756 absolute error = 0.003358 relative error = 0.1226 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.822 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4045.6MB, alloc=52.3MB, time=52.04 x[1] = -1.0067 1.757 h = 0.001 0.001 y[1] (numeric) = 2.65315361008 0.690296064845 y[1] (closed_form) = 2.65546676035 0.687855816393 absolute error = 0.003362 relative error = 0.1226 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.825 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0057 1.758 h = 0.001 0.003 y[1] (numeric) = 2.65466364863 0.688954064706 y[1] (closed_form) = 2.65697627728 0.686513067849 absolute error = 0.003363 relative error = 0.1225 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.826 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0047 1.761 h = 0.0001 0.004 y[1] (numeric) = 2.65902513525 0.687776067331 y[1] (closed_form) = 2.66133918699 0.685330739208 absolute error = 0.003367 relative error = 0.1225 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.829 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0046 1.765 h = 0.003 0.006 y[1] (numeric) = 2.66474503956 0.687955012633 y[1] (closed_form) = 2.6670648543 0.68550520247 absolute error = 0.003374 relative error = 0.1225 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.833 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0016 1.771 h = 0.0001 0.005 y[1] (numeric) = 2.67356524083 0.684131919538 y[1] (closed_form) = 2.67588569325 0.681661598884 absolute error = 0.003389 relative error = 0.1227 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.84 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4091.1MB, alloc=52.3MB, time=52.67 x[1] = -1.0015 1.776 h = 0.0001 0.003 y[1] (numeric) = 2.68074153483 0.684352962496 y[1] (closed_form) = 2.68307103414 0.681875691949 absolute error = 0.003401 relative error = 0.1228 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.845 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0014 1.779 h = 0.001 0.001 y[1] (numeric) = 2.68506096867 0.68441975257 y[1] (closed_form) = 2.68739365866 0.681939888926 absolute error = 0.003405 relative error = 0.1228 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.848 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0004 1.78 h = 0.001 0.003 y[1] (numeric) = 2.6865691447 0.683048622977 y[1] (closed_form) = 2.68890130732 0.680568014848 absolute error = 0.003405 relative error = 0.1228 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.849 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9994 1.783 h = 0.0001 0.004 y[1] (numeric) = 2.6909560049 0.681810508347 y[1] (closed_form) = 2.69328955771 0.679325557743 absolute error = 0.003409 relative error = 0.1227 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.852 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9993 1.787 h = 0.003 0.006 y[1] (numeric) = 2.69672878332 0.681926048513 y[1] (closed_form) = 2.69906806545 0.679436571561 absolute error = 0.003416 relative error = 0.1227 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.856 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4136.6MB, alloc=52.3MB, time=53.24 x[1] = -0.9963 1.793 h = 0.0001 0.005 y[1] (numeric) = 2.70558392379 0.677968983175 y[1] (closed_form) = 2.70792368729 0.675458989018 absolute error = 0.003431 relative error = 0.123 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.862 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9962 1.798 h = 0.0001 0.003 y[1] (numeric) = 2.71282640858 0.678110889595 y[1] (closed_form) = 2.71517516686 0.675593876018 absolute error = 0.003443 relative error = 0.123 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.867 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9961 1.801 h = 0.001 0.001 y[1] (numeric) = 2.71718487107 0.67812957312 y[1] (closed_form) = 2.71953680056 0.675609941883 absolute error = 0.003447 relative error = 0.123 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.87 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9951 1.802 h = 0.0001 0.004 y[1] (numeric) = 2.7186909624 0.676729325557 y[1] (closed_form) = 2.7210423588 0.674208953781 absolute error = 0.003447 relative error = 0.123 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.871 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.995 1.806 h = 0.003 0.006 y[1] (numeric) = 2.72450963322 0.676790581966 y[1] (closed_form) = 2.72686672936 0.674265646526 absolute error = 0.003454 relative error = 0.123 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.875 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4182.1MB, alloc=52.3MB, time=53.81 x[1] = -0.992 1.812 h = 0.0001 0.005 y[1] (numeric) = 2.73339563404 0.672718373248 y[1] (closed_form) = 2.73575307713 0.670172913538 absolute error = 0.003469 relative error = 0.1232 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.882 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9919 1.817 h = 0.0001 0.003 y[1] (numeric) = 2.74069556763 0.67279252954 y[1] (closed_form) = 2.74306196124 0.670239990161 absolute error = 0.003481 relative error = 0.1233 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.887 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9918 1.82 h = 0.001 0.001 y[1] (numeric) = 2.7450879128 0.672770021106 y[1] (closed_form) = 2.74745746108 0.670214842774 absolute error = 0.003485 relative error = 0.1232 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.89 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9908 1.821 h = 0.001 0.003 y[1] (numeric) = 2.74659237857 0.671344691303 y[1] (closed_form) = 2.7489613888 0.668788775779 absolute error = 0.003485 relative error = 0.1232 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.891 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9898 1.824 h = 0.0001 0.004 y[1] (numeric) = 2.75102596115 0.669994473776 y[1] (closed_form) = 2.75339630039 0.66743419494 absolute error = 0.003489 relative error = 0.1232 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.894 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9897 1.828 h = 0.003 0.006 y[1] (numeric) = 2.75689661914 0.669991561014 y[1] (closed_form) = 2.75927262507 0.667426673457 absolute error = 0.003496 relative error = 0.1232 % Correct digits = 3 memory used=4227.8MB, alloc=52.3MB, time=54.38 Radius of convergence (given) for eq 1 = 1.898 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9867 1.834 h = 0.0001 0.005 y[1] (numeric) = 2.76581566907 0.665784851115 y[1] (closed_form) = 2.76819186575 0.66319943391 absolute error = 0.003512 relative error = 0.1234 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.904 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9866 1.839 h = 0.0001 0.003 y[1] (numeric) = 2.77318068933 0.665778911762 y[1] (closed_form) = 2.7755657839 0.663186345876 absolute error = 0.003523 relative error = 0.1234 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.909 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9865 1.842 h = 0.001 0.001 y[1] (numeric) = 2.77761139221 0.665707730616 y[1] (closed_form) = 2.77999962179 0.663112501406 absolute error = 0.003527 relative error = 0.1234 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.912 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9855 1.843 h = 0.001 0.003 y[1] (numeric) = 2.7791133602 0.664253304255 y[1] (closed_form) = 2.78150104604 0.661657341843 absolute error = 0.003527 relative error = 0.1234 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.913 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9845 1.846 h = 0.0001 0.004 y[1] (numeric) = 2.78357101307 0.66284240041 y[1] (closed_form) = 2.78595999492 0.660242063924 absolute error = 0.003531 relative error = 0.1233 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.917 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4273.3MB, alloc=52.3MB, time=54.94 x[1] = -0.9844 1.85 h = 0.003 0.006 y[1] (numeric) = 2.78949317817 0.662774912744 y[1] (closed_form) = 2.79188779253 0.660169923743 absolute error = 0.003538 relative error = 0.1233 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.921 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9814 1.856 h = 0.0001 0.005 y[1] (numeric) = 2.7984442587 0.6584334308 y[1] (closed_form) = 2.80083890769 0.655807907489 absolute error = 0.003554 relative error = 0.1235 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.927 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9813 1.861 h = 0.0001 0.003 y[1] (numeric) = 2.80587376616 0.658346888507 y[1] (closed_form) = 2.8082772601 0.655714147781 absolute error = 0.003565 relative error = 0.1236 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.932 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9812 1.864 h = 0.001 0.001 y[1] (numeric) = 2.81034246256 0.658226735325 y[1] (closed_form) = 2.81274907177 0.655591307009 absolute error = 0.003569 relative error = 0.1236 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.935 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9802 1.865 h = 0.001 0.003 y[1] (numeric) = 2.81184171113 0.656743226773 y[1] (closed_form) = 2.81424777093 0.654107069268 absolute error = 0.003569 relative error = 0.1235 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.936 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4318.8MB, alloc=52.3MB, time=55.52 x[1] = -0.9792 1.868 h = 0.0001 0.004 y[1] (numeric) = 2.81632297667 0.655271443835 y[1] (closed_form) = 2.81873029946 0.652630901651 absolute error = 0.003573 relative error = 0.1235 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.939 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9791 1.872 h = 0.003 0.006 y[1] (numeric) = 2.82229616632 0.655138979049 y[1] (closed_form) = 2.82470908724 0.65249374074 absolute error = 0.00358 relative error = 0.1235 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.943 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9761 1.878 h = 0.0001 0.005 y[1] (numeric) = 2.83127825831 0.650662459006 y[1] (closed_form) = 2.8336910578 0.647996682438 absolute error = 0.003596 relative error = 0.1237 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.95 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.976 1.883 h = 0.0001 0.003 y[1] (numeric) = 2.83877165151 0.650494809514 y[1] (closed_form) = 2.84119324275 0.647821747077 absolute error = 0.003607 relative error = 0.1238 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.955 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9759 1.886 h = 0.001 0.001 y[1] (numeric) = 2.8432779761 0.650325386811 y[1] (closed_form) = 2.84570266276 0.647649612623 absolute error = 0.003611 relative error = 0.1237 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.957 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4364.3MB, alloc=52.3MB, time=56.08 x[1] = -0.9749 1.887 h = 0.001 0.003 y[1] (numeric) = 2.8447742838 0.648812811438 y[1] (closed_form) = 2.84719841541 0.646136312097 absolute error = 0.003611 relative error = 0.1237 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.959 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9739 1.89 h = 0.0001 0.004 y[1] (numeric) = 2.84927870377 0.647279958838 y[1] (closed_form) = 2.85170406532 0.644599064369 absolute error = 0.003615 relative error = 0.1237 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.962 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9738 1.894 h = 0.003 0.006 y[1] (numeric) = 2.85530243384 0.647082117156 y[1] (closed_form) = 2.85773335897 0.644396483133 absolute error = 0.003622 relative error = 0.1237 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.966 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9708 1.9 h = 0.0001 0.005 y[1] (numeric) = 2.86431451753 0.642470297768 y[1] (closed_form) = 2.86674516524 0.639764122253 absolute error = 0.003638 relative error = 0.1238 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.972 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9707 1.905 h = 0.0001 0.003 y[1] (numeric) = 2.87187119307 0.642221039858 y[1] (closed_form) = 2.87431057905 0.639507510303 absolute error = 0.003649 relative error = 0.1239 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.977 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4409.9MB, alloc=52.3MB, time=56.66 x[1] = -0.9706 1.908 h = 0.001 0.001 y[1] (numeric) = 2.87641477936 0.642002051992 y[1] (closed_form) = 2.87885724082 0.639285786627 absolute error = 0.003653 relative error = 0.1239 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.98 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9696 1.909 h = 0.0001 0.004 y[1] (numeric) = 2.87790792495 0.64046042617 y[1] (closed_form) = 2.88034982573 0.637743439712 absolute error = 0.003653 relative error = 0.1238 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.981 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9695 1.913 h = 0.003 0.006 y[1] (numeric) = 2.88397555574 0.640206585074 y[1] (closed_form) = 2.88642298984 0.637484822468 absolute error = 0.00366 relative error = 0.1238 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.985 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9665 1.919 h = 0.0001 0.005 y[1] (numeric) = 2.89301425405 0.635478439714 y[1] (closed_form) = 2.89546127656 0.632736131549 absolute error = 0.003675 relative error = 0.124 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.992 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9664 1.924 h = 0.0001 0.003 y[1] (numeric) = 2.90062589643 0.635159280963 y[1] (closed_form) = 2.90308161176 0.632409559661 absolute error = 0.003687 relative error = 0.1241 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.997 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4455.5MB, alloc=52.3MB, time=57.23 x[1] = -0.9663 1.927 h = 0.001 0.001 y[1] (numeric) = 2.9052018572 0.634897831619 y[1] (closed_form) = 2.90766063105 0.632145353645 absolute error = 0.003691 relative error = 0.124 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9653 1.928 h = 0.001 0.003 y[1] (numeric) = 2.90669244969 0.633331172766 y[1] (closed_form) = 2.90915065798 0.630577977145 absolute error = 0.003691 relative error = 0.124 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.001 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9643 1.931 h = 0.0001 0.004 y[1] (numeric) = 2.91123946574 0.63168444701 y[1] (closed_form) = 2.91369884252 0.628926836843 absolute error = 0.003695 relative error = 0.124 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.004 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9642 1.935 h = 0.003 0.006 y[1] (numeric) = 2.9173567358 0.63136448688 y[1] (closed_form) = 2.9198216119 0.628602056416 absolute error = 0.003702 relative error = 0.124 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.008 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9612 1.941 h = 0.0001 0.005 y[1] (numeric) = 2.92642352965 0.626500556694 y[1] (closed_form) = 2.92888783831 0.623717578767 absolute error = 0.003717 relative error = 0.1241 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.014 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4501.1MB, alloc=52.3MB, time=57.80 x[1] = -0.9611 1.946 h = 0.0001 0.003 y[1] (numeric) = 2.93409733231 0.626098857743 y[1] (closed_form) = 2.93657027978 0.623308399028 absolute error = 0.003729 relative error = 0.1242 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.019 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.961 1.949 h = 0.001 0.001 y[1] (numeric) = 2.9387098733 0.625787293625 y[1] (closed_form) = 2.94118585915 0.622994054374 absolute error = 0.003733 relative error = 0.1242 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.022 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.96 1.95 h = 0.001 0.003 y[1] (numeric) = 2.94019689229 0.624191614822 y[1] (closed_form) = 2.94267230701 0.621397662028 absolute error = 0.003733 relative error = 0.1241 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.023 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.959 1.953 h = 0.0001 0.004 y[1] (numeric) = 2.94476575077 0.622483280914 y[1] (closed_form) = 2.94724230084 0.619684903574 absolute error = 0.003737 relative error = 0.1241 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.027 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9589 1.957 h = 0.003 0.006 y[1] (numeric) = 2.95093217242 0.622096807896 y[1] (closed_form) = 2.95341418674 0.619293567351 absolute error = 0.003744 relative error = 0.1241 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.03 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4546.7MB, alloc=52.3MB, time=58.38 x[1] = -0.9559 1.963 h = 0.0001 0.005 y[1] (numeric) = 2.9600260403 0.617096845387 y[1] (closed_form) = 2.96250733142 0.614273056188 absolute error = 0.003759 relative error = 0.1242 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.037 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9558 1.968 h = 0.0001 0.003 y[1] (numeric) = 2.96776139427 0.616612113719 y[1] (closed_form) = 2.97025126992 0.613780776364 absolute error = 0.00377 relative error = 0.1243 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.042 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9557 1.971 h = 0.001 0.001 y[1] (numeric) = 2.97241014573 0.616250144452 y[1] (closed_form) = 2.97490303954 0.613416002803 absolute error = 0.003775 relative error = 0.1243 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.045 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9547 1.972 h = 0.001 0.003 y[1] (numeric) = 2.97389337055 0.614625464936 y[1] (closed_form) = 2.97638568766 0.611790613872 absolute error = 0.003775 relative error = 0.1242 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.046 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9537 1.975 h = 0.0001 0.004 y[1] (numeric) = 2.97848361091 0.612855340809 y[1] (closed_form) = 2.98097703021 0.610016055355 absolute error = 0.003779 relative error = 0.1242 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.049 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4592.1MB, alloc=52.3MB, time=58.94 x[1] = -0.9536 1.979 h = 0.003 0.006 y[1] (numeric) = 2.98469869407 0.61240196456 y[1] (closed_form) = 2.98719754239 0.609557773178 absolute error = 0.003786 relative error = 0.1242 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.053 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9506 1.985 h = 0.0001 0.005 y[1] (numeric) = 2.99381861393 0.607265727039 y[1] (closed_form) = 2.99631658336 0.604400986523 absolute error = 0.003801 relative error = 0.1243 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.06 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9505 1.99 h = 0.0001 0.003 y[1] (numeric) = 3.00161490833 0.606697473195 y[1] (closed_form) = 3.00412140773 0.603825117439 absolute error = 0.003812 relative error = 0.1244 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.064 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9504 1.993 h = 0.001 0.001 y[1] (numeric) = 3.0062994994 0.606284810256 y[1] (closed_form) = 3.00880899663 0.603409626555 absolute error = 0.003816 relative error = 0.1244 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.067 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9494 1.994 h = 0.001 0.003 y[1] (numeric) = 3.00777870958 0.604631150262 y[1] (closed_form) = 3.01028762457 0.601755261295 absolute error = 0.003816 relative error = 0.1243 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.069 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4637.6MB, alloc=52.3MB, time=59.52 x[1] = -0.9484 1.997 h = 0.0001 0.004 y[1] (numeric) = 3.0123898707 0.602799056055 y[1] (closed_form) = 3.0148998547 0.599918723012 absolute error = 0.003821 relative error = 0.1243 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.072 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9483 2.001 h = 0.003 0.006 y[1] (numeric) = 3.01865312378 0.602278388689 y[1] (closed_form) = 3.02116850138 0.599393107179 absolute error = 0.003828 relative error = 0.1243 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.076 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9453 2.007 h = 0.0001 0.005 y[1] (numeric) = 3.027798073 0.597005638271 y[1] (closed_form) = 3.03031241612 0.59409980786 absolute error = 0.003843 relative error = 0.1244 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.082 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9452 2.012 h = 0.0001 0.003 y[1] (numeric) = 3.03565469507 0.596353375855 y[1] (closed_form) = 3.03817751331 0.593439863405 absolute error = 0.003854 relative error = 0.1245 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.087 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9451 2.015 h = 0.001 0.001 y[1] (numeric) = 3.04037475376 0.595889732577 y[1] (closed_form) = 3.04290054942 0.592973368634 absolute error = 0.003858 relative error = 0.1244 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.09 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4683.3MB, alloc=52.3MB, time=60.09 x[1] = -0.9441 2.016 h = 0.0001 0.004 y[1] (numeric) = 3.04184972905 0.594207113336 y[1] (closed_form) = 3.04437493696 0.591290048299 absolute error = 0.003858 relative error = 0.1244 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.091 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.944 2.02 h = 0.003 0.006 y[1] (numeric) = 3.048154859 0.593628780056 y[1] (closed_form) = 3.05068542959 0.590706730694 absolute error = 0.003866 relative error = 0.1244 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.095 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.941 2.026 h = 0.0001 0.005 y[1] (numeric) = 3.05732216329 0.588238618629 y[1] (closed_form) = 3.05985156552 0.585296019283 absolute error = 0.00388 relative error = 0.1246 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.102 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9409 2.031 h = 0.0001 0.003 y[1] (numeric) = 3.06523122979 0.587514365938 y[1] (closed_form) = 3.06776906052 0.584564026626 absolute error = 0.003892 relative error = 0.1246 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.107 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9408 2.034 h = 0.001 0.001 y[1] (numeric) = 3.06998213101 0.587007028784 y[1] (closed_form) = 3.07252292178 0.584053817551 absolute error = 0.003896 relative error = 0.1246 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.109 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4728.8MB, alloc=52.3MB, time=60.66 x[1] = -0.9398 2.035 h = 0.001 0.003 y[1] (numeric) = 3.07145362944 0.585299446137 y[1] (closed_form) = 3.07399382767 0.582345537355 absolute error = 0.003896 relative error = 0.1245 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.111 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9388 2.038 h = 0.0001 0.004 y[1] (numeric) = 3.07610323312 0.583351805137 y[1] (closed_form) = 3.07864443864 0.580393434278 absolute error = 0.0039 relative error = 0.1245 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.114 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9387 2.042 h = 0.003 0.006 y[1] (numeric) = 3.08245561801 0.582705460662 y[1] (closed_form) = 3.08500215128 0.579742062246 absolute error = 0.003907 relative error = 0.1245 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.118 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9357 2.048 h = 0.0001 0.005 y[1] (numeric) = 3.09164605015 0.577178344283 y[1] (closed_form) = 3.0941912596 0.574194397439 absolute error = 0.003922 relative error = 0.1246 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.124 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9356 2.053 h = 0.0001 0.003 y[1] (numeric) = 3.09961430477 0.576369178766 y[1] (closed_form) = 3.10216788737 0.573377425684 absolute error = 0.003933 relative error = 0.1247 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.129 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4774.4MB, alloc=52.3MB, time=61.23 x[1] = -0.9355 2.056 h = 0.001 0.001 y[1] (numeric) = 3.10439998186 0.575810328331 y[1] (closed_form) = 3.10695650391 0.572815679979 absolute error = 0.003937 relative error = 0.1246 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.132 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9345 2.057 h = 0.001 0.003 y[1] (numeric) = 3.10586683587 0.574073825972 y[1] (closed_form) = 3.1084227599 0.571078484286 absolute error = 0.003938 relative error = 0.1246 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.133 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9335 2.06 h = 0.0001 0.004 y[1] (numeric) = 3.11053604008 0.572063707026 y[1] (closed_form) = 3.11309293815 0.569063894027 absolute error = 0.003942 relative error = 0.1246 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.136 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9334 2.064 h = 0.003 0.006 y[1] (numeric) = 3.11693518482 0.571348969464 y[1] (closed_form) = 3.11949737471 0.568344086896 absolute error = 0.003949 relative error = 0.1245 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.14 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9304 2.07 h = 0.0001 0.005 y[1] (numeric) = 3.12614772067 0.565684673986 y[1] (closed_form) = 3.1287084314 0.562659245255 absolute error = 0.003964 relative error = 0.1247 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.147 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4819.9MB, alloc=52.3MB, time=61.80 x[1] = -0.9303 2.075 h = 0.0001 0.003 y[1] (numeric) = 3.13417454522 0.564790118011 y[1] (closed_form) = 3.13674357347 0.561756817058 absolute error = 0.003975 relative error = 0.1247 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.152 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9302 2.078 h = 0.001 0.001 y[1] (numeric) = 3.13899462303 0.564179472932 y[1] (closed_form) = 3.14156657004 0.561143253466 absolute error = 0.003979 relative error = 0.1247 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.155 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9292 2.079 h = 0.001 0.003 y[1] (numeric) = 3.14045661298 0.562414074938 y[1] (closed_form) = 3.14302795652 0.559377166377 absolute error = 0.003979 relative error = 0.1246 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.156 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9282 2.082 h = 0.0001 0.004 y[1] (numeric) = 3.14514495443 0.560341306702 y[1] (closed_form) = 3.14771723871 0.557299917747 absolute error = 0.003983 relative error = 0.1246 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.159 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9281 2.086 h = 0.003 0.006 y[1] (numeric) = 3.15159036163 0.559557797667 y[1] (closed_form) = 3.15416790165 0.556511297318 absolute error = 0.003991 relative error = 0.1246 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.163 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9251 2.092 h = 0.0001 0.005 y[1] (numeric) = 3.1608239766 0.553756103744 y[1] (closed_form) = 3.16339988219 0.550689060207 absolute error = 0.004005 relative error = 0.1247 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.17 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4865.4MB, alloc=52.3MB, time=62.37 x[1] = -0.925 2.097 h = 0.0001 0.003 y[1] (numeric) = 3.16890875103 0.552775682759 y[1] (closed_form) = 3.17149291826 0.549700701303 absolute error = 0.004017 relative error = 0.1248 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.174 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9249 2.1 h = 0.001 0.001 y[1] (numeric) = 3.17376285332 0.552112963538 y[1] (closed_form) = 3.17634991852 0.549035040433 absolute error = 0.004021 relative error = 0.1247 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.177 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9239 2.101 h = 0.001 0.003 y[1] (numeric) = 3.1752197598 0.550318694979 y[1] (closed_form) = 3.17780621609 0.547240087039 absolute error = 0.004021 relative error = 0.1247 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.179 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9229 2.104 h = 0.0001 0.004 y[1] (numeric) = 3.17992677464 0.548183108318 y[1] (closed_form) = 3.18251413837 0.545100011061 absolute error = 0.004025 relative error = 0.1247 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.182 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9228 2.108 h = 0.003 0.006 y[1] (numeric) = 3.18641794547 0.547330451896 y[1] (closed_form) = 3.18901052867 0.544242201607 absolute error = 0.004032 relative error = 0.1246 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.186 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4911.1MB, alloc=52.3MB, time=62.93 x[1] = -0.9198 2.114 h = 0.0001 0.005 y[1] (numeric) = 3.19567161447 0.541391144985 y[1] (closed_form) = 3.19826240807 0.53828235519 absolute error = 0.004047 relative error = 0.1248 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.192 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9197 2.119 h = 0.0001 0.003 y[1] (numeric) = 3.20381371689 0.540324387521 y[1] (closed_form) = 3.20641271597 0.537207594399 absolute error = 0.004058 relative error = 0.1248 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.197 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9196 2.122 h = 0.001 0.001 y[1] (numeric) = 3.20870146634 0.539609316525 y[1] (closed_form) = 3.2113033425 0.536489558725 absolute error = 0.004062 relative error = 0.1248 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.2 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9186 2.123 h = 0.0001 0.004 y[1] (numeric) = 3.21015307017 0.53778620346 y[1] (closed_form) = 3.21275433202 0.534665765108 absolute error = 0.004062 relative error = 0.1247 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.201 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9185 2.127 h = 0.003 0.006 y[1] (numeric) = 3.21668406267 0.536874264151 y[1] (closed_form) = 3.21929051243 0.533748637655 absolute error = 0.00407 relative error = 0.1247 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.205 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4956.6MB, alloc=52.3MB, time=63.51 x[1] = -0.9155 2.133 h = 0.0001 0.005 y[1] (numeric) = 3.22595581495 0.53081655869 y[1] (closed_form) = 3.22856034156 0.527670394579 absolute error = 0.004084 relative error = 0.1249 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.212 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9154 2.138 h = 0.0001 0.003 y[1] (numeric) = 3.23414780003 0.529675783258 y[1] (closed_form) = 3.23676048434 0.526521559077 absolute error = 0.004096 relative error = 0.1249 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.216 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9153 2.141 h = 0.001 0.001 y[1] (numeric) = 3.23906483693 0.528915823374 y[1] (closed_form) = 3.24168038055 0.525758614527 absolute error = 0.0041 relative error = 0.1248 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.219 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9143 2.142 h = 0.001 0.003 y[1] (numeric) = 3.24051204424 0.52706783683 y[1] (closed_form) = 3.24312696885 0.523909951072 absolute error = 0.0041 relative error = 0.1248 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.221 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9133 2.145 h = 0.0001 0.004 y[1] (numeric) = 3.24525332248 0.524815126515 y[1] (closed_form) = 3.24786909259 0.521652734856 absolute error = 0.004104 relative error = 0.1248 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.224 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5002.2MB, alloc=52.3MB, time=64.07 x[1] = -0.9132 2.149 h = 0.003 0.006 y[1] (numeric) = 3.25182915019 0.523833341958 y[1] (closed_form) = 3.25445007233 0.52066571985 absolute error = 0.004111 relative error = 0.1247 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.228 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9102 2.155 h = 0.0001 0.005 y[1] (numeric) = 3.26111905031 0.517637624844 y[1] (closed_form) = 3.26373789432 0.51444947012 absolute error = 0.004126 relative error = 0.1249 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.234 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9101 2.16 h = 0.0001 0.003 y[1] (numeric) = 3.26936720684 0.516409636404 y[1] (closed_form) = 3.27199415188 0.513213356737 absolute error = 0.004137 relative error = 0.1249 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.239 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.91 2.163 h = 0.001 0.001 y[1] (numeric) = 3.27431718917 0.515596808588 y[1] (closed_form) = 3.27694697247 0.512397521425 absolute error = 0.004141 relative error = 0.1249 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.242 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.909 2.164 h = 0.001 0.003 y[1] (numeric) = 3.27575868628 0.513720026057 y[1] (closed_form) = 3.27838784519 0.510520066308 absolute error = 0.004142 relative error = 0.1248 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.243 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5047.8MB, alloc=52.3MB, time=64.64 x[1] = -0.908 2.167 h = 0.0001 0.004 y[1] (numeric) = 3.28051730998 0.511404020118 y[1] (closed_form) = 3.28314728102 0.508199545994 absolute error = 0.004146 relative error = 0.1248 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.246 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9079 2.171 h = 0.003 0.006 y[1] (numeric) = 3.28713747058 0.510352020465 y[1] (closed_form) = 3.28977255689 0.507142274788 absolute error = 0.004153 relative error = 0.1248 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.25 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9049 2.177 h = 0.0001 0.005 y[1] (numeric) = 3.29644449216 0.504018090875 y[1] (closed_form) = 3.29907734545 0.500787818288 absolute error = 0.004167 relative error = 0.1249 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.257 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9048 2.182 h = 0.0001 0.003 y[1] (numeric) = 3.30474819299 0.502702426784 y[1] (closed_form) = 3.30738909039 0.499463964672 absolute error = 0.004179 relative error = 0.1249 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.262 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9047 2.185 h = 0.001 0.001 y[1] (numeric) = 3.30973074036 0.501836458745 y[1] (closed_form) = 3.31237445485 0.498594966414 absolute error = 0.004183 relative error = 0.1249 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.265 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5093.3MB, alloc=52.3MB, time=65.21 x[1] = -0.9037 2.186 h = 0.001 0.003 y[1] (numeric) = 3.31116630873 0.499930909114 y[1] (closed_form) = 3.3138093935 0.496688748546 absolute error = 0.004183 relative error = 0.1248 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.266 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9027 2.189 h = 0.0001 0.004 y[1] (numeric) = 3.31594181201 0.497551446944 y[1] (closed_form) = 3.3185856755 0.494304763682 absolute error = 0.004187 relative error = 0.1248 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.269 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9026 2.193 h = 0.003 0.006 y[1] (numeric) = 3.32260580103 0.496428865845 y[1] (closed_form) = 3.32525474288 0.493176870116 absolute error = 0.004194 relative error = 0.1248 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.273 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8996 2.199 h = 0.0001 0.005 y[1] (numeric) = 3.33192891729 0.489956527756 y[1] (closed_form) = 3.33457547133 0.486684011528 absolute error = 0.004209 relative error = 0.1249 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.279 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8995 2.204 h = 0.0001 0.003 y[1] (numeric) = 3.34028753348 0.488552728471 y[1] (closed_form) = 3.34294207442 0.485271958426 absolute error = 0.00422 relative error = 0.1249 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.284 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5138.7MB, alloc=52.3MB, time=65.77 x[1] = -0.8994 2.207 h = 0.001 0.001 y[1] (numeric) = 3.34530226441 0.487633349792 y[1] (closed_form) = 3.3479596012 0.484349526914 absolute error = 0.004224 relative error = 0.1249 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.287 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8984 2.208 h = 0.001 0.003 y[1] (numeric) = 3.34673168578 0.485699062938 y[1] (closed_form) = 3.34938838752 0.482414576192 absolute error = 0.004224 relative error = 0.1248 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.288 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8974 2.211 h = 0.0001 0.004 y[1] (numeric) = 3.35152360224 0.48325598614 y[1] (closed_form) = 3.35418104928 0.47996696854 absolute error = 0.004228 relative error = 0.1248 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.292 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8973 2.215 h = 0.003 0.006 y[1] (numeric) = 3.3582309138 0.482062459736 y[1] (closed_form) = 3.36089340211 0.478768088943 absolute error = 0.004236 relative error = 0.1248 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.296 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8943 2.221 h = 0.0001 0.005 y[1] (numeric) = 3.36756909756 0.475451521919 y[1] (closed_form) = 3.37022904339 0.472136637742 absolute error = 0.00425 relative error = 0.1249 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.302 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5184.4MB, alloc=52.3MB, time=66.34 x[1] = -0.8942 2.226 h = 0.0001 0.003 y[1] (numeric) = 3.37598199836 0.473959131 y[1] (closed_form) = 3.37864987362 0.470635929008 absolute error = 0.004262 relative error = 0.1249 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.307 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8941 2.229 h = 0.001 0.001 y[1] (numeric) = 3.38102853034 0.472986073145 y[1] (closed_form) = 3.38369918012 0.469659795814 absolute error = 0.004266 relative error = 0.1249 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.31 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8931 2.23 h = 0.0001 0.004 y[1] (numeric) = 3.38245158666 0.471023079924 y[1] (closed_form) = 3.38512159609 0.467696143117 absolute error = 0.004266 relative error = 0.1248 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.311 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.893 2.234 h = 0.003 0.006 y[1] (numeric) = 3.38919663423 0.46976870354 y[1] (closed_form) = 3.3918716527 0.466436379184 absolute error = 0.004273 relative error = 0.1248 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.315 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.89 2.24 h = 0.0001 0.005 y[1] (numeric) = 3.39854861878 0.463038477052 y[1] (closed_form) = 3.40122096162 0.459685644163 absolute error = 0.004288 relative error = 0.1249 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.322 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5229.9MB, alloc=52.3MB, time=66.91 x[1] = -0.8899 2.245 h = 0.0001 0.003 y[1] (numeric) = 3.40700880215 0.461470102658 y[1] (closed_form) = 3.40968902551 0.458108896411 absolute error = 0.004299 relative error = 0.125 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.326 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8898 2.248 h = 0.001 0.001 y[1] (numeric) = 3.41208304406 0.46045099855 y[1] (closed_form) = 3.41476602375 0.457086697422 absolute error = 0.004303 relative error = 0.1249 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.329 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8888 2.249 h = 0.001 0.003 y[1] (numeric) = 3.41350078858 0.458463241958 y[1] (closed_form) = 3.41618312334 0.45509828509 absolute error = 0.004303 relative error = 0.1249 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.331 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8878 2.252 h = 0.0001 0.004 y[1] (numeric) = 3.41832276528 0.455901561555 y[1] (closed_form) = 3.42100578318 0.452532058665 absolute error = 0.004307 relative error = 0.1248 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.334 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8877 2.256 h = 0.003 0.006 y[1] (numeric) = 3.42511019389 0.454575564376 y[1] (closed_form) = 3.42779818407 0.451200632568 absolute error = 0.004315 relative error = 0.1248 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.338 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5275.6MB, alloc=52.3MB, time=67.48 x[1] = -0.8847 2.262 h = 0.0001 0.005 y[1] (numeric) = 3.43447533579 0.447706382838 y[1] (closed_form) = 3.43716049584 0.444310950924 absolute error = 0.004329 relative error = 0.1249 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.344 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8846 2.267 h = 0.0001 0.003 y[1] (numeric) = 3.44298863071 0.446048568198 y[1] (closed_form) = 3.44568161332 0.442644699469 absolute error = 0.00434 relative error = 0.1249 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.349 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8845 2.27 h = 0.001 0.001 y[1] (numeric) = 3.44809396227 0.444975285651 y[1] (closed_form) = 3.45078967971 0.441568299736 absolute error = 0.004344 relative error = 0.1249 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.352 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8835 2.271 h = 0.001 0.003 y[1] (numeric) = 3.4495049363 0.442958880138 y[1] (closed_form) = 3.45220000354 0.439551242916 absolute error = 0.004345 relative error = 0.1248 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.353 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8825 2.274 h = 0.0001 0.004 y[1] (numeric) = 3.45434199104 0.440333138613 y[1] (closed_form) = 3.45703770794 0.436920947658 absolute error = 0.004349 relative error = 0.1248 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.356 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5321.1MB, alloc=52.3MB, time=68.04 x[1] = -0.8824 2.278 h = 0.003 0.006 y[1] (numeric) = 3.46117129139 0.43893516291 y[1] (closed_form) = 3.463871943 0.435517502852 absolute error = 0.004356 relative error = 0.1248 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.36 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8794 2.284 h = 0.0001 0.005 y[1] (numeric) = 3.47054856237 0.431926848799 y[1] (closed_form) = 3.47324622948 0.428488697765 absolute error = 0.00437 relative error = 0.1249 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.367 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8793 2.289 h = 0.0001 0.003 y[1] (numeric) = 3.47911433298 0.430179146358 y[1] (closed_form) = 3.48181976442 0.426732495346 absolute error = 0.004382 relative error = 0.1249 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.372 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8792 2.292 h = 0.001 0.001 y[1] (numeric) = 3.48425036869 0.429051422209 y[1] (closed_form) = 3.48695851337 0.425601631814 absolute error = 0.004386 relative error = 0.1249 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.375 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8782 2.293 h = 0.001 0.003 y[1] (numeric) = 3.4856543549 0.427006401445 y[1] (closed_form) = 3.48836184414 0.423555964199 absolute error = 0.004386 relative error = 0.1248 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.376 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5366.7MB, alloc=52.3MB, time=68.61 x[1] = -0.8772 2.296 h = 0.0001 0.004 y[1] (numeric) = 3.4905060194 0.424316448938 y[1] (closed_form) = 3.49321412479 0.420861450404 absolute error = 0.00439 relative error = 0.1248 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.379 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8771 2.3 h = 0.003 0.006 y[1] (numeric) = 3.49737668014 0.42284614048 y[1] (closed_form) = 3.50008968251 0.419385632847 absolute error = 0.004397 relative error = 0.1247 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.383 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8741 2.306 h = 0.0001 0.005 y[1] (numeric) = 3.5067650516 0.415698521062 y[1] (closed_form) = 3.50947491522 0.412217532286 absolute error = 0.004411 relative error = 0.1248 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.389 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.874 2.311 h = 0.0001 0.003 y[1] (numeric) = 3.51538266031 0.413860486385 y[1] (closed_form) = 3.51810022977 0.410370934763 absolute error = 0.004423 relative error = 0.1249 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.394 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8739 2.314 h = 0.001 0.001 y[1] (numeric) = 3.52054901364 0.41267805936 y[1] (closed_form) = 3.52326927465 0.409185346267 absolute error = 0.004427 relative error = 0.1248 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.397 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8729 2.315 h = 0.001 0.003 y[1] (numeric) = 3.52194579495 0.410604457994 y[1] (closed_form) = 3.5246653953 0.407111102527 absolute error = 0.004427 relative error = 0.1248 % Correct digits = 3 memory used=5412.4MB, alloc=52.3MB, time=69.18 Radius of convergence (given) for eq 1 = 2.398 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8719 2.318 h = 0.0001 0.004 y[1] (numeric) = 3.52681160045 0.407850146858 y[1] (closed_form) = 3.52953178343 0.404352222705 absolute error = 0.004431 relative error = 0.1247 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.402 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8718 2.322 h = 0.003 0.006 y[1] (numeric) = 3.53372310885 0.406307153917 y[1] (closed_form) = 3.53644815091 0.402803680862 absolute error = 0.004438 relative error = 0.1247 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.405 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8688 2.328 h = 0.0001 0.005 y[1] (numeric) = 3.54312155191 0.399020061249 y[1] (closed_form) = 3.54584330107 0.395496117584 absolute error = 0.004453 relative error = 0.1248 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.412 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8687 2.333 h = 0.0001 0.003 y[1] (numeric) = 3.55179035936 0.397091253025 y[1] (closed_form) = 3.55451975563 0.393558683941 absolute error = 0.004464 relative error = 0.1248 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.417 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8686 2.336 h = 0.001 0.001 y[1] (numeric) = 3.55698664277 0.395853863738 y[1] (closed_form) = 3.5597187088 0.392318111206 absolute error = 0.004468 relative error = 0.1248 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.42 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5457.9MB, alloc=52.3MB, time=69.75 x[1] = -0.8676 2.337 h = 0.0001 0.004 y[1] (numeric) = 3.55837600236 0.393751717396 y[1] (closed_form) = 3.56110740254 0.390215326989 absolute error = 0.004468 relative error = 0.1247 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.421 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8675 2.341 h = 0.003 0.006 y[1] (numeric) = 3.56532313149 0.392146357603 y[1] (closed_form) = 3.56805935789 0.388604384707 absolute error = 0.004476 relative error = 0.1247 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.425 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8645 2.347 h = 0.0001 0.005 y[1] (numeric) = 3.57473108373 0.38473918347 y[1] (closed_form) = 3.5774638845 0.381176747757 absolute error = 0.00449 relative error = 0.1248 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.432 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8644 2.352 h = 0.0001 0.003 y[1] (numeric) = 3.58344453645 0.382732488884 y[1] (closed_form) = 3.58618493431 0.379161373426 absolute error = 0.004501 relative error = 0.1248 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.436 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8643 2.355 h = 0.001 0.001 y[1] (numeric) = 3.58866693045 0.381447933877 y[1] (closed_form) = 3.5914099795 0.377873615879 absolute error = 0.004506 relative error = 0.1248 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.439 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5503.5MB, alloc=52.3MB, time=70.31 x[1] = -0.8633 2.356 h = 0.001 0.003 y[1] (numeric) = 3.59005006767 0.37932115433 y[1] (closed_form) = 3.59279244637 0.375746202285 absolute error = 0.004506 relative error = 0.1247 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.441 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8623 2.359 h = 0.0001 0.004 y[1] (numeric) = 3.59494170777 0.376446856663 y[1] (closed_form) = 3.59768460676 0.372867322182 absolute error = 0.00451 relative error = 0.1247 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.444 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8622 2.363 h = 0.003 0.006 y[1] (numeric) = 3.60192873039 0.374768159413 y[1] (closed_form) = 3.60467641796 0.371183002019 absolute error = 0.004517 relative error = 0.1246 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.448 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8592 2.369 h = 0.0001 0.005 y[1] (numeric) = 3.61134484077 0.3672212 y[1] (closed_form) = 3.61408894879 0.363615591628 absolute error = 0.004531 relative error = 0.1247 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.454 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8591 2.374 h = 0.0001 0.003 y[1] (numeric) = 3.62010830314 0.365122911355 y[1] (closed_form) = 3.62285994901 0.361508561215 absolute error = 0.004543 relative error = 0.1248 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.459 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5549.0MB, alloc=52.3MB, time=70.88 x[1] = -0.859 2.377 h = 0.001 0.001 y[1] (numeric) = 3.62535990644 0.363782911824 y[1] (closed_form) = 3.62811418155 0.360165337369 absolute error = 0.004547 relative error = 0.1247 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.462 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.858 2.378 h = 0.001 0.003 y[1] (numeric) = 3.62673521873 0.361627653617 y[1] (closed_form) = 3.62948881835 0.358009449655 absolute error = 0.004547 relative error = 0.1247 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.463 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.857 2.381 h = 0.0001 0.004 y[1] (numeric) = 3.63163965798 0.358688581564 y[1] (closed_form) = 3.63439374432 0.355065788214 absolute error = 0.004551 relative error = 0.1246 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.466 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8569 2.385 h = 0.003 0.006 y[1] (numeric) = 3.638666058 0.356936201325 y[1] (closed_form) = 3.64142489453 0.353307745807 absolute error = 0.004558 relative error = 0.1246 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.47 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8539 2.391 h = 0.0001 0.005 y[1] (numeric) = 3.64808929675 0.349249302374 y[1] (closed_form) = 3.65084439992 0.345600408415 absolute error = 0.004572 relative error = 0.1247 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.477 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5594.7MB, alloc=52.3MB, time=71.44 x[1] = -0.8538 2.396 h = 0.0001 0.003 y[1] (numeric) = 3.65690212447 0.347058987301 y[1] (closed_form) = 3.65966470602 0.343401289847 absolute error = 0.004584 relative error = 0.1247 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.482 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8537 2.399 h = 0.001 0.001 y[1] (numeric) = 3.66218254662 0.345663289269 y[1] (closed_form) = 3.66494773537 0.342002345835 absolute error = 0.004588 relative error = 0.1246 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.485 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8527 2.4 h = 0.001 0.003 y[1] (numeric) = 3.66354981791 0.34347959082 y[1] (closed_form) = 3.66631432605 0.339818022441 absolute error = 0.004588 relative error = 0.1246 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.486 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8517 2.403 h = 0.0001 0.004 y[1] (numeric) = 3.6684665858 0.340475605277 y[1] (closed_form) = 3.67123154705 0.336809440718 absolute error = 0.004592 relative error = 0.1246 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.489 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8516 2.407 h = 0.003 0.006 y[1] (numeric) = 3.67553184519 0.33864920001 y[1] (closed_form) = 3.6783015181 0.334977334218 absolute error = 0.004599 relative error = 0.1245 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.493 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5640.1MB, alloc=52.3MB, time=72.01 x[1] = -0.8486 2.413 h = 0.0001 0.005 y[1] (numeric) = 3.68496118229 0.330822212047 y[1] (closed_form) = 3.68772696817 0.32712992105 absolute error = 0.004613 relative error = 0.1246 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.499 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8485 2.418 h = 0.0001 0.003 y[1] (numeric) = 3.69382272938 0.328539441314 y[1] (closed_form) = 3.69659593389 0.324838285393 absolute error = 0.004625 relative error = 0.1246 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.504 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8484 2.421 h = 0.001 0.001 y[1] (numeric) = 3.69913157894 0.327087792701 y[1] (closed_form) = 3.70190736852 0.323383369247 absolute error = 0.004629 relative error = 0.1246 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.507 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8474 2.422 h = 0.001 0.003 y[1] (numeric) = 3.70049059343 0.324875693404 y[1] (closed_form) = 3.70326569729 0.321170649586 absolute error = 0.004629 relative error = 0.1245 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.508 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8464 2.425 h = 0.0001 0.004 y[1] (numeric) = 3.705419219 0.321806657484 y[1] (closed_form) = 3.70819474237 0.318097010848 absolute error = 0.004633 relative error = 0.1245 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.512 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5685.6MB, alloc=52.3MB, time=72.58 x[1] = -0.8463 2.429 h = 0.003 0.006 y[1] (numeric) = 3.71252281841 0.319905887669 y[1] (closed_form) = 3.71530301474 0.316190500931 absolute error = 0.00464 relative error = 0.1245 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.515 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8433 2.435 h = 0.0001 0.005 y[1] (numeric) = 3.7219572236 0.311938665999 y[1] (closed_form) = 3.72473337935 0.30820286799 absolute error = 0.004654 relative error = 0.1245 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.522 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8432 2.44 h = 0.0001 0.003 y[1] (numeric) = 3.73086684237 0.309563013519 y[1] (closed_form) = 3.73365035676 0.305818289457 absolute error = 0.004666 relative error = 0.1246 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.527 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8431 2.443 h = 0.001 0.001 y[1] (numeric) = 3.73620372693 0.308055164148 y[1] (closed_form) = 3.73898980416 0.304307151109 absolute error = 0.00467 relative error = 0.1245 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.53 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8421 2.444 h = 0.0001 0.004 y[1] (numeric) = 3.73755426908 0.305814704365 y[1] (closed_form) = 3.74033965552 0.302066075566 absolute error = 0.00467 relative error = 0.1245 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.531 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5731.1MB, alloc=52.3MB, time=73.14 x[1] = -0.842 2.448 h = 0.003 0.006 y[1] (numeric) = 3.74469134521 0.303850101383 y[1] (closed_form) = 3.7474813711 0.300095699669 absolute error = 0.004678 relative error = 0.1244 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.535 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.839 2.454 h = 0.0001 0.005 y[1] (numeric) = 3.75413096039 0.295762102665 y[1] (closed_form) = 3.75691681345 0.291987300404 absolute error = 0.004691 relative error = 0.1245 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.541 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8389 2.459 h = 0.0001 0.003 y[1] (numeric) = 3.763082551 0.293306723975 y[1] (closed_form) = 3.76587571157 0.289522942565 absolute error = 0.004703 relative error = 0.1245 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.546 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8388 2.462 h = 0.001 0.001 y[1] (numeric) = 3.76844392564 0.291750627556 y[1] (closed_form) = 3.77123963011 0.287963538533 absolute error = 0.004707 relative error = 0.1245 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.549 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8378 2.463 h = 0.001 0.003 y[1] (numeric) = 3.76978733986 0.289485684664 y[1] (closed_form) = 3.77258234914 0.285697983801 absolute error = 0.004707 relative error = 0.1244 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.55 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5776.8MB, alloc=52.3MB, time=73.71 x[1] = -0.8368 2.466 h = 0.0001 0.004 y[1] (numeric) = 3.77473755353 0.286295376409 y[1] (closed_form) = 3.77753291981 0.282503060395 absolute error = 0.004711 relative error = 0.1244 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.554 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8367 2.47 h = 0.003 0.006 y[1] (numeric) = 3.78191200318 0.284255778563 y[1] (closed_form) = 3.78471197044 0.280457650168 absolute error = 0.004719 relative error = 0.1243 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.558 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8337 2.476 h = 0.0001 0.005 y[1] (numeric) = 3.7913547704 0.276027277338 y[1] (closed_form) = 3.79415041151 0.272208763628 absolute error = 0.004733 relative error = 0.1244 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.564 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8336 2.481 h = 0.0001 0.003 y[1] (numeric) = 3.80035322804 0.273478224669 y[1] (closed_form) = 3.80315611619 0.269650671236 absolute error = 0.004744 relative error = 0.1244 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.569 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8335 2.484 h = 0.001 0.001 y[1] (numeric) = 3.8057419078 0.271865462334 y[1] (closed_form) = 3.80854731747 0.268034580049 absolute error = 0.004748 relative error = 0.1244 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.572 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5822.3MB, alloc=52.3MB, time=74.27 x[1] = -0.8325 2.485 h = 0.001 0.003 y[1] (numeric) = 3.80707644886 0.269572234084 y[1] (closed_form) = 3.8098811583 0.265740744602 absolute error = 0.004748 relative error = 0.1243 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.573 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8315 2.488 h = 0.0001 0.004 y[1] (numeric) = 3.81203717215 0.266316490453 y[1] (closed_form) = 3.81484220493 0.262480379632 absolute error = 0.004752 relative error = 0.1243 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.576 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8314 2.492 h = 0.003 0.006 y[1] (numeric) = 3.81924847268 0.264201564482 y[1] (closed_form) = 3.82205806728 0.260359602963 absolute error = 0.00476 relative error = 0.1242 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.58 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8284 2.498 h = 0.0001 0.005 y[1] (numeric) = 3.82869336104 0.255832429723 y[1] (closed_form) = 3.8314984763 0.251970098815 absolute error = 0.004773 relative error = 0.1243 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.587 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8283 2.503 h = 0.0001 0.003 y[1] (numeric) = 3.83773803323 0.253189285982 y[1] (closed_form) = 3.84055033481 0.249317855078 absolute error = 0.004785 relative error = 0.1243 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.592 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5867.9MB, alloc=52.3MB, time=74.84 x[1] = -0.8282 2.506 h = 0.001 0.001 y[1] (numeric) = 3.84315362288 0.251519612993 y[1] (closed_form) = 3.84596842351 0.247644832109 absolute error = 0.004789 relative error = 0.1243 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.594 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8272 2.507 h = 0.001 0.003 y[1] (numeric) = 3.84447907604 0.249198142521 y[1] (closed_form) = 3.84729317142 0.245322759105 absolute error = 0.004789 relative error = 0.1242 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.596 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8262 2.51 h = 0.0001 0.004 y[1] (numeric) = 3.84944983638 0.245876835176 y[1] (closed_form) = 3.85226422144 0.241996824389 absolute error = 0.004793 relative error = 0.1242 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.599 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8261 2.514 h = 0.003 0.006 y[1] (numeric) = 3.8566974633 0.243686251305 y[1] (closed_form) = 3.85951637086 0.239800351697 absolute error = 0.004801 relative error = 0.1241 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.603 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8231 2.52 h = 0.0001 0.005 y[1] (numeric) = 3.86614344171 0.235176356758 y[1] (closed_form) = 3.86895771687 0.231270104383 absolute error = 0.004814 relative error = 0.1242 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.609 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5913.5MB, alloc=52.3MB, time=75.41 x[1] = -0.823 2.525 h = 0.0001 0.003 y[1] (numeric) = 3.87523367433 0.232438708011 y[1] (closed_form) = 3.87805507485 0.228523295667 absolute error = 0.004826 relative error = 0.1242 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.614 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8229 2.528 h = 0.001 0.001 y[1] (numeric) = 3.88067577768 0.230711881537 y[1] (closed_form) = 3.88349965468 0.226793098198 absolute error = 0.00483 relative error = 0.1242 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.617 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8219 2.529 h = 0.001 0.003 y[1] (numeric) = 3.88199192848 0.228362212945 y[1] (closed_form) = 3.88481509525 0.224442831761 absolute error = 0.00483 relative error = 0.1241 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.618 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8209 2.532 h = 0.0001 0.004 y[1] (numeric) = 3.8869722529 0.224975215764 y[1] (closed_form) = 3.88979567566 0.221051201333 absolute error = 0.004834 relative error = 0.1241 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.621 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8208 2.536 h = 0.003 0.006 y[1] (numeric) = 3.89425568044 0.222708646755 y[1] (closed_form) = 3.89708358621 0.218778705575 absolute error = 0.004842 relative error = 0.124 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.625 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5959.0MB, alloc=52.3MB, time=75.98 x[1] = -0.8178 2.542 h = 0.0001 0.005 y[1] (numeric) = 3.90370171765 0.214057870938 y[1] (closed_form) = 3.90652483812 0.210107594307 absolute error = 0.004855 relative error = 0.1241 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.632 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8177 2.547 h = 0.0001 0.003 y[1] (numeric) = 3.91283685494 0.211225306411 y[1] (closed_form) = 3.91566703955 0.207265810143 absolute error = 0.004867 relative error = 0.1241 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.637 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8176 2.55 h = 0.001 0.001 y[1] (numeric) = 3.91830507486 0.209441085535 y[1] (closed_form) = 3.9211377133 0.205478197367 absolute error = 0.004871 relative error = 0.1241 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.64 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8166 2.551 h = 0.0001 0.004 y[1] (numeric) = 3.91961170912 0.207063263892 y[1] (closed_form) = 3.92244363236 0.203099782585 absolute error = 0.004871 relative error = 0.124 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.641 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8165 2.555 h = 0.003 0.006 y[1] (numeric) = 3.92692644148 0.204731446275 y[1] (closed_form) = 3.92976281361 0.200762006194 absolute error = 0.004879 relative error = 0.124 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.645 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8135 2.561 h = 0.0001 0.005 y[1] (numeric) = 3.93637338346 0.195959294903 memory used=6004.6MB, alloc=52.3MB, time=76.54 y[1] (closed_form) = 3.93920483856 0.191969533012 absolute error = 0.004892 relative error = 0.124 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.651 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8134 2.566 h = 0.0001 0.003 y[1] (numeric) = 3.94554778409 0.193045227764 y[1] (closed_form) = 3.94838625113 0.189046194384 absolute error = 0.004904 relative error = 0.1241 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.656 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8133 2.569 h = 0.001 0.001 y[1] (numeric) = 3.95103885308 0.191211716885 y[1] (closed_form) = 3.95387975464 0.187209273429 absolute error = 0.004908 relative error = 0.124 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.659 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8123 2.57 h = 0.001 0.003 y[1] (numeric) = 3.95233745916 0.188809582031 y[1] (closed_form) = 3.9551776412 0.184806549446 absolute error = 0.004908 relative error = 0.124 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.66 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8113 2.573 h = 0.0001 0.004 y[1] (numeric) = 3.95733510588 0.18530012391 y[1] (closed_form) = 3.96017548127 0.18129244716 absolute error = 0.004912 relative error = 0.1239 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.664 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8112 2.577 h = 0.003 0.006 y[1] (numeric) = 3.96468466043 0.182891713635 y[1] (closed_form) = 3.96752944541 0.178878039608 absolute error = 0.00492 relative error = 0.1239 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.667 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6050.4MB, alloc=52.3MB, time=77.11 x[1] = -0.8082 2.583 h = 0.0001 0.005 y[1] (numeric) = 3.97412974324 0.173978455353 y[1] (closed_form) = 3.97696945853 0.169944478122 absolute error = 0.004933 relative error = 0.1239 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.674 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8081 2.588 h = 0.0001 0.003 y[1] (numeric) = 3.98334782883 0.170968708655 y[1] (closed_form) = 3.98619449437 0.166925400827 absolute error = 0.004945 relative error = 0.1239 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.679 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.808 2.591 h = 0.001 0.001 y[1] (numeric) = 3.9888642757 0.169077355419 y[1] (closed_form) = 3.99171335295 0.165030616819 absolute error = 0.004949 relative error = 0.1239 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.682 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.807 2.592 h = 0.001 0.003 y[1] (numeric) = 3.99015296694 0.166647151392 y[1] (closed_form) = 3.99300131975 0.162599828408 absolute error = 0.004949 relative error = 0.1238 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.683 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.806 2.595 h = 0.0001 0.004 y[1] (numeric) = 3.99515882397 0.163071649217 y[1] (closed_form) = 3.99800733641 0.15901967664 absolute error = 0.004953 relative error = 0.1238 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.686 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6096.0MB, alloc=52.3MB, time=77.68 x[1] = -0.8059 2.599 h = 0.003 0.006 y[1] (numeric) = 4.00254267172 0.160586325361 y[1] (closed_form) = 4.00539555381 0.15652831814 absolute error = 0.00496 relative error = 0.1238 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.69 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8029 2.605 h = 0.0001 0.005 y[1] (numeric) = 4.01198486369 0.151531852328 y[1] (closed_form) = 4.01483252358 0.147453561202 absolute error = 0.004974 relative error = 0.1238 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.697 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8028 2.61 h = 0.0001 0.003 y[1] (numeric) = 4.02124597383 0.148426024347 y[1] (closed_form) = 4.02410052204 0.14433834382 absolute error = 0.004986 relative error = 0.1238 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.702 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8027 2.613 h = 0.001 0.001 y[1] (numeric) = 4.02678739873 0.146476593305 y[1] (closed_form) = 4.02964433576 0.14238546142 absolute error = 0.00499 relative error = 0.1238 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.704 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8017 2.614 h = 0.001 0.003 y[1] (numeric) = 4.02806596178 0.144018367928 y[1] (closed_form) = 4.03092216947 0.139926656426 absolute error = 0.00499 relative error = 0.1237 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.706 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6141.6MB, alloc=52.3MB, time=78.25 x[1] = -0.8007 2.617 h = 0.0001 0.004 y[1] (numeric) = 4.03307955467 0.140376704129 y[1] (closed_form) = 4.03593588824 0.136280337762 absolute error = 0.004994 relative error = 0.1237 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.709 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8006 2.621 h = 0.003 0.006 y[1] (numeric) = 4.04049716488 0.137814149253 y[1] (closed_form) = 4.04335782801 0.133711711071 absolute error = 0.005001 relative error = 0.1236 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.713 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7976 2.627 h = 0.0001 0.005 y[1] (numeric) = 4.04993543422 0.128618358395 y[1] (closed_form) = 4.0527907228 0.124495656297 absolute error = 0.005015 relative error = 0.1237 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.719 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7975 2.632 h = 0.0001 0.003 y[1] (numeric) = 4.05923890693 0.125416050582 y[1] (closed_form) = 4.06210102164 0.121283900583 absolute error = 0.005027 relative error = 0.1237 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.724 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7974 2.635 h = 0.001 0.001 y[1] (numeric) = 4.06480490908 0.123408308205 y[1] (closed_form) = 4.06766938962 0.119272686377 absolute error = 0.005031 relative error = 0.1236 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.727 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6187.2MB, alloc=52.3MB, time=78.81 x[1] = -0.7964 2.636 h = 0.001 0.003 y[1] (numeric) = 4.06607313089 0.120922110257 y[1] (closed_form) = 4.06893687723 0.116785913599 absolute error = 0.005031 relative error = 0.1236 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.728 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7954 2.639 h = 0.0001 0.004 y[1] (numeric) = 4.07109398482 0.117214169481 y[1] (closed_form) = 4.0739578233 0.113073312843 absolute error = 0.005035 relative error = 0.1235 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.731 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7953 2.643 h = 0.003 0.006 y[1] (numeric) = 4.0785448255 0.114574068698 y[1] (closed_form) = 4.08141295329 0.110427103271 absolute error = 0.005042 relative error = 0.1235 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.735 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7923 2.649 h = 0.0001 0.005 y[1] (numeric) = 4.08797814036 0.105236861702 y[1] (closed_form) = 4.09084074137 0.101069653037 absolute error = 0.005056 relative error = 0.1235 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.742 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7922 2.654 h = 0.0001 0.003 y[1] (numeric) = 4.09732331205 0.101937678687 y[1] (closed_form) = 4.10019267678 0.0977609639293 absolute error = 0.005067 relative error = 0.1236 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.747 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6232.8MB, alloc=52.3MB, time=79.38 x[1] = -0.7921 2.657 h = 0.001 0.001 y[1] (numeric) = 4.10291348975 0.0998713933682 y[1] (closed_form) = 4.10578519725 0.0956911864217 absolute error = 0.005072 relative error = 0.1235 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.75 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7911 2.658 h = 0.0001 0.004 y[1] (numeric) = 4.10417115758 0.0973572725888 y[1] (closed_form) = 4.10704212602 0.0931764956193 absolute error = 0.005072 relative error = 0.1235 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.751 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.791 2.662 h = 0.003 0.006 y[1] (numeric) = 4.11165110418 0.0946505589421 y[1] (closed_form) = 4.1145263272 0.0904636419534 absolute error = 0.005079 relative error = 0.1234 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.755 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.788 2.668 h = 0.0001 0.005 y[1] (numeric) = 4.12108101409 0.0851914748142 y[1] (closed_form) = 4.12395057916 0.0809843311297 absolute error = 0.005093 relative error = 0.1235 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.761 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7879 2.673 h = 0.0001 0.003 y[1] (numeric) = 4.13046270664 0.0818090766175 y[1] (closed_form) = 4.13333898219 0.0775923762464 absolute error = 0.005104 relative error = 0.1235 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.766 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6278.3MB, alloc=52.3MB, time=79.95 x[1] = -0.7878 2.676 h = 0.001 0.001 y[1] (numeric) = 4.13607407256 0.0796924969403 y[1] (closed_form) = 4.13895267119 0.07547228667 absolute error = 0.005108 relative error = 0.1234 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.769 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7868 2.677 h = 0.001 0.003 y[1] (numeric) = 4.13732281755 0.0771542525158 y[1] (closed_form) = 4.14020067291 0.0729334763197 absolute error = 0.005109 relative error = 0.1234 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.77 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7858 2.68 h = 0.0001 0.004 y[1] (numeric) = 4.14235671027 0.0733227594519 y[1] (closed_form) = 4.145234595 0.0690973137717 absolute error = 0.005112 relative error = 0.1233 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.774 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7857 2.684 h = 0.003 0.006 y[1] (numeric) = 4.14986889738 0.0705379153053 y[1] (closed_form) = 4.15275099657 0.0663062920784 absolute error = 0.00512 relative error = 0.1233 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.777 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7827 2.69 h = 0.0001 0.005 y[1] (numeric) = 4.1592919336 0.0609372324809 y[1] (closed_form) = 4.1621682229 0.0566854045213 absolute error = 0.005133 relative error = 0.1233 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.784 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6323.9MB, alloc=52.3MB, time=80.52 x[1] = -0.7826 2.695 h = 0.0001 0.003 y[1] (numeric) = 4.16871409085 0.0574572239206 y[1] (closed_form) = 4.17159702774 0.0531957816486 absolute error = 0.005145 relative error = 0.1233 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.789 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7825 2.698 h = 0.001 0.001 y[1] (numeric) = 4.17434888512 0.0552816706459 y[1] (closed_form) = 4.17723412188 0.0510166983245 absolute error = 0.005149 relative error = 0.1233 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.792 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7815 2.699 h = 0.001 0.003 y[1] (numeric) = 4.17558668046 0.0527155959587 y[1] (closed_form) = 4.17847116915 0.0484500625572 absolute error = 0.005149 relative error = 0.1232 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.793 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7805 2.702 h = 0.0001 0.004 y[1] (numeric) = 4.18062647525 0.0488175024928 y[1] (closed_form) = 4.18351095952 0.0445472949392 absolute error = 0.005153 relative error = 0.1232 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.796 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7804 2.706 h = 0.003 0.006 y[1] (numeric) = 4.18817036772 0.0459542193319 y[1] (closed_form) = 4.19105902577 0.0416777978225 absolute error = 0.005161 relative error = 0.1231 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.8 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6369.5MB, alloc=52.3MB, time=81.08 x[1] = -0.7774 2.712 h = 0.0001 0.005 y[1] (numeric) = 4.19758549817 0.0362118531132 y[1] (closed_form) = 4.20046819454 0.0319152495217 absolute error = 0.005174 relative error = 0.1232 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.807 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7773 2.717 h = 0.0001 0.003 y[1] (numeric) = 4.20704745205 0.0326338479184 y[1] (closed_form) = 4.20993673289 0.0283275726961 absolute error = 0.005186 relative error = 0.1232 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.811 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7772 2.72 h = 0.001 0.001 y[1] (numeric) = 4.21270527035 0.0303990949376 y[1] (closed_form) = 4.21559682775 0.0260892696289 absolute error = 0.00519 relative error = 0.1231 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.814 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7762 2.721 h = 0.001 0.003 y[1] (numeric) = 4.21393190418 0.0278052424606 y[1] (closed_form) = 4.21682270872 0.023494860938 absolute error = 0.00519 relative error = 0.1231 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.816 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7752 2.724 h = 0.0001 0.004 y[1] (numeric) = 4.21897712488 0.023840441795 y[1] (closed_form) = 4.22186789121 0.0195253816087 absolute error = 0.005194 relative error = 0.123 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.819 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6415.2MB, alloc=52.3MB, time=81.66 x[1] = -0.7751 2.728 h = 0.003 0.006 y[1] (numeric) = 4.22655218593 0.0208984145854 y[1] (closed_form) = 4.2294470852 0.0165771042328 absolute error = 0.005201 relative error = 0.123 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.823 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7721 2.734 h = 0.0001 0.005 y[1] (numeric) = 4.2359583785 0.0110142850296 y[1] (closed_form) = 4.23884716446 0.00667281593264 absolute error = 0.005215 relative error = 0.123 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.829 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.772 2.739 h = 0.0001 0.003 y[1] (numeric) = 4.2454594594 0.00733790012302 y[1] (closed_form) = 4.24835476648 0.00298670238474 absolute error = 0.005226 relative error = 0.123 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.834 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7719 2.742 h = 0.001 0.001 y[1] (numeric) = 4.25113989653 0.0050437232568 y[1] (closed_form) = 4.25403745677 0.000688955508971 absolute error = 0.005231 relative error = 0.123 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.837 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7709 2.743 h = 0.001 0.003 y[1] (numeric) = 4.25235515728 0.00242214641505 y[1] (closed_form) = 4.2552519599 -0.00193317266055 absolute error = 0.005231 relative error = 0.1229 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.838 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6460.8MB, alloc=52.3MB, time=82.23 x[1] = -0.7699 2.746 h = 0.0001 0.004 y[1] (numeric) = 4.25740532739 -0.00160946603077 y[1] (closed_form) = 4.26030205801 -0.00596946812552 absolute error = 0.005235 relative error = 0.1229 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.841 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7698 2.75 h = 0.003 0.006 y[1] (numeric) = 4.26501101903 -0.00463053976074 y[1] (closed_form) = 4.2679118416 -0.00899682803288 absolute error = 0.005242 relative error = 0.1228 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.845 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7668 2.756 h = 0.0001 0.005 y[1] (numeric) = 4.27440724161 -0.0146565078434 y[1] (closed_form) = 4.27730179939 -0.0190429308362 absolute error = 0.005255 relative error = 0.1229 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.852 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7667 2.761 h = 0.0001 0.003 y[1] (numeric) = 4.28394677841 -0.0184316523423 y[1] (closed_form) = 4.2868477937 -0.022827860678 absolute error = 0.005267 relative error = 0.1229 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.857 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7666 2.764 h = 0.001 0.001 y[1] (numeric) = 4.28964942825 -0.0207854753413 y[1] (closed_form) = 4.29255267323 -0.0251852734961 absolute error = 0.005271 relative error = 0.1228 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.86 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6506.3MB, alloc=52.3MB, time=82.79 x[1] = -0.7656 2.765 h = 0.0001 0.004 y[1] (numeric) = 4.29085310468 -0.0234347221726 y[1] (closed_form) = 4.29375558732 -0.0278350667488 absolute error = 0.005271 relative error = 0.1228 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.861 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7655 2.769 h = 0.003 0.006 y[1] (numeric) = 4.29848567721 -0.0265237215389 y[1] (closed_form) = 4.30139221645 -0.0309303827178 absolute error = 0.005279 relative error = 0.1227 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.865 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7625 2.775 h = 0.0001 0.005 y[1] (numeric) = 4.30787418216 -0.0366719715719 y[1] (closed_form) = 4.31077432605 -0.0410987480456 absolute error = 0.005292 relative error = 0.1228 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.871 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7624 2.78 h = 0.0001 0.003 y[1] (numeric) = 4.31744746446 -0.0405319796106 y[1] (closed_form) = 4.3203540116 -0.044968590748 absolute error = 0.005304 relative error = 0.1228 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.876 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7623 2.783 h = 0.001 0.001 y[1] (numeric) = 4.32316962247 -0.0429370625074 y[1] (closed_form) = 4.32607837926 -0.0473772807048 absolute error = 0.005308 relative error = 0.1227 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.879 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7613 2.784 h = 0.001 0.003 y[1] (numeric) = 4.32436348729 -0.0456102238867 y[1] (closed_form) = 4.32727147762 -0.0500509843223 absolute error = 0.005308 relative error = 0.1227 % Correct digits = 3 memory used=6551.9MB, alloc=52.3MB, time=83.36 Radius of convergence (given) for eq 1 = 2.88 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7603 2.787 h = 0.0001 0.004 y[1] (numeric) = 4.32942239654 -0.0497663826744 y[1] (closed_form) = 4.332330252 -0.0542118342208 absolute error = 0.005312 relative error = 0.1226 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.883 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7602 2.791 h = 0.003 0.006 y[1] (numeric) = 4.33708459855 -0.0529349900987 y[1] (closed_form) = 4.33999646971 -0.0573867947917 absolute error = 0.00532 relative error = 0.1226 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.887 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7572 2.797 h = 0.0001 0.005 y[1] (numeric) = 4.34646121375 -0.0632252182217 y[1] (closed_form) = 4.34936653838 -0.0676971129094 absolute error = 0.005333 relative error = 0.1226 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.894 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7571 2.802 h = 0.0001 0.003 y[1] (numeric) = 4.35607170356 -0.0671846922376 y[1] (closed_form) = 4.35898336739 -0.0716664777173 absolute error = 0.005345 relative error = 0.1226 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.899 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.757 2.805 h = 0.001 0.001 y[1] (numeric) = 4.36181531886 -0.0696498345322 y[1] (closed_form) = 4.36472916872 -0.0741352466701 absolute error = 0.005349 relative error = 0.1225 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.902 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6597.5MB, alloc=52.3MB, time=83.92 x[1] = -0.756 2.806 h = 0.001 0.003 y[1] (numeric) = 4.36299720648 -0.0723505647042 y[1] (closed_form) = 4.36591028518 -0.0768365141365 absolute error = 0.005349 relative error = 0.1225 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.903 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.755 2.809 h = 0.0001 0.004 y[1] (numeric) = 4.36805970145 -0.0765738278979 y[1] (closed_form) = 4.37097261147 -0.0810644723498 absolute error = 0.005353 relative error = 0.1224 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.906 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7549 2.813 h = 0.003 0.006 y[1] (numeric) = 4.37575099186 -0.0798223394218 y[1] (closed_form) = 4.37866787616 -0.0843193724611 absolute error = 0.00536 relative error = 0.1224 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.91 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7519 2.819 h = 0.0001 0.005 y[1] (numeric) = 4.38511468519 -0.09025460724 y[1] (closed_form) = 4.38802487194 -0.0947717042902 absolute error = 0.005373 relative error = 0.1224 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.917 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7518 2.824 h = 0.0001 0.003 y[1] (numeric) = 4.39476170704 -0.0943139179667 y[1] (closed_form) = 4.39767816871 -0.0988409616267 absolute error = 0.005385 relative error = 0.1224 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.921 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6643.0MB, alloc=52.3MB, time=84.48 x[1] = -0.7517 2.827 h = 0.001 0.001 y[1] (numeric) = 4.40052637102 -0.0968393363802 y[1] (closed_form) = 4.403444995 -0.101370026182 absolute error = 0.005389 relative error = 0.1224 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.924 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7507 2.828 h = 0.001 0.003 y[1] (numeric) = 4.40169607109 -0.0995675782552 y[1] (closed_form) = 4.40461391926 -0.104098800388 absolute error = 0.005389 relative error = 0.1223 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.926 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7497 2.831 h = 0.0001 0.004 y[1] (numeric) = 4.40676167409 -0.10385804188 y[1] (closed_form) = 4.40967931974 -0.108393962785 absolute error = 0.005393 relative error = 0.1223 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.929 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7496 2.835 h = 0.003 0.006 y[1] (numeric) = 4.4144815103 -0.107186750069 y[1] (closed_form) = 4.41740308865 -0.111729094801 absolute error = 0.005401 relative error = 0.1222 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.933 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7466 2.841 h = 0.0001 0.005 y[1] (numeric) = 4.42383124968 -0.117761114443 y[1] (closed_form) = 4.42674597964 -0.12232349652 absolute error = 0.005414 relative error = 0.1223 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.939 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6688.6MB, alloc=52.3MB, time=85.04 x[1] = -0.7465 2.846 h = 0.0001 0.003 y[1] (numeric) = 4.43351412662 -0.121920629404 y[1] (closed_form) = 4.43643506698 -0.126493013597 absolute error = 0.005426 relative error = 0.1222 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.944 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7464 2.849 h = 0.001 0.001 y[1] (numeric) = 4.43929942978 -0.124506538719 y[1] (closed_form) = 4.44222250866 -0.129082588423 absolute error = 0.00543 relative error = 0.1222 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.947 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7454 2.85 h = 0.001 0.003 y[1] (numeric) = 4.4404567323 -0.127262234262 y[1] (closed_form) = 4.44337903072 -0.131838811314 absolute error = 0.00543 relative error = 0.1222 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.948 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7444 2.853 h = 0.0001 0.004 y[1] (numeric) = 4.44552496535 -0.131619992125 y[1] (closed_form) = 4.44844702741 -0.136201271546 absolute error = 0.005434 relative error = 0.1221 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.951 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7443 2.857 h = 0.003 0.006 y[1] (numeric) = 4.45327280356 -0.135029186969 y[1] (closed_form) = 4.45619875661 -0.139616925256 absolute error = 0.005441 relative error = 0.122 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.955 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6734.2MB, alloc=52.3MB, time=85.61 x[1] = -0.7413 2.863 h = 0.0001 0.005 y[1] (numeric) = 4.46260755699 -0.145745700019 y[1] (closed_form) = 4.46552651096 -0.150353448302 absolute error = 0.005455 relative error = 0.1221 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.962 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7412 2.868 h = 0.0001 0.003 y[1] (numeric) = 4.4723256106 -0.150005783524 y[1] (closed_form) = 4.47525071023 -0.154623589118 absolute error = 0.005466 relative error = 0.1221 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.967 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7411 2.871 h = 0.001 0.001 y[1] (numeric) = 4.47813114259 -0.152652396581 y[1] (closed_form) = 4.48105835687 -0.15727388694 absolute error = 0.005471 relative error = 0.122 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.97 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7401 2.872 h = 0.001 0.003 y[1] (numeric) = 4.47927583789 -0.155435486815 y[1] (closed_form) = 4.48220226709 -0.160057499519 absolute error = 0.005471 relative error = 0.122 % Correct digits = 3 Radius of convergence (given) for eq 1 = 2.971 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = cos ( sqrt ( 2.0 * x + 3.0 ) ) ; Iterations = 754 Total Elapsed Time = 1 Minutes 26 Seconds Expected Time Remaining = 0 Seconds Optimized Time Remaining = 0 Seconds Expected Total Time = 1 Minutes 26 Seconds > quit memory used=6776.4MB, alloc=52.3MB, time=86.10