|\^/| Maple 2016 (X86 64 LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2016 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. #BEGIN OUTFILE1 # before write maple top matter # before write_ats library and user def block #BEGIN ATS LIBRARY BLOCK # Begin Function number 2 > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s\n",str); > fi;# end if 1; > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc # End Function number 2 # Begin Function number 3 > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s",str); > fi;# end if 1; > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc # End Function number 3 # Begin Function number 4 > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > print(label,str); > fi;# end if 1; > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc # End Function number 4 # Begin Function number 5 > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc # End Function number 5 # Begin Function number 6 > omniout_complex := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > if vallen = 4 then > printf("%-30s = %-20.4g %-20g %s \n",prelabel,Re(value), Im(value), postlabel); > else > printf("%-30s = %-20.12g %-20.12g %s \n",prelabel,Re(value),Im(value), postlabel); > fi;# end if 0; > fi;# end if -1; > end; omniout_complex := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-20.4g %-20g %s \n", prelabel, Re(value), Im(value), postlabel) else printf("%-30s = %-20.12g %-20.12g %s \n", prelabel, Re(value), Im(value), postlabel) end if end if end proc # End Function number 6 # Begin Function number 7 > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number -1 > if vallen = 5 then # if number 0 > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi;# end if 0; > fi;# end if -1; > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc # End Function number 7 # Begin Function number 8 > logitem_time := proc(fd,secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > fprintf(fd,""); > if (secs_in >= 0) then # if number -1 > years_int := int_trunc(secs_in / glob_sec_in_year); > sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year); > days_int := int_trunc(sec_temp / glob_sec_in_day) ; > sec_temp := sec_temp mod int_trunc(glob_sec_in_day) ; > hours_int := int_trunc(sec_temp / glob_sec_in_hour); > sec_temp := sec_temp mod int_trunc(glob_sec_in_hour); > minutes_int := int_trunc(sec_temp / glob_sec_in_minute); > sec_int := sec_temp mod int_trunc(glob_sec_in_minute); > if (years_int > 0) then # if number 0 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 1 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 2 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 3 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 3 > else > fprintf(fd," 0.0 Seconds"); > fi;# end if 2 > fprintf(fd,"\n"); > end; logitem_time := proc(fd, secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; fprintf(fd, ""); if 0 <= secs_in then years_int := int_trunc(secs_in/glob_sec_in_year); sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year); days_int := int_trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod int_trunc(glob_sec_in_day); hours_int := int_trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod int_trunc(glob_sec_in_hour); minutes_int := int_trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod int_trunc(glob_sec_in_minute); if 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, " 0.0 Seconds") end if; fprintf(fd, "\n") end proc # End Function number 8 # Begin Function number 9 > omniout_timestr := proc(secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > if (secs_in >= 0) then # if number 2 > years_int := int_trunc(secs_in / glob_sec_in_year); > sec_temp := (int_trunc(secs_in) mod int_trunc(glob_sec_in_year)); > days_int := int_trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod int_trunc(glob_sec_in_day)) ; > hours_int := int_trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod int_trunc(glob_sec_in_hour)); > minutes_int := int_trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod int_trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 3 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 4 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 5 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 6 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 6 > else > printf(" 0.0 Seconds\n"); > fi;# end if 5 > end; omniout_timestr := proc(secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; if 0 <= secs_in then years_int := int_trunc(secs_in/glob_sec_in_year); sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year); days_int := int_trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod int_trunc(glob_sec_in_day); hours_int := int_trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod int_trunc(glob_sec_in_hour); minutes_int := int_trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod int_trunc(glob_sec_in_minute); if 0 < years_int then printf( " = %d Years %d Days %d Hours %d Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" 0.0 Seconds\n") end if end proc # End Function number 9 # Begin Function number 10 > zero_ats_ar := proc(arr_a) > global ATS_MAX_TERMS; > local iii; > iii := 1; > while (iii <= ATS_MAX_TERMS) do # do number 1 > arr_a [iii] := glob__0; > iii := iii + 1; > od;# end do number 1 > end; zero_ats_ar := proc(arr_a) local iii; global ATS_MAX_TERMS; iii := 1; while iii <= ATS_MAX_TERMS do arr_a[iii] := glob__0; iii := iii + 1 end do end proc # End Function number 10 # Begin Function number 11 > ats := proc(mmm_ats,arr_a,arr_b,jjj_ats) > global ATS_MAX_TERMS; > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := glob__0; > if (jjj_ats <= mmm_ats) then # if number 5 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > if ((lll_ats <= ATS_MAX_TERMS and (iii_ats <= ATS_MAX_TERMS) )) then # if number 6 > ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]); > fi;# end if 6; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 5; > ret_ats; > end; ats := proc(mmm_ats, arr_a, arr_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; global ATS_MAX_TERMS; ret_ats := glob__0; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; if lll_ats <= ATS_MAX_TERMS and iii_ats <= ATS_MAX_TERMS then ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]) end if; iii_ats := iii_ats + 1 end do end if; ret_ats end proc # End Function number 11 # Begin Function number 12 > att := proc(mmm_att,arr_aa,arr_bb,jjj_att) > global ATS_MAX_TERMS; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := glob__0; > if (jjj_att < mmm_att) then # if number 5 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while ((iii_att < mmm_att) and (iii_att <= ATS_MAX_TERMS) ) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if ((lll_att <= ATS_MAX_TERMS and (iii_att <= ATS_MAX_TERMS) )) then # if number 6 > ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att); > fi;# end if 6; > iii_att := iii_att + 1; > od;# end do number 1; > ret_att := ret_att / c(mmm_att) ; > fi;# end if 5; > ret_att; > end; att := proc(mmm_att, arr_aa, arr_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global ATS_MAX_TERMS; ret_att := glob__0; if jjj_att < mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att < mmm_att and iii_att <= ATS_MAX_TERMS do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= ATS_MAX_TERMS and iii_att <= ATS_MAX_TERMS then ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])*c(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/c(mmm_att) end if; ret_att end proc # End Function number 12 # Begin Function number 13 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc # End Function number 13 # Begin Function number 14 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc # End Function number 14 # Begin Function number 15 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc # End Function number 15 # Begin Function number 16 > logitem_good_digits := proc(file,rel_error) > global glob_small_float,glob_prec; > local good_digits; > fprintf(file,""); > fprintf(file,"%d",glob_min_good_digits); > fprintf(file,""); > end; logitem_good_digits := proc(file, rel_error) local good_digits; global glob_small_float, glob_prec; fprintf(file, ""); fprintf(file, "%d", glob_min_good_digits); fprintf(file, "") end proc # End Function number 16 # Begin Function number 17 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc # End Function number 17 # Begin Function number 18 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc # End Function number 18 # Begin Function number 19 > logitem_complex := proc(file,x) > fprintf(file,""); > fprintf(file,"%g + %g I",Re(x),Im(x)); > fprintf(file,""); > end; logitem_complex := proc(file, x) fprintf(file, ""); fprintf(file, "%g + %g I", Re(x), Im(x)); fprintf(file, "") end proc # End Function number 19 # Begin Function number 20 > logitem_h_reason := proc(file) > global glob_h_reason; > fprintf(file,""); > if (glob_h_reason = 1) then # if number 5 > fprintf(file,"Max H"); > elif > (glob_h_reason = 2) then # if number 6 > fprintf(file,"Display Interval"); > elif > (glob_h_reason = 3) then # if number 7 > fprintf(file,"Optimal"); > elif > (glob_h_reason = 4) then # if number 8 > fprintf(file,"Pole Accuracy"); > elif > (glob_h_reason = 5) then # if number 9 > fprintf(file,"Min H (Pole)"); > elif > (glob_h_reason = 6) then # if number 10 > fprintf(file,"Pole"); > elif > (glob_h_reason = 7) then # if number 11 > fprintf(file,"Opt Iter"); > else > fprintf(file,"Impossible"); > fi;# end if 11 > fprintf(file,""); > end; logitem_h_reason := proc(file) global glob_h_reason; fprintf(file, ""); if glob_h_reason = 1 then fprintf(file, "Max H") elif glob_h_reason = 2 then fprintf(file, "Display Interval") elif glob_h_reason = 3 then fprintf(file, "Optimal") elif glob_h_reason = 4 then fprintf(file, "Pole Accuracy") elif glob_h_reason = 5 then fprintf(file, "Min H (Pole)") elif glob_h_reason = 6 then fprintf(file, "Pole") elif glob_h_reason = 7 then fprintf(file, "Opt Iter") else fprintf(file, "Impossible") end if; fprintf(file, "") end proc # End Function number 20 # Begin Function number 21 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc # End Function number 21 # Begin Function number 22 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, "\n") end proc # End Function number 22 # Begin Function number 23 > chk_data := proc() > global glob_max_iter,ALWAYS, ATS_MAX_TERMS; > local errflag; > errflag := false; > if (glob_max_iter < 2) then # if number 11 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 11; > if (errflag) then # if number 11 > quit; > fi;# end if 11 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, ATS_MAX_TERMS; errflag := false; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc # End Function number 23 # Begin Function number 24 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := c(clock_sec2); > sub1 := c(t_end2-t_start2); > sub2 := c(t2-t_start2); > if (sub1 = glob__0) then # if number 11 > sec_left := glob__0; > else > if (sub2 > glob__0) then # if number 12 > rrr := (sub1/sub2); > sec_left := rrr * c(ms2) - c(ms2); > else > sec_left := glob__0; > fi;# end if 12 > fi;# end if 11; > sec_left; > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := c(clock_sec2); sub1 := c(t_end2 - t_start2); sub2 := c(t2 - t_start2); if sub1 = glob__0 then sec_left := glob__0 else if glob__0 < sub2 then rrr := sub1/sub2; sec_left := rrr*c(ms2) - c(ms2) else sec_left := glob__0 end if end if; sec_left end proc # End Function number 24 # Begin Function number 25 > comp_percent := proc(t_end2,t_start2, t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub2 > glob_small_float) then # if number 11 > rrr := (glob__100*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 11; > rrr; > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < sub2 then rrr := glob__100*sub2/sub1 else rrr := 0. end if; rrr end proc # End Function number 25 # Begin Function number 26 > comp_rad_from_ratio := proc(term1,term2,last_no) > #TOP TWO TERM RADIUS ANALYSIS > global glob_h,glob_larger_float; > local ret; > if (float_abs(term2) > glob__0) then # if number 11 > ret := float_abs(term1 * glob_h / term2); > else > ret := glob_larger_float; > fi;# end if 11; > ret; > #BOTTOM TWO TERM RADIUS ANALYSIS > end; comp_rad_from_ratio := proc(term1, term2, last_no) local ret; global glob_h, glob_larger_float; if glob__0 < float_abs(term2) then ret := float_abs(term1*glob_h/term2) else ret := glob_larger_float end if; ret end proc # End Function number 26 # Begin Function number 27 > comp_ord_from_ratio := proc(term1,term2,last_no) > #TOP TWO TERM ORDER ANALYSIS > global glob_h,glob_larger_float; > local ret; > if (float_abs(term2) > glob__0) then # if number 11 > ret := glob__1 + float_abs(term2) * c(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(c(last_no)); > else > ret := glob_larger_float; > fi;# end if 11; > ret; > #BOTTOM TWO TERM ORDER ANALYSIS > end; comp_ord_from_ratio := proc(term1, term2, last_no) local ret; global glob_h, glob_larger_float; if glob__0 < float_abs(term2) then ret := glob__1 + float_abs(term2)* c(last_no)*ln(float_abs(term1*glob_h/term2))/ln(c(last_no)) else ret := glob_larger_float end if; ret end proc # End Function number 27 # Begin Function number 28 > c := proc(in_val) > #To Force Conversion when needed > local ret; > ret := evalc(in_val); > ret; > #End Conversion > end; c := proc(in_val) local ret; ret := evalc(in_val); ret end proc # End Function number 28 # Begin Function number 29 > comp_rad_from_three_terms := proc(term1,term2,term3,last_no) > #TOP THREE TERM RADIUS ANALYSIS > global glob_h,glob_larger_float; > local ret,temp; > temp := float_abs(term2*term2*c(last_no)+glob__m2*term2*term2-term1*term3*c(last_no)+term1*term3); > if (float_abs(temp) > glob__0) then # if number 11 > ret := float_abs((term2*glob_h*term1)/(temp)); > else > ret := glob_larger_float; > fi;# end if 11; > ret; > #BOTTOM THREE TERM RADIUS ANALYSIS > end; comp_rad_from_three_terms := proc(term1, term2, term3, last_no) local ret, temp; global glob_h, glob_larger_float; temp := float_abs(term2*term2*c(last_no) + glob__m2*term2*term2 - term1*term3*c(last_no) + term1*term3); if glob__0 < float_abs(temp) then ret := float_abs(term2*glob_h*term1/temp) else ret := glob_larger_float end if; ret end proc # End Function number 29 # Begin Function number 30 > comp_ord_from_three_terms := proc(term1,term2,term3,last_no) > #TOP THREE TERM ORDER ANALYSIS > local ret; > ret := float_abs((glob__4*term1*term3*c(last_no)-glob__3*term1*term3-glob__4*term2*term2*c(last_no)+glob__4*term2*term2+term2*term2*c(last_no*last_no)-term1*term3*c(last_no*last_no))/(term2*term2*c(last_no)-glob__2*term2*term2-term1*term3*c(last_no)+term1*term3)); > ret; > #TOP THREE TERM ORDER ANALYSIS > end; comp_ord_from_three_terms := proc(term1, term2, term3, last_no) local ret; ret := float_abs((glob__4*term1*term3*c(last_no) - glob__3*term1*term3 - glob__4*term2*term2*c(last_no) + glob__4*term2*term2 + term2*term2*c(last_no*last_no) - term1*term3*c(last_no*last_no)) /(term2*term2*c(last_no) - glob__2*term2*term2 - term1*term3*c(last_no) + term1*term3)); ret end proc # End Function number 30 # Begin Function number 31 > comp_rad_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no) > #TOP SIX TERM RADIUS ANALYSIS > global glob_h,glob_larger_float,glob_six_term_ord_save; > local ret,rm0,rm1,rm2,rm3,rm4,nr1,nr2,dr1,dr2,ds2,rad_c,ord_no,ds1,rcs; > if ((term5 <> glob__0) and (term4 <> glob__0) and (term3 <> glob__0) and (term2 <> glob__0) and (term1 <> glob__0)) then # if number 11 > rm0 := term6/term5; > rm1 := term5/term4; > rm2 := term4/term3; > rm3 := term3/term2; > rm4 := term2/term1; > nr1 := c(last_no-1)*rm0 - glob__2*c(last_no-2)*rm1 + c(last_no-3)*rm2; > nr2 := c(last_no-2)*rm1 - glob__2*c(last_no-3)*rm2 + c(last_no-4)*rm3; > dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3; > dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4; > ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3; > ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4; > if ((float_abs(nr1 * dr2 - nr2 * dr1) = glob__0) or (float_abs(dr1) = glob__0)) then # if number 12 > rad_c := glob_larger_float; > ord_no := glob_larger_float; > else > if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0) then # if number 13 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) -c(last_no)/glob__2; > if (float_abs(rcs) <> glob__0) then # if number 14 > if (rcs > glob__0) then # if number 15 > rad_c := float_abs( sqrt(rcs) * float_abs(glob_h)); > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 15 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 14 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 13 > fi;# end if 12 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 11; > glob_six_term_ord_save := ord_no; > rad_c; > #BOTTOM SIX TERM RADIUS ANALYSIS > end; comp_rad_from_six_terms := proc( term1, term2, term3, term4, term5, term6, last_no) local ret, rm0, rm1, rm2, rm3, rm4, nr1, nr2, dr1, dr2, ds2, rad_c, ord_no, ds1, rcs; global glob_h, glob_larger_float, glob_six_term_ord_save; if term5 <> glob__0 and term4 <> glob__0 and term3 <> glob__0 and term2 <> glob__0 and term1 <> glob__0 then rm0 := term6/term5; rm1 := term5/term4; rm2 := term4/term3; rm3 := term3/term2; rm4 := term2/term1; nr1 := c(last_no - 1)*rm0 - glob__2*c(last_no - 2)*rm1 + c(last_no - 3)*rm2; nr2 := c(last_no - 2)*rm1 - glob__2*c(last_no - 3)*rm2 + c(last_no - 4)*rm3; dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3; dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4; ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3; ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4; if float_abs(nr1*dr2 - nr2*dr1) = glob__0 or float_abs(dr1) = glob__0 then rad_c := glob_larger_float; ord_no := glob_larger_float else if glob__0 < float_abs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) - c(last_no)/glob__2; if float_abs(rcs) <> glob__0 then if glob__0 < rcs then rad_c := float_abs(sqrt(rcs)*float_abs(glob_h)) else rad_c := glob_larger_float; ord_no := glob_larger_float end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if; glob_six_term_ord_save := ord_no; rad_c end proc # End Function number 31 # Begin Function number 32 > comp_ord_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no) > global glob_six_term_ord_save; > #TOP SIX TERM ORDER ANALYSIS > #TOP SAVED FROM SIX TERM RADIUS ANALYSIS > glob_six_term_ord_save; > #BOTTOM SIX TERM ORDER ANALYSIS > end; comp_ord_from_six_terms := proc( term1, term2, term3, term4, term5, term6, last_no) global glob_six_term_ord_save; glob_six_term_ord_save end proc # End Function number 32 # Begin Function number 33 > factorial_2 := proc(nnn) > ret := nnn!; > ret;; > end; Warning, `ret` is implicitly declared local to procedure `factorial_2` factorial_2 := proc(nnn) local ret; ret := nnn!; ret end proc # End Function number 33 # Begin Function number 34 > factorial_1 := proc(nnn) > global ATS_MAX_TERMS,array_fact_1; > local ret; > if (nnn <= ATS_MAX_TERMS) then # if number 11 > if (array_fact_1[nnn] = 0) then # if number 12 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 12; > else > ret := factorial_2(nnn); > fi;# end if 11; > ret; > end; factorial_1 := proc(nnn) local ret; global ATS_MAX_TERMS, array_fact_1; if nnn <= ATS_MAX_TERMS then if array_fact_1[nnn] = 0 then ret := factorial_2(nnn); array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := factorial_2(nnn) end if; ret end proc # End Function number 34 # Begin Function number 35 > factorial_3 := proc(mmm,nnn) > global ATS_MAX_TERMS,array_fact_2; > local ret; > if ((nnn <= ATS_MAX_TERMS) and (mmm <= ATS_MAX_TERMS)) then # if number 11 > if (array_fact_2[mmm,nnn] = 0) then # if number 12 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 12; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 11; > ret; > end; factorial_3 := proc(mmm, nnn) local ret; global ATS_MAX_TERMS, array_fact_2; if nnn <= ATS_MAX_TERMS and mmm <= ATS_MAX_TERMS then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := factorial_2(mmm)/factorial_2(nnn) end if; ret end proc # End Function number 35 # Begin Function number 36 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc # End Function number 36 # Begin Function number 37 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc # End Function number 37 # Begin Function number 38 > float_abs := proc(x) > abs(x); > end; float_abs := proc(x) abs(x) end proc # End Function number 38 # Begin Function number 39 > expt := proc(x,y) > x^y; > end; expt := proc(x, y) x^y end proc # End Function number 39 # Begin Function number 40 > neg := proc(x) > -x; > end; neg := proc(x) -x end proc # End Function number 40 # Begin Function number 41 > int_trunc := proc(x) > trunc(x); > end; int_trunc := proc(x) trunc(x) end proc # End Function number 41 # Begin Function number 42 > estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer) > local desired_abs_gbl_error,range,estimated_steps,step_error; > global glob_desired_digits_correct,ALWAYS,ATS_MAX_TERMS; > omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,""); > desired_abs_gbl_error := expt(glob__10,c( -glob_desired_digits_correct)) * c(float_abs(c(estimated_answer))); > omniout_float(ALWAYS,"estimated_h",32,estimated_h,32,""); > omniout_float(ALWAYS,"estimated_answer",32,estimated_answer,32,""); > omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,""); > range := (x_end - x_start); > omniout_float(ALWAYS,"range",32,range,32,""); > estimated_steps := range / estimated_h; > omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,""); > step_error := (c(float_abs(desired_abs_gbl_error) /sqrt(c( estimated_steps))/c(ATS_MAX_TERMS))); > omniout_float(ALWAYS,"step_error",32,step_error,32,""); > (step_error);; > end; estimated_needed_step_error := proc( x_start, x_end, estimated_h, estimated_answer) local desired_abs_gbl_error, range, estimated_steps, step_error; global glob_desired_digits_correct, ALWAYS, ATS_MAX_TERMS; omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""); desired_abs_gbl_error := expt(glob__10, c(-glob_desired_digits_correct))* c(float_abs(c(estimated_answer))); omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, ""); omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, "") ; omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""); range := x_end - x_start; omniout_float(ALWAYS, "range", 32, range, 32, ""); estimated_steps := range/estimated_h; omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, ""); step_error := c(float_abs(desired_abs_gbl_error)/( sqrt(c(estimated_steps))*c(ATS_MAX_TERMS))); omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""); step_error end proc # End Function number 42 #END ATS LIBRARY BLOCK #BEGIN USER FUNCTION BLOCK #BEGIN BLOCK 3 #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > return(c(20.0) * sqrt(c(0.1) * c(x) + c(0.2)) * sinh( sqrt(c(0.1) * c(x) + c(0.2))) - c(20.0) * cosh( sqrt(c(0.1) * c(x) + c(0.2)))); > end; exact_soln_y := proc(x) return c(20.0)*sqrt(c(0.1)*c(x) + c(0.2))*sinh(sqrt(c(0.1)*c(x) + c(0.2))) - c(20.0)*cosh(sqrt(c(0.1)*c(x) + c(0.2))) 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 + 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#END USER FUNCTION BLOCK # before write_aux functions # Begin Function number 2 > display_poles := proc() > local rad_given; > global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ; > if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1 > rad_given := float_abs(array_x[1] - (array_given_rad_poles[1,1] + array_given_rad_poles[1,2] * I )); > omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," "); > omniout_complex(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," "); > if ((float_abs(rad_given) < float_abs(glob_least_given_sing)) and > (float_abs(rad_given) > 0.0)) then # if number 2 > glob_least_given_sing := rad_given; > fi;# end if 2; > elif > (glob_type_given_pole = 3) then # if number 2 > omniout_str(ALWAYS,"NO POLE (given) for Equation 1"); > elif > (glob_type_given_pole = 5) then # if number 3 > omniout_str(ALWAYS,"SOME POLE (given) for Equation 1"); > else > omniout_str(ALWAYS,"NO INFO (given) for Equation 1"); > fi;# end if 3; > if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," "); > if ((float_abs(array_rad_test_poles[1,1]) < glob_least_ratio_sing)) then # if number 4 > glob_least_ratio_sing := array_rad_test_poles[1,1]; > fi;# end if 4; > omniout_complex(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," "); > else > omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1"); > fi;# end if 3; > if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," "); > if ((float_abs(array_rad_test_poles[1,2]) < glob_least_3_sing)) then # if number 4 > glob_least_3_sing := array_rad_test_poles[1,2]; > fi;# end if 4; > omniout_complex(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," "); > else > omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1"); > fi;# end if 3; > if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," "); > if ((float_abs(array_rad_test_poles[1,3]) < glob_least_6_sing)) then # if number 4 > glob_least_6_sing := array_rad_test_poles[1,3]; > fi;# end if 4; > omniout_complex(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," "); > else > omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1"); > fi;# end if 3 > ; > end; display_poles := proc() local rad_given; global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, glob_least_3_sing, glob_least_6_sing, glob_least_given_sing, glob_least_ratio_sing, array_x; if glob_type_given_pole = 1 or glob_type_given_pole = 2 then rad_given := float_abs(array_x[1] - array_given_rad_poles[1, 1] - array_given_rad_poles[1, 2]*I); omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4, rad_given, 4, " "); omniout_complex(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles[1, 1], 4, " "); if float_abs(rad_given) < float_abs(glob_least_given_sing) and 0. < float_abs(rad_given) then glob_least_given_sing := rad_given end if elif glob_type_given_pole = 3 then omniout_str(ALWAYS, "NO POLE (given) for Equation 1") elif glob_type_given_pole = 5 then omniout_str(ALWAYS, "SOME POLE (given) for Equation 1") else omniout_str(ALWAYS, "NO INFO (given) for Equation 1") end if; if array_rad_test_poles[1, 1] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (ratio test) for eq 1 ", 4, array_rad_test_poles[1, 1], 4, " "); if float_abs(array_rad_test_poles[1, 1]) < glob_least_ratio_sing then glob_least_ratio_sing := array_rad_test_poles[1, 1] end if; omniout_complex(ALWAYS, "Order of pole (ratio test) ", 4, array_ord_test_poles[1, 1], 4, " ") else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1") end if; if glob__small < array_rad_test_poles[1, 2] and array_rad_test_poles[1, 2] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 1 ", 4, array_rad_test_poles[1, 2], 4, " "); if float_abs(array_rad_test_poles[1, 2]) < glob_least_3_sing then glob_least_3_sing := array_rad_test_poles[1, 2] end if; omniout_complex(ALWAYS, "Order of pole (three term test) ", 4, array_ord_test_poles[1, 2], 4, " ") else omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 1") end if; if glob__small < array_rad_test_poles[1, 3] and array_rad_test_poles[1, 3] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 1 ", 4, array_rad_test_poles[1, 3], 4, " "); if float_abs(array_rad_test_poles[1, 3]) < glob_least_6_sing then glob_least_6_sing := array_rad_test_poles[1, 3] end if; omniout_complex(ALWAYS, "Order of pole (six term test) ", 4, array_ord_test_poles[1, 3], 4, " ") else omniout_str(ALWAYS, "NO COMPLEX POLE (six term test) for Equation 1") end if end proc # End Function number 2 # Begin Function number 3 > my_check_sign := proc( x0 ,xf) > local ret; > if (xf > x0) then # if number 3 > ret := glob__1; > else > ret := glob__m1; > fi;# end if 3; > ret;; > end; my_check_sign := proc(x0, xf) local ret; if x0 < xf then ret := glob__1 else ret := glob__m1 end if; ret end proc # End Function number 3 # Begin Function number 4 > est_size_answer := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, #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_0D1, array_const_0D2, 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_0D1, > array_const_0D2, #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_0D1, array_const_0D2, 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_0D1, > array_const_0D2, #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_0D1, array_const_0D2, 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_0D1, > array_const_0D2, #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_0D1, array_const_0D2, 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_0D1, > array_const_0D2, #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_0D1, array_const_0D2, 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_0D1, > array_const_0D2, #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_0D1, array_const_0D2, 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_0D1, > array_const_0D2, #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_0D1, array_const_0D2, 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_0D1, > array_const_0D2, #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_0D1[1] * array_x[1]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 1 > array_tmp2[1] := array_tmp1[1] + array_const_0D2[1]; > #emit pre sqrt 1 $eq_no = 1 > array_tmp3[1] := sqrt(array_tmp2[1]); > #emit pre cosh $eq_no = 1 > array_tmp4_g[1] := sinh(array_tmp3[1]); > array_tmp4[1] := cosh(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_0D1[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 cosh $eq_no = 1 > array_tmp4_g[2] := att(1,array_tmp4,array_tmp3,1); > array_tmp4[2] := 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 cosh $eq_no = 1 > array_tmp4_g[3] := att(2,array_tmp4,array_tmp3,1); > array_tmp4[3] := 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 cosh $eq_no = 1 > array_tmp4_g[4] := att(3,array_tmp4,array_tmp3,1); > array_tmp4[4] := 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 cosh $eq_no = 1 > array_tmp4_g[5] := att(4,array_tmp4,array_tmp3,1); > array_tmp4[5] := 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 cosh $eq_no = 1 > array_tmp4_g[kkk] := att(kkk-1,array_tmp4,array_tmp3,1); > array_tmp4[kkk] := att(kkk-1,array_tmp4_g,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_0D1, array_const_0D2, 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_0D1[1]*array_x[1]; array_tmp2[1] := array_tmp1[1] + array_const_0D2[1]; array_tmp3[1] := sqrt(array_tmp2[1]); array_tmp4_g[1] := sinh(array_tmp3[1]); array_tmp4[1] := cosh(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_0D1[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] := 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] := 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] := 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] := 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_g[kkk] := att(kkk - 1, array_tmp4, array_tmp3, 1); array_tmp4[kkk] := att(kkk - 1, array_tmp4_g, 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_0D1, > array_const_0D2, > #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_0D1); > array_const_0D1[1] := c(0.1); > zero_ats_ar(array_const_0D2); > array_const_0D2[1] := c(0.2); > 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/cosh_sqrtpostcpx.cpx#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = cosh ( sqrt ( 0.1 * x + 0.2 ) ) ; "); > 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 := -1.7 + 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 := 0.01;"); > 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,"glob_type_given_pole := 1;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_rad_poles[1,1] := c(-2.0);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_rad_poles[1,2] := c(0.0);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_ord_poles[1,1] := c(0.5);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_ord_poles[1,2] := c(0.0);"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_desired_digits_correct:=8;"); > omniout_str(ALWAYS,"glob_max_minutes:=(3.0);"); > omniout_str(ALWAYS,"glob_subiter_method:=3;"); > omniout_str(ALWAYS,"glob_max_iter:=10000;"); > omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);"); > omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);"); > omniout_str(ALWAYS,"glob_look_poles:=true;"); > omniout_str(ALWAYS,"glob_h:=c(0.001);"); > omniout_str(ALWAYS,"glob_display_interval:=c(0.01);"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"return(c(20.0) * sqrt(c(0.1) * c(x) + c(0.2)) * sinh( sqrt(c(0.1) * c(x) + c(0.2))) - c(20.0) * cosh( sqrt(c(0.1) * c(x) + c(0.2))));"); > 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 := -1.7 + 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 := 0.01; > 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(-2.0); > 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 ) = cosh ( sqrt ( 0.1 * x + 0.2 ) ) ; "); > 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,"2017-11-26T14:40:19-06:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"cosh_sqrt") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = cosh ( sqrt ( 0.1 * x + 0.2 ) ) ; ") > ; > 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,"cosh_sqrt diffeq.mxt") > ; > logitem_str(html_log_file,"cosh_sqrt maple results") > ; > logitem_str(html_log_file,"OK") > ; > logend(html_log_file) > ; > ; > fi;# end if 15; > if (glob_html_log) then # if number 15 > fclose(html_log_file); > fi;# end if 15 > ; > ;; > end; > # End Function number 12 > #END OUTFILEMAIN > end; Warning, `h_new` is implicitly declared local to procedure `main` Warning, `ratio` is implicitly declared local to procedure `main` main := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err, estimated_step_error, min_value, est_answer, found_h, repeat_it, h_new, ratio; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, 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_0D1); array_const_0D1[1] := c(0.1); zero_ats_ar(array_const_0D2); array_const_0D2[1] := c(0.2); 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/cosh_sqrtpostcpx.cpx#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = cosh ( sqrt ( 0.1\ * x + 0.2 ) ) ; "); 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 := -1.7 + 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 := 0.01;"); 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, "glob_type_given_pole := 1;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_rad_poles[1,1] := c(-2.0);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_rad_poles[1,2] := c(0.0);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_ord_poles[1,1] := c(0.5);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_ord_poles[1,2] := c(0.0);"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_desired_digits_correct:=8;"); omniout_str(ALWAYS, "glob_max_minutes:=(3.0);"); omniout_str(ALWAYS, "glob_subiter_method:=3;"); omniout_str(ALWAYS, "glob_max_iter:=10000;"); omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);"); omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);"); omniout_str(ALWAYS, "glob_look_poles:=true;"); omniout_str(ALWAYS, "glob_h:=c(0.001);"); omniout_str(ALWAYS, "glob_display_interval:=c(0.01);"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "return(c(20.0) * sqrt(c(0.1) * c(x) + c(0.2)) * \ sinh( sqrt(c(0.1) * c(x) + c(0.2))) - c(20.0) * cosh( sqrt(c(0.1\ ) * c(x) + c(0.2))));"); 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,"); 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omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 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 := -1.7 + 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 := 0.01; 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(-2.0); 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 ) = cosh ( sqrt ( 0\ .1 * x + 0.2 ) ) ; "); 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, "2017-11-26T14:40:19-06:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "cosh_sqrt"); logitem_str(html_log_file, "diff ( y , x , 1 ) = co\ sh ( sqrt ( 0.1 * x + 0.2 ) ) ; "); 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, "cosh_sqrt diffeq.mxt"); logitem_str(html_log_file, "cosh_sqrt maple results"); logitem_str(html_log_file, "OK"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end if end proc # End Function number 12 > main(); memory used=3.9MB, alloc=40.3MB, time=0.08 ##############ECHO OF PROBLEM################# ##############temp/cosh_sqrtpostcpx.cpx################# diff ( y , x , 1 ) = cosh ( sqrt ( 0.1 * x + 0.2 ) ) ; ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := -1.7 + 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 := 0.01; 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(-2.0); 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(c(20.0) * sqrt(c(0.1) * c(x) + c(0.2)) * sinh( sqrt(c(0.1) * c(x) + c(0.2))) - c(20.0) * cosh( sqrt(c(0.1) * c(x) + c(0.2)))); 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] = -1.7 0.1 h = 0.0001 0.005 y[1] (numeric) = -19.697997499 0.101503614446 y[1] (closed_form) = -19.697997499 0.101503614446 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 0.3162 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6999 0.105 h = 0.0001 0.003 y[1] (numeric) = -19.6979211205 0.106579284719 y[1] (closed_form) = -19.6979217488 0.106579307805 absolute error = 6.288e-07 relative error = 3.192e-06 % Correct digits = 7 Radius of convergence (given) for eq 1 = 0.3179 Order of pole (given) = 0.5 0 NO 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=0.40 x[1] = -1.6998 0.108 h = 0.001 0.001 y[1] (numeric) = -19.6978354452 0.109624927117 y[1] (closed_form) = -19.6978362998 0.109624963976 absolute error = 8.554e-07 relative error = 4.343e-06 % Correct digits = 7 Radius of convergence (given) for eq 1 = 0.319 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6988 0.109 h = 0.001 0.003 y[1] (numeric) = -19.6968258294 0.110645396947 y[1] (closed_form) = -19.6968266842 0.110645483997 absolute error = 8.593e-07 relative error = 4.363e-06 % Correct digits = 7 Radius of convergence (given) for eq 1 = 0.3203 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6978 0.112 h = 0.0001 0.004 y[1] (numeric) = -19.6958271686 0.113696152914 y[1] (closed_form) = -19.6958282248 0.113696390402 absolute error = 1.083e-06 relative error = 5.496e-06 % Correct digits = 7 Radius of convergence (given) for eq 1 = 0.3223 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6977 0.116 h = 0.003 0.006 y[1] (numeric) = -19.6957481669 0.1177572874 y[1] (closed_form) = -19.6957496253 0.117757543962 absolute error = 1.481e-06 relative error = 7.519e-06 % Correct digits = 7 Radius of convergence (given) for eq 1 = 0.3238 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6947 0.122 h = 0.0001 0.005 y[1] (numeric) = -19.6927376989 0.123865661026 y[1] (closed_form) = -19.6927398386 0.12386681993 absolute error = 2.433e-06 relative error = 1.236e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 0.3288 Order of pole (given) = 0.5 0 NO 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=0.99 x[1] = -1.6946 0.127 h = 0.0001 0.003 y[1] (numeric) = -19.6926668218 0.128942763091 y[1] (closed_form) = -19.6926695923 0.128943945153 absolute error = 3.012e-06 relative error = 1.530e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 0.3308 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6945 0.13 h = 0.001 0.001 y[1] (numeric) = -19.6925844382 0.131989308655 y[1] (closed_form) = -19.6925874351 0.131990504467 absolute error = 3.227e-06 relative error = 1.638e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 0.332 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6935 0.131 h = 0.001 0.003 y[1] (numeric) = -19.6915756644 0.133011148712 y[1] (closed_form) = -19.6915786615 0.13301239473 absolute error = 3.246e-06 relative error = 1.648e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 0.3333 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6925 0.134 h = 0.0001 0.004 y[1] (numeric) = -19.6905800578 0.136063803198 y[1] (closed_form) = -19.6905832563 0.136065199595 absolute error = 3.490e-06 relative error = 1.772e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 0.3354 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6924 0.138 h = 0.003 0.006 y[1] (numeric) = -19.6905054542 0.140126104608 y[1] (closed_form) = -19.690509055 0.140127519969 absolute error = 3.869e-06 relative error = 1.965e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 0.3371 Order of pole (given) = 0.5 0 NO 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=122.1MB, alloc=52.3MB, time=1.55 x[1] = -1.6894 0.144 h = 0.0001 0.005 y[1] (numeric) = -19.6875008312 0.146239380702 y[1] (closed_form) = -19.6875051137 0.146241698328 absolute error = 4.869e-06 relative error = 2.473e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 0.3424 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6893 0.149 h = 0.0001 0.003 y[1] (numeric) = -19.687435459 0.151317912802 y[1] (closed_form) = -19.6874403722 0.151320253527 absolute error = 5.442e-06 relative error = 2.764e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 0.3446 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6892 0.152 h = 0.001 0.001 y[1] (numeric) = -19.6873563678 0.154365360409 y[1] (closed_form) = -19.6873615074 0.15436771486 absolute error = 5.653e-06 relative error = 2.871e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 0.346 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6882 0.153 h = 0.001 0.003 y[1] (numeric) = -19.6863484365 0.155388570508 y[1] (closed_form) = -19.6863535764 0.155390975178 absolute error = 5.675e-06 relative error = 2.882e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 0.3473 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6872 0.156 h = 0.0001 0.004 y[1] (numeric) = -19.6853558851 0.158443122564 y[1] (closed_form) = -19.6853612265 0.158445677553 absolute error = 5.921e-06 relative error = 3.008e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 0.3495 Order of pole (given) = 0.5 0 NO 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=167.7MB, alloc=52.3MB, time=2.12 x[1] = -1.6871 0.16 h = 0.003 0.006 y[1] (numeric) = -19.6852856805 0.162506589396 y[1] (closed_form) = -19.6852914242 0.162509163235 absolute error = 6.294e-06 relative error = 3.197e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.3514 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6841 0.166 h = 0.0001 0.005 y[1] (numeric) = -19.6822869047 0.168624766259 y[1] (closed_form) = -19.6822933304 0.16862824228 absolute error = 7.306e-06 relative error = 3.712e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.3569 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.684 0.171 h = 0.0001 0.003 y[1] (numeric) = -19.6822270384 0.173704726529 y[1] (closed_form) = -19.6822340948 0.173708225568 absolute error = 7.876e-06 relative error = 4.002e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.3593 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6839 0.174 h = 0.001 0.001 y[1] (numeric) = -19.6821512403 0.176753075057 y[1] (closed_form) = -19.6821585231 0.176756587795 absolute error = 8.086e-06 relative error = 4.108e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.3608 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6829 0.175 h = 0.001 0.003 y[1] (numeric) = -19.681144152 0.17777765501 y[1] (closed_form) = -19.6811514352 0.17778121798 absolute error = 8.108e-06 relative error = 4.120e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.3622 Order of pole (given) = 0.5 0 NO 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=213.3MB, alloc=52.3MB, time=2.67 x[1] = -1.6819 0.178 h = 0.0001 0.004 y[1] (numeric) = -19.6801546567 0.180834103687 y[1] (closed_form) = -19.6801621415 0.180837816916 absolute error = 8.355e-06 relative error = 4.245e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.3645 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6818 0.182 h = 0.003 0.006 y[1] (numeric) = -19.6800888519 0.184898734438 y[1] (closed_form) = -19.680096739 0.184902466399 absolute error = 8.725e-06 relative error = 4.433e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.3666 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6788 0.188 h = 0.0001 0.005 y[1] (numeric) = -19.6770959257 0.191021810374 y[1] (closed_form) = -19.6771044952 0.191026444425 absolute error = 9.742e-06 relative error = 4.951e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.3722 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6787 0.193 h = 0.0001 0.003 y[1] (numeric) = -19.6770415663 0.196103196945 y[1] (closed_form) = -19.6770507665 0.196107853914 absolute error = 1.031e-05 relative error = 5.240e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.3748 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6786 0.196 h = 0.001 0.001 y[1] (numeric) = -19.6769690618 0.199152445272 y[1] (closed_form) = -19.6769784885 0.199157115909 absolute error = 1.052e-05 relative error = 5.346e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.3764 Order of pole (given) = 0.5 0 NO 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=259.0MB, alloc=52.3MB, time=3.24 x[1] = -1.6776 0.197 h = 0.0001 0.004 y[1] (numeric) = -19.6759628172 0.200178394895 y[1] (closed_form) = -19.6759722442 0.200183115776 absolute error = 1.054e-05 relative error = 5.358e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.3778 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6775 0.201 h = 0.003 0.006 y[1] (numeric) = -19.6759008144 0.204243973679 y[1] (closed_form) = -19.6759106435 0.20424871339 absolute error = 1.091e-05 relative error = 5.546e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.38 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6745 0.207 h = 0.0001 0.005 y[1] (numeric) = -19.6729129835 0.210371195496 y[1] (closed_form) = -19.6729234952 0.210376837207 absolute error = 1.193e-05 relative error = 6.064e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.3857 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6744 0.212 h = 0.0001 0.003 y[1] (numeric) = -19.6728633821 0.215453742667 y[1] (closed_form) = -19.6728745245 0.215459407195 absolute error = 1.250e-05 relative error = 6.353e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.3885 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6743 0.215 h = 0.001 0.001 y[1] (numeric) = -19.6727937238 0.21850372537 y[1] (closed_form) = -19.6728050928 0.218509403536 absolute error = 1.271e-05 relative error = 6.459e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.3903 Order of pole (given) = 0.5 0 NO 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=304.5MB, alloc=52.3MB, time=3.80 x[1] = -1.6733 0.216 h = 0.001 0.003 y[1] (numeric) = -19.6717882222 0.219530843749 y[1] (closed_form) = -19.6717995915 0.219536572169 absolute error = 1.273e-05 relative error = 6.471e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.3916 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6723 0.219 h = 0.0001 0.004 y[1] (numeric) = -19.6708044388 0.222590782635 y[1] (closed_form) = -19.6708160097 0.222596661201 absolute error = 1.298e-05 relative error = 6.597e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.3941 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6722 0.223 h = 0.003 0.006 y[1] (numeric) = -19.670746837 0.226657522732 y[1] (closed_form) = -19.6707588103 0.226663419803 absolute error = 1.335e-05 relative error = 6.785e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.3965 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6692 0.229 h = 0.0001 0.005 y[1] (numeric) = -19.6677648599 0.232789640433 y[1] (closed_form) = -19.6677775163 0.232796439397 absolute error = 1.437e-05 relative error = 7.304e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.4023 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6691 0.234 h = 0.0001 0.003 y[1] (numeric) = -19.6677207673 0.237873610412 y[1] (closed_form) = -19.6677340543 0.237880432061 absolute error = 1.494e-05 relative error = 7.594e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.4053 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.669 0.237 h = 0.001 0.001 y[1] (numeric) = -19.6676544038 0.240924490819 y[1] (closed_form) = -19.6676679174 0.24093132607 absolute error = 1.514e-05 relative error = 7.699e-05 % Correct digits = 6 memory used=350.1MB, alloc=52.3MB, time=4.36 Radius of convergence (given) for eq 1 = 0.4071 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.668 0.238 h = 0.001 0.003 y[1] (numeric) = -19.666649747 0.241952978514 y[1] (closed_form) = -19.6666632609 0.241959864028 absolute error = 1.517e-05 relative error = 7.711e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.4085 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.667 0.241 h = 0.0001 0.004 y[1] (numeric) = -19.6656690224 0.245014811291 y[1] (closed_form) = -19.6656827381 0.24502184689 absolute error = 1.541e-05 relative error = 7.838e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.4111 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6669 0.245 h = 0.003 0.006 y[1] (numeric) = -19.6656158227 0.249082710996 y[1] (closed_form) = -19.6656299408 0.249089764974 absolute error = 1.578e-05 relative error = 8.025e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.4135 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6639 0.251 h = 0.0001 0.005 y[1] (numeric) = -19.6626397018 0.255219722879 y[1] (closed_form) = -19.6626545034 0.255227678638 absolute error = 1.680e-05 relative error = 8.546e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.4195 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6638 0.256 h = 0.0001 0.003 y[1] (numeric) = -19.6626011189 0.260305113792 y[1] (closed_form) = -19.6626165511 0.260313092088 absolute error = 1.737e-05 relative error = 8.835e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.4226 Order of pole (given) = 0.5 0 NO 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=395.7MB, alloc=52.3MB, time=4.92 x[1] = -1.6637 0.259 h = 0.001 0.001 y[1] (numeric) = -19.6625380509 0.263356890782 y[1] (closed_form) = -19.6625537097 0.263364882639 absolute error = 1.758e-05 relative error = 8.940e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.4245 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6627 0.26 h = 0.001 0.003 y[1] (numeric) = -19.6615342394 0.264386747605 y[1] (closed_form) = -19.6615498984 0.264394789735 absolute error = 1.760e-05 relative error = 8.952e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.4259 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6617 0.263 h = 0.0001 0.004 y[1] (numeric) = -19.6605565747 0.267450473323 y[1] (closed_form) = -19.6605724356 0.267458665476 absolute error = 1.785e-05 relative error = 9.079e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.4285 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6616 0.267 h = 0.003 0.006 y[1] (numeric) = -19.6605077779 0.271519531129 y[1] (closed_form) = -19.6605240413 0.271527741534 absolute error = 1.822e-05 relative error = 9.266e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.431 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6586 0.273 h = 0.0001 0.005 y[1] (numeric) = -19.6575375154 0.277661435495 y[1] (closed_form) = -19.6575544626 0.27767054756 absolute error = 1.924e-05 relative error = 9.787e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.4371 Order of pole (given) = 0.5 0 NO 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=441.5MB, alloc=52.3MB, time=5.48 x[1] = -1.6585 0.278 h = 0.0001 0.003 y[1] (numeric) = -19.6575044434 0.282748245465 y[1] (closed_form) = -19.6575220211 0.282757379908 absolute error = 1.981e-05 relative error = 0.0001008 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.4403 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6584 0.281 h = 0.001 0.001 y[1] (numeric) = -19.6574446714 0.285800917914 y[1] (closed_form) = -19.6574624758 0.285810065875 absolute error = 2.002e-05 relative error = 0.0001018 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.4423 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6574 0.282 h = 0.001 0.003 y[1] (numeric) = -19.6564417057 0.286832143679 y[1] (closed_form) = -19.6564595104 0.286841341921 absolute error = 2.004e-05 relative error = 0.0001019 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.4437 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6564 0.285 h = 0.0001 0.004 y[1] (numeric) = -19.6554671018 0.289897761387 y[1] (closed_form) = -19.6554851084 0.28990710959 absolute error = 2.029e-05 relative error = 0.0001032 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.4464 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6563 0.289 h = 0.003 0.006 y[1] (numeric) = -19.6554227088 0.29396797579 y[1] (closed_form) = -19.6554411179 0.293977342115 absolute error = 2.065e-05 relative error = 0.0001051 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.4491 Order of pole (given) = 0.5 0 NO 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=487.3MB, alloc=52.3MB, time=6.04 x[1] = -1.6533 0.295 h = 0.0001 0.005 y[1] (numeric) = -19.6524583071 0.300114770934 y[1] (closed_form) = -19.6524774004 0.300125038794 absolute error = 2.168e-05 relative error = 0.0001103 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.4552 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6532 0.3 h = 0.0001 0.003 y[1] (numeric) = -19.6524307469 0.305202998083 y[1] (closed_form) = -19.6524504707 0.30521328815 absolute error = 2.225e-05 relative error = 0.0001132 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.4586 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6531 0.303 h = 0.001 0.001 y[1] (numeric) = -19.6523742716 0.30825656487 y[1] (closed_form) = -19.652394222 0.308266868408 absolute error = 2.245e-05 relative error = 0.0001142 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.4606 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6521 0.304 h = 0.0001 0.004 y[1] (numeric) = -19.6513721523 0.309289159389 y[1] (closed_form) = -19.6513921032 0.309299513216 absolute error = 2.248e-05 relative error = 0.0001144 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.462 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] = -1.652 0.308 h = 0.003 0.006 y[1] (numeric) = -19.6513315646 0.31336031556 y[1] (closed_form) = -19.6513519176 0.31337068751 absolute error = 2.284e-05 relative error = 0.0001162 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.4647 Order of pole (given) = 0.5 0 NO 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=532.9MB, alloc=52.3MB, time=6.60 x[1] = -1.649 0.314 h = 0.0001 0.005 y[1] (numeric) = -19.6483722677 0.319511249308 y[1] (closed_form) = -19.6483933053 0.319522522677 absolute error = 2.387e-05 relative error = 0.0001215 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.471 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6489 0.319 h = 0.0001 0.003 y[1] (numeric) = -19.6483494696 0.324600629138 y[1] (closed_form) = -19.6483711376 0.324611924561 absolute error = 2.444e-05 relative error = 0.0001243 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.4744 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6488 0.322 h = 0.001 0.001 y[1] (numeric) = -19.648295843 0.327654925561 y[1] (closed_form) = -19.6483177377 0.327666234412 absolute error = 2.464e-05 relative error = 0.0001254 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.4765 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6478 0.323 h = 0.001 0.003 y[1] (numeric) = -19.6472944692 0.328688688016 y[1] (closed_form) = -19.6473163643 0.328700047162 absolute error = 2.467e-05 relative error = 0.0001255 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.4779 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6468 0.326 h = 0.0001 0.004 y[1] (numeric) = -19.6463255858 0.331757787255 y[1] (closed_form) = -19.6463476829 0.331769296247 absolute error = 2.491e-05 relative error = 0.0001268 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.4807 Order of pole (given) = 0.5 0 NO 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=578.7MB, alloc=52.3MB, time=7.17 x[1] = -1.6467 0.33 h = 0.003 0.006 y[1] (numeric) = -19.646289403 0.335830097328 y[1] (closed_form) = -19.6463119026 0.335841624193 absolute error = 2.528e-05 relative error = 0.0001287 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.4834 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6437 0.336 h = 0.0001 0.005 y[1] (numeric) = -19.6433359712 0.341985918655 y[1] (closed_form) = -19.6433591557 0.341998346805 absolute error = 2.631e-05 relative error = 0.0001339 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.4897 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6436 0.341 h = 0.0001 0.003 y[1] (numeric) = -19.6433186867 0.347076712152 y[1] (closed_form) = -19.6433425017 0.347089162168 absolute error = 2.687e-05 relative error = 0.0001368 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.4933 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6435 0.344 h = 0.001 0.001 y[1] (numeric) = -19.643268358 0.350131900815 y[1] (closed_form) = -19.6432923996 0.350144364207 absolute error = 2.708e-05 relative error = 0.0001378 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.4954 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6425 0.345 h = 0.001 0.003 y[1] (numeric) = -19.6422678316 0.351167031668 y[1] (closed_form) = -19.6422918737 0.351179545362 absolute error = 2.710e-05 relative error = 0.000138 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.4968 Order of pole (given) = 0.5 0 NO 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=624.5MB, alloc=52.3MB, time=7.73 x[1] = -1.6415 0.348 h = 0.0001 0.004 y[1] (numeric) = -19.6413020118 0.354238020163 y[1] (closed_form) = -19.6413262559 0.354250683642 absolute error = 2.735e-05 relative error = 0.0001392 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.4996 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6414 0.352 h = 0.003 0.006 y[1] (numeric) = -19.641270235 0.358311482514 y[1] (closed_form) = -19.6412948818 0.35832416373 absolute error = 2.772e-05 relative error = 0.0001411 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.5025 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6384 0.358 h = 0.0001 0.005 y[1] (numeric) = -19.6383226706 0.364472189714 y[1] (closed_form) = -19.6383480025 0.364485772077 absolute error = 2.874e-05 relative error = 0.0001463 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.5088 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6383 0.363 h = 0.0001 0.003 y[1] (numeric) = -19.6383109007 0.369564394994 y[1] (closed_form) = -19.6383368632 0.369577999029 absolute error = 2.931e-05 relative error = 0.0001492 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.5124 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6382 0.366 h = 0.001 0.001 y[1] (numeric) = -19.6382638704 0.372620474773 y[1] (closed_form) = -19.6382900595 0.372634092129 absolute error = 2.952e-05 relative error = 0.0001503 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.5146 Order of pole (given) = 0.5 0 NO 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=670.1MB, alloc=52.3MB, time=8.29 x[1] = -1.6372 0.367 h = 0.001 0.003 y[1] (numeric) = -19.6372641922 0.373656973836 y[1] (closed_form) = -19.6372903817 0.373670641501 absolute error = 2.954e-05 relative error = 0.0001504 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.5161 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6362 0.37 h = 0.0001 0.004 y[1] (numeric) = -19.6363014369 0.376729850635 y[1] (closed_form) = -19.6363278286 0.376743668023 absolute error = 2.979e-05 relative error = 0.0001517 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.5189 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6361 0.374 h = 0.003 0.006 y[1] (numeric) = -19.636274067 0.380804463757 y[1] (closed_form) = -19.6363008613 0.380818298746 absolute error = 3.016e-05 relative error = 0.0001535 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.5218 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6331 0.38 h = 0.0001 0.005 y[1] (numeric) = -19.6333323722 0.386970055123 y[1] (closed_form) = -19.6333598521 0.386984791117 absolute error = 3.118e-05 relative error = 0.0001588 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.5282 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.633 0.385 h = 0.0001 0.003 y[1] (numeric) = -19.633326118 0.392063670301 y[1] (closed_form) = -19.6333542284 0.392078427767 absolute error = 3.175e-05 relative error = 0.0001617 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.5319 Order of pole (given) = 0.5 0 NO 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=715.8MB, alloc=52.3MB, time=8.85 x[1] = -1.6329 0.388 h = 0.001 0.001 y[1] (numeric) = -19.6332823867 0.395120640071 y[1] (closed_form) = -19.6333107238 0.395135410801 absolute error = 3.196e-05 relative error = 0.0001627 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.5341 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6319 0.389 h = 0.001 0.003 y[1] (numeric) = -19.6322835572 0.396158507157 y[1] (closed_form) = -19.6323118947 0.396173328203 absolute error = 3.198e-05 relative error = 0.0001629 % Correct digits = 6 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] = -1.6309 0.392 h = 0.0001 0.004 y[1] (numeric) = -19.6313238673 0.399233271308 y[1] (closed_form) = -19.631352407 0.399248242014 absolute error = 3.223e-05 relative error = 0.0001641 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.5384 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6308 0.396 h = 0.003 0.006 y[1] (numeric) = -19.6313009051 0.403309033692 y[1] (closed_form) = -19.6313298475 0.403324021862 absolute error = 3.259e-05 relative error = 0.000166 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.5414 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6278 0.402 h = 0.0001 0.005 y[1] (numeric) = -19.6283650823 0.409479507517 y[1] (closed_form) = -19.6283947106 0.409495396546 absolute error = 3.362e-05 relative error = 0.0001712 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.5478 Order of pole (given) = 0.5 0 NO 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=761.5MB, alloc=52.3MB, time=9.42 x[1] = -1.6277 0.407 h = 0.0001 0.003 y[1] (numeric) = -19.6283643448 0.414574530707 y[1] (closed_form) = -19.6283946035 0.414590441004 absolute error = 3.419e-05 relative error = 0.0001741 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.5516 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6276 0.41 h = 0.001 0.001 y[1] (numeric) = -19.6283239132 0.417632389344 y[1] (closed_form) = -19.6283543987 0.417648312846 absolute error = 3.439e-05 relative error = 0.0001752 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.5539 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6266 0.411 h = 0.0001 0.004 y[1] (numeric) = -19.6273259329 0.418671624264 y[1] (closed_form) = -19.6273564188 0.418687598087 absolute error = 3.442e-05 relative error = 0.0001753 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.5553 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6265 0.415 h = 0.003 0.006 y[1] (numeric) = -19.6273067793 0.422748322103 y[1] (closed_form) = -19.6273376676 0.422764313338 absolute error = 3.478e-05 relative error = 0.0001772 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.5583 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6235 0.421 h = 0.0001 0.005 y[1] (numeric) = -19.6243760708 0.428922927232 y[1] (closed_form) = -19.6244076454 0.428939819194 absolute error = 3.581e-05 relative error = 0.0001824 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.5648 Order of pole (given) = 0.5 0 NO 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=807.2MB, alloc=52.3MB, time=9.98 x[1] = -1.6234 0.426 h = 0.0001 0.003 y[1] (numeric) = -19.6243800994 0.43401909515 y[1] (closed_form) = -19.6244123045 0.434036008201 absolute error = 3.638e-05 relative error = 0.0001853 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.5686 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6233 0.429 h = 0.001 0.001 y[1] (numeric) = -19.6243425191 0.437077678677 y[1] (closed_form) = -19.6243749509 0.43709460488 absolute error = 3.658e-05 relative error = 0.0001864 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.5709 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6223 0.43 h = 0.001 0.003 y[1] (numeric) = -19.6233452866 0.438118080707 y[1] (closed_form) = -19.6233777189 0.438135057236 absolute error = 3.661e-05 relative error = 0.0001865 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.5723 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6213 0.433 h = 0.0001 0.004 y[1] (numeric) = -19.6223913259 0.4411963177 y[1] (closed_form) = -19.6224239605 0.441213443774 absolute error = 3.686e-05 relative error = 0.0001878 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.5752 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6212 0.437 h = 0.003 0.006 y[1] (numeric) = -19.6223765811 0.445274162054 y[1] (closed_form) = -19.6224096184 0.445291305333 absolute error = 3.722e-05 relative error = 0.0001896 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.5783 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6182 0.443 h = 0.0001 0.005 y[1] (numeric) = -19.6194517489 0.451453646432 y[1] (closed_form) = -19.6194854729 0.451471690288 absolute error = 3.825e-05 relative error = 0.0001949 % Correct digits = 6 memory used=852.9MB, alloc=52.3MB, time=10.54 Radius of convergence (given) for eq 1 = 0.5848 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6181 0.448 h = 0.0001 0.003 y[1] (numeric) = -19.619461296 0.456551218838 y[1] (closed_form) = -19.6194956504 0.45656928357 absolute error = 3.881e-05 relative error = 0.0001978 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.5887 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.618 0.451 h = 0.001 0.001 y[1] (numeric) = -19.6194270165 0.459610689131 y[1] (closed_form) = -19.6194615977 0.459628766953 absolute error = 3.902e-05 relative error = 0.0001988 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.591 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] = -1.617 0.452 h = 0.001 0.003 y[1] (numeric) = -19.6184306343 0.460652458637 y[1] (closed_form) = -19.618465216 0.460670586791 absolute error = 3.905e-05 relative error = 0.000199 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.5924 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.616 0.455 h = 0.0001 0.004 y[1] (numeric) = -19.6174797418 0.463732580244 y[1] (closed_form) = -19.6175145259 0.46375085788 absolute error = 3.929e-05 relative error = 0.0002002 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.5954 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6159 0.459 h = 0.003 0.006 y[1] (numeric) = -19.617469407 0.467811569536 y[1] (closed_form) = -19.6175045938 0.467829864238 absolute error = 3.966e-05 relative error = 0.0002021 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.5985 Order of pole (given) = 0.5 0 NO 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=898.7MB, alloc=52.3MB, time=11.10 x[1] = -1.6129 0.465 h = 0.0001 0.005 y[1] (numeric) = -19.6145504534 0.473995931452 y[1] (closed_form) = -19.6145863272 0.474015126578 absolute error = 4.069e-05 relative error = 0.0002074 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.605 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] = -1.6128 0.47 h = 0.0001 0.003 y[1] (numeric) = -19.61456552 0.479094906458 y[1] (closed_form) = -19.6146020242 0.479114122245 absolute error = 4.125e-05 relative error = 0.0002103 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.609 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 x[1] = -1.6127 0.473 h = 0.001 0.001 y[1] (numeric) = -19.6145345419 0.48215526239 y[1] (closed_form) = -19.6145712729 0.482174491202 absolute error = 4.146e-05 relative error = 0.0002113 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.6113 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6117 0.474 h = 0.001 0.003 y[1] (numeric) = -19.6135390107 0.483198399185 y[1] (closed_form) = -19.6135757421 0.483217678334 absolute error = 4.148e-05 relative error = 0.0002114 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.6127 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6107 0.477 h = 0.0001 0.004 y[1] (numeric) = -19.6125911873 0.486280404451 y[1] (closed_form) = -19.6126281213 0.486299833022 absolute error = 4.173e-05 relative error = 0.0002127 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.6157 Order of pole (given) = 0.5 0 NO 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=944.5MB, alloc=52.3MB, time=11.66 x[1] = -1.6106 0.481 h = 0.003 0.006 y[1] (numeric) = -19.6125852633 0.490360537173 y[1] (closed_form) = -19.6126226001 0.490379982668 absolute error = 4.210e-05 relative error = 0.0002146 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.6189 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6076 0.487 h = 0.0001 0.005 y[1] (numeric) = -19.6096721905 0.496549774916 y[1] (closed_form) = -19.6097102147 0.49657012068 absolute error = 4.313e-05 relative error = 0.0002198 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.6254 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6075 0.492 h = 0.0001 0.003 y[1] (numeric) = -19.6096927776 0.501650150631 y[1] (closed_form) = -19.6097314322 0.501670516839 absolute error = 4.369e-05 relative error = 0.0002227 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.6294 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6074 0.495 h = 0.001 0.001 y[1] (numeric) = -19.6096651016 0.504711391076 y[1] (closed_form) = -19.609703983 0.504731770244 absolute error = 4.390e-05 relative error = 0.0002238 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.6318 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6064 0.496 h = 0.001 0.003 y[1] (numeric) = -19.6086704218 0.50575589497 y[1] (closed_form) = -19.6087093037 0.50577632448 absolute error = 4.392e-05 relative error = 0.0002239 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.6332 Order of pole (given) = 0.5 0 NO 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=990.3MB, alloc=52.3MB, time=12.23 x[1] = -1.6054 0.499 h = 0.0001 0.004 y[1] (numeric) = -19.6077256686 0.508839782943 y[1] (closed_form) = -19.607764753 0.508860361813 absolute error = 4.417e-05 relative error = 0.0002252 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.6362 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6053 0.503 h = 0.003 0.006 y[1] (numeric) = -19.6077241562 0.512921057585 y[1] (closed_form) = -19.6077636434 0.512941653237 absolute error = 4.454e-05 relative error = 0.0002271 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.6394 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6023 0.509 h = 0.0001 0.005 y[1] (numeric) = -19.6048169666 0.519115169442 y[1] (closed_form) = -19.6048571416 0.519136665207 absolute error = 4.556e-05 relative error = 0.0002323 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.6459 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.6022 0.514 h = 0.0001 0.003 y[1] (numeric) = -19.6048430751 0.524216943976 y[1] (closed_form) = -19.6048838806 0.524238459966 absolute error = 4.613e-05 relative error = 0.0002352 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.65 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 x[1] = -1.6021 0.517 h = 0.001 0.001 y[1] (numeric) = -19.6048187018 0.527279067808 y[1] (closed_form) = -19.6048597341 0.527300596691 absolute error = 4.634e-05 relative error = 0.0002363 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.6524 Order of pole (given) = 0.5 0 NO 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=1036.0MB, alloc=52.3MB, time=12.79 x[1] = -1.6011 0.518 h = 0.0001 0.004 y[1] (numeric) = -19.6038248741 0.528324938613 y[1] (closed_form) = -19.6038659068 0.528346517842 absolute error = 4.636e-05 relative error = 0.0002364 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.6538 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.601 0.522 h = 0.003 0.006 y[1] (numeric) = -19.6038271735 0.532407142368 y[1] (closed_form) = -19.6038686089 0.532428738297 absolute error = 4.673e-05 relative error = 0.0002383 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.657 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.598 0.528 h = 0.0001 0.005 y[1] (numeric) = -19.6009251078 0.53860537821 y[1] (closed_form) = -19.6009672312 0.538627874112 absolute error = 4.775e-05 relative error = 0.0002435 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.6636 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5979 0.533 h = 0.0001 0.003 y[1] (numeric) = -19.6009559865 0.543708289499 y[1] (closed_form) = -19.6009987405 0.543730805434 absolute error = 4.832e-05 relative error = 0.0002464 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.6677 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5978 0.536 h = 0.001 0.001 y[1] (numeric) = -19.600934467 0.546771133468 y[1] (closed_form) = -19.6009774477 0.546793662237 absolute error = 4.853e-05 relative error = 0.0002475 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.6701 Order of pole (given) = 0.5 0 NO 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=1081.8MB, alloc=52.3MB, time=13.36 x[1] = -1.5968 0.537 h = 0.001 0.003 y[1] (numeric) = -19.5999413894 0.547818170552 y[1] (closed_form) = -19.5999843707 0.547840749672 absolute error = 4.855e-05 relative error = 0.0002476 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.6715 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5958 0.54 h = 0.0001 0.004 y[1] (numeric) = -19.5990023739 0.550905522665 y[1] (closed_form) = -19.5990455579 0.550928251029 absolute error = 4.880e-05 relative error = 0.0002489 % Correct digits = 6 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] = -1.5957 0.544 h = 0.003 0.006 y[1] (numeric) = -19.5990090862 0.554988865562 y[1] (closed_form) = -19.5990526731 0.555011610443 absolute error = 4.916e-05 relative error = 0.0002508 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.6778 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5927 0.55 h = 0.0001 0.005 y[1] (numeric) = -19.596112908 0.561191972301 y[1] (closed_form) = -19.5961571833 0.561215616996 absolute error = 5.019e-05 relative error = 0.000256 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.6844 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5926 0.555 h = 0.0001 0.003 y[1] (numeric) = -19.59614931 0.566296278878 y[1] (closed_form) = -19.5961942158 0.566319943384 absolute error = 5.076e-05 relative error = 0.0002589 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.6885 Order of pole (given) = 0.5 0 NO 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=1127.7MB, alloc=52.3MB, time=13.92 x[1] = -1.5925 0.558 h = 0.001 0.001 y[1] (numeric) = -19.5961310943 0.56936000413 y[1] (closed_form) = -19.5961762269 0.5693836814 absolute error = 5.097e-05 relative error = 0.00026 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.691 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5915 0.559 h = 0.001 0.003 y[1] (numeric) = -19.5951388699 0.570408407765 y[1] (closed_form) = -19.595184003 0.570432135391 absolute error = 5.099e-05 relative error = 0.0002601 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.6924 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5905 0.562 h = 0.0001 0.004 y[1] (numeric) = -19.5942029273 0.573497639844 y[1] (closed_form) = -19.5942482632 0.573521516652 absolute error = 5.124e-05 relative error = 0.0002614 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.6954 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5904 0.566 h = 0.003 0.006 y[1] (numeric) = -19.5942140535 0.57758212033 y[1] (closed_form) = -19.5942597923 0.577606013513 absolute error = 5.160e-05 relative error = 0.0002632 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.6987 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5874 0.572 h = 0.0001 0.005 y[1] (numeric) = -19.5913237649 0.583790096252 y[1] (closed_form) = -19.5913701926 0.583814889089 absolute error = 5.263e-05 relative error = 0.0002685 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.7053 Order of pole (given) = 0.5 0 NO 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=1173.5MB, alloc=52.3MB, time=14.48 x[1] = -1.5873 0.577 h = 0.0001 0.003 y[1] (numeric) = -19.5913656913 0.588895796226 y[1] (closed_form) = -19.5914127495 0.588920608648 absolute error = 5.320e-05 relative error = 0.0002714 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.7094 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5872 0.58 h = 0.001 0.001 y[1] (numeric) = -19.59135078 0.591960401632 y[1] (closed_form) = -19.591398065 0.591985226749 absolute error = 5.341e-05 relative error = 0.0002725 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.7119 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5862 0.581 h = 0.001 0.003 y[1] (numeric) = -19.5903594093 0.59301017163 y[1] (closed_form) = -19.5904066948 0.593035047107 absolute error = 5.343e-05 relative error = 0.0002726 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.7133 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5852 0.584 h = 0.0001 0.004 y[1] (numeric) = -19.5894265405 0.596101282719 y[1] (closed_form) = -19.5894740289 0.596126307316 absolute error = 5.368e-05 relative error = 0.0002739 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.7163 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5851 0.588 h = 0.003 0.006 y[1] (numeric) = -19.5894420814 0.600186899285 y[1] (closed_form) = -19.5894899728 0.600211940114 absolute error = 5.404e-05 relative error = 0.0002757 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.7196 Order of pole (given) = 0.5 0 NO 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=1219.3MB, alloc=52.3MB, time=15.04 x[1] = -1.5821 0.594 h = 0.0001 0.005 y[1] (numeric) = -19.5865576849 0.606399742674 y[1] (closed_form) = -19.5866062654 0.606425682995 absolute error = 5.507e-05 relative error = 0.000281 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.7263 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.582 0.599 h = 0.0001 0.003 y[1] (numeric) = -19.5866051367 0.611506834152 y[1] (closed_form) = -19.5866543478 0.611532793832 absolute error = 5.564e-05 relative error = 0.0002839 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.7304 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5819 0.602 h = 0.001 0.001 y[1] (numeric) = -19.5865935304 0.614572318586 y[1] (closed_form) = -19.5866429683 0.61459829089 absolute error = 5.585e-05 relative error = 0.000285 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.7329 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5809 0.603 h = 0.001 0.003 y[1] (numeric) = -19.5856030139 0.615623454755 y[1] (closed_form) = -19.5856524524 0.615649477425 absolute error = 5.587e-05 relative error = 0.0002851 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.7343 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5799 0.606 h = 0.0001 0.004 y[1] (numeric) = -19.58467322 0.618716443899 y[1] (closed_form) = -19.5847228614 0.618742615628 absolute error = 5.612e-05 relative error = 0.0002864 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.7374 Order of pole (given) = 0.5 0 NO 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=1265.2MB, alloc=52.3MB, time=15.61 x[1] = -1.5798 0.61 h = 0.003 0.006 y[1] (numeric) = -19.5846931764 0.622803195035 y[1] (closed_form) = -19.5847432208 0.622829382852 absolute error = 5.648e-05 relative error = 0.0002883 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.7407 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5768 0.616 h = 0.0001 0.005 y[1] (numeric) = -19.5818146742 0.629020904175 y[1] (closed_form) = -19.5818654082 0.629047991321 absolute error = 5.751e-05 relative error = 0.0002935 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.7474 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5767 0.621 h = 0.0001 0.003 y[1] (numeric) = -19.5818676523 0.634129385263 y[1] (closed_form) = -19.5819190169 0.634156491542 absolute error = 5.808e-05 relative error = 0.0002964 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.7515 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5766 0.624 h = 0.001 0.001 y[1] (numeric) = -19.5818593517 0.637195747596 y[1] (closed_form) = -19.5819109431 0.637222866428 absolute error = 5.828e-05 relative error = 0.0002975 % Correct digits = 6 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] = -1.5756 0.625 h = 0.0001 0.004 y[1] (numeric) = -19.5808696901 0.638248249748 y[1] (closed_form) = -19.580921282 0.638275418949 absolute error = 5.831e-05 relative error = 0.0002976 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.7555 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5755 0.629 h = 0.003 0.006 y[1] (numeric) = -19.5808934615 0.642335923638 y[1] (closed_form) = -19.5809454563 0.642363108826 absolute error = 5.867e-05 relative error = 0.0002995 % Correct digits = 6 memory used=1311.0MB, alloc=52.3MB, time=16.17 Radius of convergence (given) for eq 1 = 0.7588 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5725 0.635 h = 0.0001 0.005 y[1] (numeric) = -19.5780200929 0.648557749428 y[1] (closed_form) = -19.5780727775 0.648585833801 absolute error = 5.970e-05 relative error = 0.0003048 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.7655 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5724 0.64 h = 0.0001 0.003 y[1] (numeric) = -19.5780778452 0.653667359286 y[1] (closed_form) = -19.5781311604 0.653695462594 absolute error = 6.027e-05 relative error = 0.0003077 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.7697 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5723 0.643 h = 0.001 0.001 y[1] (numeric) = -19.5780724009 0.656734436995 y[1] (closed_form) = -19.578125943 0.656762552794 absolute error = 6.048e-05 relative error = 0.0003087 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.7723 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5713 0.644 h = 0.001 0.003 y[1] (numeric) = -19.5770834918 0.657788104594 y[1] (closed_form) = -19.5771370345 0.657816270766 absolute error = 6.050e-05 relative error = 0.0003089 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.7736 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5703 0.647 h = 0.0001 0.004 y[1] (numeric) = -19.5761594442 0.660884549165 y[1] (closed_form) = -19.57621319 0.660912864281 absolute error = 6.075e-05 relative error = 0.0003101 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.7767 Order of pole (given) = 0.5 0 NO 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=1356.9MB, alloc=52.3MB, time=16.73 x[1] = -1.5702 0.651 h = 0.003 0.006 y[1] (numeric) = -19.5761876325 0.664973354826 y[1] (closed_form) = -19.5762417813 0.665001685761 absolute error = 6.111e-05 relative error = 0.000312 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.7801 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5672 0.657 h = 0.0001 0.005 y[1] (numeric) = -19.5733201624 0.671200043144 y[1] (closed_form) = -19.5733750015 0.6712292731 absolute error = 6.214e-05 relative error = 0.0003173 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.7867 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5671 0.662 h = 0.0001 0.003 y[1] (numeric) = -19.5733834429 0.676311039077 y[1] (closed_form) = -19.5734389126 0.676340287739 absolute error = 6.271e-05 relative error = 0.0003202 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.791 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.567 0.665 h = 0.001 0.001 y[1] (numeric) = -19.5733813054 0.679378992579 y[1] (closed_form) = -19.573437002 0.679408253659 absolute error = 6.292e-05 relative error = 0.0003212 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.7935 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.566 0.666 h = 0.001 0.003 y[1] (numeric) = -19.5723932522 0.6804340258 y[1] (closed_form) = -19.5724489494 0.680463337258 absolute error = 6.294e-05 relative error = 0.0003214 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.7949 Order of pole (given) = 0.5 0 NO 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=1402.6MB, alloc=52.3MB, time=17.30 x[1] = -1.565 0.669 h = 0.0001 0.004 y[1] (numeric) = -19.5714722822 0.683532345682 y[1] (closed_form) = -19.5715281825 0.683561806021 absolute error = 6.319e-05 relative error = 0.0003227 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.798 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5649 0.673 h = 0.003 0.006 y[1] (numeric) = -19.5715048883 0.687622281577 y[1] (closed_form) = -19.5715611917 0.687651757592 absolute error = 6.355e-05 relative error = 0.0003245 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.8014 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5619 0.679 h = 0.0001 0.005 y[1] (numeric) = -19.5686433191 0.693853830705 y[1] (closed_form) = -19.5687003131 0.693884205576 absolute error = 6.458e-05 relative error = 0.0003298 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.8081 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5618 0.684 h = 0.0001 0.003 y[1] (numeric) = -19.5687121288 0.698966210819 y[1] (closed_form) = -19.5687697535 0.698996604167 absolute error = 6.515e-05 relative error = 0.0003327 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.8123 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5617 0.687 h = 0.001 0.001 y[1] (numeric) = -19.5687132987 0.702035038984 y[1] (closed_form) = -19.5687711503 0.702065444677 absolute error = 6.536e-05 relative error = 0.0003338 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.8149 Order of pole (given) = 0.5 0 NO 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=1448.5MB, alloc=52.3MB, time=17.86 x[1] = -1.5607 0.688 h = 0.001 0.003 y[1] (numeric) = -19.567726102 0.703091437637 y[1] (closed_form) = -19.5677839542 0.703121893712 absolute error = 6.538e-05 relative error = 0.0003339 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.8163 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5597 0.691 h = 0.0001 0.004 y[1] (numeric) = -19.5668082104 0.706191631874 y[1] (closed_form) = -19.5668662659 0.706222236768 absolute error = 6.563e-05 relative error = 0.0003352 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.8194 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5596 0.695 h = 0.003 0.006 y[1] (numeric) = -19.5668452352 0.710282696492 y[1] (closed_form) = -19.5669036937 0.710313316918 absolute error = 6.599e-05 relative error = 0.000337 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.8228 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5566 0.701 h = 0.0001 0.005 y[1] (numeric) = -19.5639895692 0.716519104711 y[1] (closed_form) = -19.5640487188 0.716550623827 absolute error = 6.702e-05 relative error = 0.0003424 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.8295 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5565 0.706 h = 0.0001 0.003 y[1] (numeric) = -19.5640639091 0.721632867111 y[1] (closed_form) = -19.5641236894 0.721664404475 absolute error = 6.759e-05 relative error = 0.0003452 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.8337 Order of pole (given) = 0.5 0 NO 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=1494.3MB, alloc=52.3MB, time=18.44 x[1] = -1.5564 0.709 h = 0.001 0.001 y[1] (numeric) = -19.564068387 0.724702568811 y[1] (closed_form) = -19.5641283941 0.724734118445 absolute error = 6.780e-05 relative error = 0.0003463 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.8363 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5554 0.71 h = 0.001 0.003 y[1] (numeric) = -19.5630820474 0.725760332705 y[1] (closed_form) = -19.5631420552 0.725791932726 absolute error = 6.782e-05 relative error = 0.0003464 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.8377 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5544 0.713 h = 0.0001 0.004 y[1] (numeric) = -19.5621672353 0.72886240034 y[1] (closed_form) = -19.5622274464 0.728894149119 absolute error = 6.807e-05 relative error = 0.0003477 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.8408 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5543 0.717 h = 0.003 0.006 y[1] (numeric) = -19.5622086794 0.732954592169 y[1] (closed_form) = -19.5622692937 0.732986356335 absolute error = 6.843e-05 relative error = 0.0003496 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.8442 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5513 0.723 h = 0.0001 0.005 y[1] (numeric) = -19.559358919 0.73919585776 y[1] (closed_form) = -19.5594202246 0.739228520449 absolute error = 6.946e-05 relative error = 0.0003549 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.8509 Order of pole (given) = 0.5 0 NO 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=1540.3MB, alloc=52.3MB, time=19.02 x[1] = -1.5512 0.728 h = 0.0001 0.003 y[1] (numeric) = -19.5594387901 0.744311000551 y[1] (closed_form) = -19.5595007264 0.744343681258 absolute error = 7.003e-05 relative error = 0.0003578 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.8552 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5511 0.731 h = 0.001 0.001 y[1] (numeric) = -19.5594465766 0.747381574656 y[1] (closed_form) = -19.5595087399 0.747414267559 absolute error = 7.024e-05 relative error = 0.0003588 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.8578 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5501 0.732 h = 0.0001 0.004 y[1] (numeric) = -19.5584610946 0.748440703601 y[1] (closed_form) = -19.5585232586 0.748473446895 absolute error = 7.026e-05 relative error = 0.000359 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.8592 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.55 0.736 h = 0.003 0.006 y[1] (numeric) = -19.5585063571 0.752533811814 y[1] (closed_form) = -19.5585689241 0.752566570382 absolute error = 7.062e-05 relative error = 0.0003608 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.8627 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.547 0.742 h = 0.0001 0.005 y[1] (numeric) = -19.5556617396 0.758779186707 y[1] (closed_form) = -19.5557249983 0.758812843651 absolute error = 7.166e-05 relative error = 0.0003661 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.8694 Order of pole (given) = 0.5 0 NO 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=1586.3MB, alloc=52.3MB, time=19.60 x[1] = -1.5469 0.747 h = 0.0001 0.003 y[1] (numeric) = -19.555746389 0.763895450271 y[1] (closed_form) = -19.5558102784 0.763929125033 absolute error = 7.222e-05 relative error = 0.000369 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.8737 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5468 0.75 h = 0.001 0.001 y[1] (numeric) = -19.5557570343 0.766966734988 y[1] (closed_form) = -19.5558211507 0.767000421881 absolute error = 7.243e-05 relative error = 0.0003701 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.8763 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5458 0.751 h = 0.001 0.003 y[1] (numeric) = -19.5547723073 0.768027028545 y[1] (closed_form) = -19.5548364243 0.768060765832 absolute error = 7.245e-05 relative error = 0.0003702 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.8777 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5448 0.754 h = 0.0001 0.004 y[1] (numeric) = -19.5538632502 0.771132542882 y[1] (closed_form) = -19.5539275706 0.771166428812 absolute error = 7.270e-05 relative error = 0.0003715 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.8808 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5447 0.758 h = 0.0001 0.004 y[1] (numeric) = -19.5539129334 0.775226775493 y[1] (closed_form) = -19.5539776571 0.775260676541 absolute error = 7.306e-05 relative error = 0.0003734 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.8842 Order of pole (given) = 0.5 0 NO 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=1632.1MB, alloc=52.3MB, time=20.16 x[1] = -1.5446 0.762 h = 0.003 0.006 y[1] (numeric) = -19.5539634226 0.779321038449 y[1] (closed_form) = -19.5540285496 0.779354954426 absolute error = 7.343e-05 relative error = 0.0003752 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.8877 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5416 0.768 h = 0.0001 0.005 y[1] (numeric) = -19.5511259169 0.785571887167 y[1] (closed_form) = -19.551191736 0.785606701309 absolute error = 7.446e-05 relative error = 0.0003805 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.8944 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5415 0.773 h = 0.0001 0.003 y[1] (numeric) = -19.551217107 0.790689560105 y[1] (closed_form) = -19.5512835569 0.790724391794 absolute error = 7.503e-05 relative error = 0.0003834 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.8987 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5414 0.776 h = 0.001 0.001 y[1] (numeric) = -19.5512316666 0.793761742644 y[1] (closed_form) = -19.5512983434 0.793796586375 absolute error = 7.523e-05 relative error = 0.0003845 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9014 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5404 0.777 h = 0.001 0.003 y[1] (numeric) = -19.5502479974 0.794823604924 y[1] (closed_form) = -19.5503146749 0.794858499053 absolute error = 7.526e-05 relative error = 0.0003846 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9028 Order of pole (given) = 0.5 0 NO 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=1678.0MB, alloc=52.3MB, time=20.73 x[1] = -1.5394 0.78 h = 0.0001 0.004 y[1] (numeric) = -19.5493426248 0.79793119883 y[1] (closed_form) = -19.5494095059 0.797966241527 absolute error = 7.551e-05 relative error = 0.0003859 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9058 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5393 0.784 h = 0.003 0.006 y[1] (numeric) = -19.5493975359 0.802026584205 y[1] (closed_form) = -19.5494648202 0.802061641848 absolute error = 7.587e-05 relative error = 0.0003878 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9093 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5363 0.79 h = 0.0001 0.005 y[1] (numeric) = -19.5465659426 0.808282284961 y[1] (closed_form) = -19.5466339195 0.808318240601 absolute error = 7.690e-05 relative error = 0.0003931 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.916 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5362 0.795 h = 0.0001 0.003 y[1] (numeric) = -19.5466626668 0.81340133249 y[1] (closed_form) = -19.5467312744 0.813437305445 absolute error = 7.747e-05 relative error = 0.000396 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9204 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5361 0.798 h = 0.001 0.001 y[1] (numeric) = -19.5466805368 0.816474383978 y[1] (closed_form) = -19.5467493715 0.816510368899 absolute error = 7.767e-05 relative error = 0.000397 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.923 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5351 0.799 h = 0.001 0.003 y[1] (numeric) = -19.545697727 0.817537610701 y[1] (closed_form) = -19.5457665624 0.817573646025 absolute error = 7.770e-05 relative error = 0.0003972 % Correct digits = 5 memory used=1723.9MB, alloc=52.3MB, time=21.30 Radius of convergence (given) for eq 1 = 0.9244 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5341 0.802 h = 0.0001 0.004 y[1] (numeric) = -19.5447954377 0.820647074099 y[1] (closed_form) = -19.5448644766 0.820683257929 absolute error = 7.795e-05 relative error = 0.0003985 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9275 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.534 0.806 h = 0.003 0.006 y[1] (numeric) = -19.5448547715 0.824743580542 y[1] (closed_form) = -19.5449242137 0.824779779173 absolute error = 7.831e-05 relative error = 0.0004003 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.931 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.531 0.812 h = 0.0001 0.005 y[1] (numeric) = -19.5420290929 0.831004131614 y[1] (closed_form) = -19.542099228 0.831041228074 absolute error = 7.934e-05 relative error = 0.0004056 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9377 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5309 0.817 h = 0.0001 0.003 y[1] (numeric) = -19.5421313522 0.836124551837 y[1] (closed_form) = -19.5422021182 0.83616166538 absolute error = 7.991e-05 relative error = 0.0004085 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9421 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5308 0.82 h = 0.001 0.001 y[1] (numeric) = -19.5421525333 0.839198471142 y[1] (closed_form) = -19.5422235262 0.839235596575 absolute error = 8.011e-05 relative error = 0.0004096 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9447 Order of pole (given) = 0.5 0 NO 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=1770.0MB, alloc=52.3MB, time=21.86 x[1] = -1.5298 0.821 h = 0.001 0.003 y[1] (numeric) = -19.5411705834 0.840263062119 y[1] (closed_form) = -19.5412415771 0.840300237959 absolute error = 8.014e-05 relative error = 0.0004097 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9461 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5288 0.824 h = 0.0001 0.004 y[1] (numeric) = -19.5402713784 0.84337439405 y[1] (closed_form) = -19.5403425757 0.843411718336 absolute error = 8.039e-05 relative error = 0.000411 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9492 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5287 0.828 h = 0.003 0.006 y[1] (numeric) = -19.5403351355 0.847472020048 y[1] (closed_form) = -19.5404067362 0.847509358989 absolute error = 8.075e-05 relative error = 0.0004129 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9527 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5257 0.834 h = 0.0001 0.005 y[1] (numeric) = -19.537515374 0.853737419713 y[1] (closed_form) = -19.5375876679 0.853775656314 absolute error = 8.178e-05 relative error = 0.0004182 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9594 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5256 0.839 h = 0.0001 0.003 y[1] (numeric) = -19.5376231694 0.858859210733 y[1] (closed_form) = -19.5376960943 0.858897464185 absolute error = 8.235e-05 relative error = 0.0004211 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9638 Order of pole (given) = 0.5 0 NO 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=1815.9MB, alloc=52.3MB, time=22.43 x[1] = -1.5255 0.842 h = 0.001 0.001 y[1] (numeric) = -19.5376476621 0.861933996726 y[1] (closed_form) = -19.537720814 0.861972261992 absolute error = 8.256e-05 relative error = 0.0004221 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9665 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5245 0.843 h = 0.001 0.003 y[1] (numeric) = -19.5366665728 0.862999951765 y[1] (closed_form) = -19.5367397255 0.863038267442 absolute error = 8.258e-05 relative error = 0.0004223 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9679 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5235 0.846 h = 0.0001 0.004 y[1] (numeric) = -19.535770453 0.866113151272 y[1] (closed_form) = -19.5358438093 0.866151615333 absolute error = 8.283e-05 relative error = 0.0004236 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.971 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 x[1] = -1.5234 0.85 h = 0.003 0.006 y[1] (numeric) = -19.5358386344 0.87021189531 y[1] (closed_form) = -19.535912394 0.870250373881 absolute error = 8.319e-05 relative error = 0.0004254 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9745 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5204 0.856 h = 0.0001 0.005 y[1] (numeric) = -19.5330247922 0.876482141845 y[1] (closed_form) = -19.5330992455 0.876521517906 absolute error = 8.422e-05 relative error = 0.0004308 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9812 Order of pole (given) = 0.5 0 NO 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=1861.8MB, alloc=52.3MB, time=22.99 x[1] = -1.5203 0.861 h = 0.0001 0.003 y[1] (numeric) = -19.5331381247 0.881605301764 y[1] (closed_form) = -19.533213209 0.881644694445 absolute error = 8.479e-05 relative error = 0.0004336 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9856 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5202 0.864 h = 0.001 0.001 y[1] (numeric) = -19.5331659297 0.884680953315 y[1] (closed_form) = -19.533241241 0.884720357732 absolute error = 8.500e-05 relative error = 0.0004347 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9883 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5192 0.865 h = 0.0001 0.004 y[1] (numeric) = -19.5321857015 0.885748272224 y[1] (closed_form) = -19.5322610136 0.885787727057 absolute error = 8.502e-05 relative error = 0.0004348 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9896 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5191 0.869 h = 0.003 0.006 y[1] (numeric) = -19.5322577052 0.889847924702 y[1] (closed_form) = -19.5323334206 0.889887393925 absolute error = 8.539e-05 relative error = 0.0004367 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9932 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5161 0.875 h = 0.0001 0.005 y[1] (numeric) = -19.5294490178 0.896122271332 y[1] (closed_form) = -19.5295254271 0.896162637895 absolute error = 8.642e-05 relative error = 0.000442 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9999 Order of pole (given) = 0.5 0 NO 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=1907.6MB, alloc=52.3MB, time=23.56 x[1] = -1.516 0.88 h = 0.0001 0.003 y[1] (numeric) = -19.5295671335 0.90124654206 y[1] (closed_form) = -19.5296441738 0.901286925042 absolute error = 8.698e-05 relative error = 0.0004449 % Correct digits = 5 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] = -1.5159 0.883 h = 0.001 0.001 y[1] (numeric) = -19.5295978004 0.904322898283 y[1] (closed_form) = -19.5296750678 0.904363292935 absolute error = 8.719e-05 relative error = 0.000446 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.007 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5149 0.884 h = 0.001 0.003 y[1] (numeric) = -19.5286183301 0.905391380747 y[1] (closed_form) = -19.5286955983 0.905431825817 absolute error = 8.721e-05 relative error = 0.0004461 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.008 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] = -1.5139 0.887 h = 0.0001 0.004 y[1] (numeric) = -19.5277279759 0.908508016049 y[1] (closed_form) = -19.5278054479 0.908548609388 absolute error = 8.746e-05 relative error = 0.0004474 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.011 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5138 0.891 h = 0.003 0.006 y[1] (numeric) = -19.5278044051 0.912608783745 y[1] (closed_form) = -19.5278822805 0.912649391323 absolute error = 8.783e-05 relative error = 0.0004493 % Correct digits = 5 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=1953.5MB, alloc=52.3MB, time=24.12 x[1] = -1.5108 0.897 h = 0.0001 0.005 y[1] (numeric) = -19.5250016413 0.918887974009 y[1] (closed_form) = -19.525080211 0.918929478758 absolute error = 8.886e-05 relative error = 0.0004546 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.022 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] = -1.5107 0.902 h = 0.0001 0.003 y[1] (numeric) = -19.525125296 0.924013610093 y[1] (closed_form) = -19.5252044968 0.924055131029 absolute error = 8.942e-05 relative error = 0.0004575 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.026 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5106 0.905 h = 0.001 0.001 y[1] (numeric) = -19.5251592763 0.927090829762 y[1] (closed_form) = -19.5252387042 0.92713236229 absolute error = 8.963e-05 relative error = 0.0004585 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.029 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5096 0.906 h = 0.001 0.003 y[1] (numeric) = -19.5241806681 0.928160675733 y[1] (closed_form) = -19.5242600968 0.928202258684 absolute error = 8.966e-05 relative error = 0.0004587 % Correct digits = 5 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] = -1.5086 0.909 h = 0.0001 0.004 y[1] (numeric) = -19.5232934018 0.931279175858 y[1] (closed_form) = -19.5233730344 0.931320907016 absolute error = 8.990e-05 relative error = 0.00046 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.033 Order of pole (given) = 0.5 0 NO 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=1999.4MB, alloc=52.3MB, time=24.69 x[1] = -1.5085 0.913 h = 0.003 0.006 y[1] (numeric) = -19.5233742576 0.935381057252 y[1] (closed_form) = -19.5234542937 0.935422802503 absolute error = 9.027e-05 relative error = 0.0004618 % Correct digits = 5 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] = -1.5055 0.919 h = 0.0001 0.005 y[1] (numeric) = -19.5205774197 0.941665089425 y[1] (closed_form) = -19.5206581505 0.941707731677 absolute error = 9.130e-05 relative error = 0.0004672 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.044 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5054 0.924 h = 0.0001 0.003 y[1] (numeric) = -19.5207066143 0.946792088966 y[1] (closed_form) = -19.5207879762 0.946834747173 absolute error = 9.187e-05 relative error = 0.0004701 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.048 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5053 0.927 h = 0.001 0.001 y[1] (numeric) = -19.5207439086 0.94987017095 y[1] (closed_form) = -19.5208254976 0.949912840671 absolute error = 9.207e-05 relative error = 0.0004711 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.051 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5043 0.928 h = 0.001 0.003 y[1] (numeric) = -19.5197661633 0.950941380236 y[1] (closed_form) = -19.5198477531 0.950984100385 absolute error = 9.210e-05 relative error = 0.0004713 % Correct digits = 5 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=2045.4MB, alloc=52.3MB, time=25.26 x[1] = -1.5033 0.931 h = 0.0001 0.004 y[1] (numeric) = -19.5188819858 0.954061744226 y[1] (closed_form) = -19.5189637796 0.95410461252 absolute error = 9.235e-05 relative error = 0.0004725 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.055 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5032 0.935 h = 0.003 0.006 y[1] (numeric) = -19.5189672689 0.958164737803 y[1] (closed_form) = -19.5190494662 0.958207620045 absolute error = 9.271e-05 relative error = 0.0004744 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.059 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5002 0.941 h = 0.0001 0.005 y[1] (numeric) = -19.5161763592 0.964453610159 y[1] (closed_form) = -19.5162592516 0.964497389231 absolute error = 9.374e-05 relative error = 0.0004797 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.065 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5001 0.946 h = 0.0001 0.003 y[1] (numeric) = -19.5163110948 0.969581971259 y[1] (closed_form) = -19.5163946183 0.969625766053 absolute error = 9.431e-05 relative error = 0.0004826 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.07 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.5 0.949 h = 0.001 0.001 y[1] (numeric) = -19.5163517037 0.972660914425 y[1] (closed_form) = -19.5164354544 0.972704720657 absolute error = 9.452e-05 relative error = 0.0004837 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.073 Order of pole (given) = 0.5 0 NO 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=2091.2MB, alloc=52.3MB, time=25.82 x[1] = -1.499 0.95 h = 0.001 0.003 y[1] (numeric) = -19.5153748217 0.973733486836 y[1] (closed_form) = -19.5154585732 0.973777343498 absolute error = 9.454e-05 relative error = 0.0004838 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.074 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.498 0.953 h = 0.0001 0.004 y[1] (numeric) = -19.5144937341 0.976855713731 y[1] (closed_form) = -19.5145776897 0.976899718477 absolute error = 9.479e-05 relative error = 0.0004851 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.077 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4979 0.957 h = 0.003 0.006 y[1] (numeric) = -19.5145834454 0.980959817976 y[1] (closed_form) = -19.5146678044 0.981003836524 absolute error = 9.515e-05 relative error = 0.000487 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.081 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4949 0.963 h = 0.0001 0.005 y[1] (numeric) = -19.5117984661 0.987253528788 y[1] (closed_form) = -19.5118835207 0.987298443996 absolute error = 9.619e-05 relative error = 0.0004923 % Correct digits = 5 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] = -1.4948 0.968 h = 0.0001 0.003 y[1] (numeric) = -19.5119387436 0.992383249548 y[1] (closed_form) = -19.5120244294 0.992428180246 absolute error = 9.675e-05 relative error = 0.0004952 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.092 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4947 0.971 h = 0.001 0.001 y[1] (numeric) = -19.5119826678 0.995463052766 y[1] (closed_form) = -19.5120685807 0.995507994823 absolute error = 9.696e-05 relative error = 0.0004963 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.095 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 memory used=2137.1MB, alloc=52.3MB, time=26.38 x[1] = -1.4937 0.972 h = 0.0001 0.004 y[1] (numeric) = -19.5110066497 0.996536988108 y[1] (closed_form) = -19.5110925634 0.996581980601 absolute error = 9.698e-05 relative error = 0.0004964 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.096 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4936 0.976 h = 0.003 0.006 y[1] (numeric) = -19.5111001865 1.0006419944 y[1] (closed_form) = -19.5111865037 1.00068700057 absolute error = 9.735e-05 relative error = 0.0004983 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.1 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4906 0.982 h = 0.0001 0.005 y[1] (numeric) = -19.5083203715 1.00693979793 y[1] (closed_form) = -19.5084073845 1.00698570061 absolute error = 9.838e-05 relative error = 0.0005036 % Correct digits = 5 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] = -1.4905 0.987 h = 0.0001 0.003 y[1] (numeric) = -19.5084654363 1.01207062149 y[1] (closed_form) = -19.5085530804 1.01211653946 absolute error = 9.894e-05 relative error = 0.0005065 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.111 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] = -1.4904 0.99 h = 0.001 0.001 y[1] (numeric) = -19.5085122248 1.01515112461 y[1] (closed_form) = -19.5086000962 1.01519705386 absolute error = 9.915e-05 relative error = 0.0005076 % Correct digits = 5 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 memory used=2183.1MB, alloc=52.3MB, time=26.95 x[1] = -1.4894 0.991 h = 0.001 0.003 y[1] (numeric) = -19.507536967 1.01622622266 y[1] (closed_form) = -19.5076248392 1.01627220236 absolute error = 9.917e-05 relative error = 0.0005077 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.115 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4884 0.994 h = 0.0001 0.004 y[1] (numeric) = -19.5066616536 1.0193518766 y[1] (closed_form) = -19.5067497301 1.01939800427 absolute error = 9.942e-05 relative error = 0.000509 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.118 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] = -1.4883 0.998 h = 0.003 0.006 y[1] (numeric) = -19.5067596199 1.02345799074 y[1] (closed_form) = -19.5068480999 1.02350413193 absolute error = 9.979e-05 relative error = 0.0005109 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.122 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4853 1.004 h = 0.0001 0.005 y[1] (numeric) = -19.5039857397 1.02976062948 y[1] (closed_form) = -19.5040749159 1.02980766701 absolute error = 0.0001008 relative error = 0.0005162 % Correct digits = 5 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] = -1.4852 1.009 h = 0.0001 0.003 y[1] (numeric) = -19.5041363482 1.03489280915 y[1] (closed_form) = -19.5042261557 1.03493986174 absolute error = 0.0001014 relative error = 0.0005191 % Correct digits = 5 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 memory used=2229.0MB, alloc=52.3MB, time=27.52 x[1] = -1.4851 1.012 h = 0.001 0.001 y[1] (numeric) = -19.5041864532 1.0379741702 y[1] (closed_form) = -19.5042764878 1.03802123401 absolute error = 0.0001016 relative error = 0.0005201 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.135 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4841 1.013 h = 0.001 0.003 y[1] (numeric) = -19.5032120603 1.03905063083 y[1] (closed_form) = -19.5033020958 1.03909774507 absolute error = 0.0001016 relative error = 0.0005203 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.137 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4831 1.016 h = 0.0001 0.004 y[1] (numeric) = -19.5023398395 1.04217814491 y[1] (closed_form) = -19.5024300793 1.04222540707 absolute error = 0.0001019 relative error = 0.0005216 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.14 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] = -1.483 1.02 h = 0.003 0.006 y[1] (numeric) = -19.5024422362 1.04628536537 y[1] (closed_form) = -19.5025328797 1.04633264091 absolute error = 0.0001022 relative error = 0.0005234 % Correct digits = 5 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] = -1.48 1.026 h = 0.0001 0.005 y[1] (numeric) = -19.499674293 1.0525928376 y[1] (closed_form) = -19.4997656331 1.05264100931 absolute error = 0.0001033 relative error = 0.0005288 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.15 Order of pole (given) = 0.5 0 NO 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=2275.0MB, alloc=52.3MB, time=28.08 x[1] = -1.4799 1.031 h = 0.0001 0.003 y[1] (numeric) = -19.4998304463 1.05772637149 y[1] (closed_form) = -19.4999224177 1.05777455801 absolute error = 0.0001038 relative error = 0.0005317 % Correct digits = 5 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] = -1.4798 1.034 h = 0.001 0.001 y[1] (numeric) = -19.4998838683 1.06080858935 y[1] (closed_form) = -19.4999760668 1.06085678701 absolute error = 0.000104 relative error = 0.0005327 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.157 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4788 1.035 h = 0.001 0.003 y[1] (numeric) = -19.498910341 1.06188641234 y[1] (closed_form) = -19.4990025404 1.06193466045 absolute error = 0.0001041 relative error = 0.0005329 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.159 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] = -1.4778 1.038 h = 0.0001 0.004 y[1] (numeric) = -19.4980412137 1.06501578562 y[1] (closed_form) = -19.4981336175 1.06506418157 absolute error = 0.0001043 relative error = 0.0005342 % Correct digits = 5 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] = -1.4777 1.042 h = 0.003 0.006 y[1] (numeric) = -19.4981480416 1.06912411088 y[1] (closed_form) = -19.4982408491 1.06917252007 absolute error = 0.0001047 relative error = 0.000536 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.166 Order of pole (given) = 0.5 0 NO 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=2321.0MB, alloc=52.3MB, time=28.65 x[1] = -1.4747 1.048 h = 0.0001 0.005 y[1] (numeric) = -19.4953860378 1.07543641487 y[1] (closed_form) = -19.4954795422 1.07548572006 absolute error = 0.0001057 relative error = 0.0005414 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.172 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4746 1.053 h = 0.0001 0.003 y[1] (numeric) = -19.4955477369 1.08057130107 y[1] (closed_form) = -19.4956418726 1.08062062085 absolute error = 0.0001063 relative error = 0.0005443 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.177 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] = -1.4745 1.056 h = 0.001 0.001 y[1] (numeric) = -19.4956044764 1.0836543746 y[1] (closed_form) = -19.4956988394 1.08370370543 absolute error = 0.0001065 relative error = 0.0005453 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.18 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4735 1.057 h = 0.001 0.003 y[1] (numeric) = -19.4946318152 1.08473355978 y[1] (closed_form) = -19.4947261791 1.08478294106 absolute error = 0.0001065 relative error = 0.0005455 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.181 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4725 1.06 h = 0.0001 0.004 y[1] (numeric) = -19.4937657825 1.08786479129 y[1] (closed_form) = -19.4938603508 1.08791432035 absolute error = 0.0001068 relative error = 0.0005468 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.184 Order of pole (given) = 0.5 0 NO 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=2366.9MB, alloc=52.3MB, time=29.22 x[1] = -1.4724 1.064 h = 0.003 0.006 y[1] (numeric) = -19.4938770424 1.09197421984 y[1] (closed_form) = -19.4939720144 1.092023762 absolute error = 0.0001071 relative error = 0.0005486 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.188 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4694 1.07 h = 0.0001 0.005 y[1] (numeric) = -19.4911209802 1.09829135386 y[1] (closed_form) = -19.4912166496 1.09834179184 absolute error = 0.0001082 relative error = 0.000554 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.194 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4693 1.075 h = 0.0001 0.003 y[1] (numeric) = -19.4912882261 1.10342759047 y[1] (closed_form) = -19.4913845268 1.10347804281 absolute error = 0.0001087 relative error = 0.0005569 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.199 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4692 1.078 h = 0.001 0.001 y[1] (numeric) = -19.4913482838 1.10651151854 y[1] (closed_form) = -19.4914448118 1.10656198186 absolute error = 0.0001089 relative error = 0.0005579 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.202 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4682 1.079 h = 0.0001 0.004 y[1] (numeric) = -19.4903764893 1.10759206571 y[1] (closed_form) = -19.4904730183 1.10764257948 absolute error = 0.0001089 relative error = 0.0005581 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.203 Order of pole (given) = 0.5 0 NO 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=2412.9MB, alloc=52.3MB, time=29.79 x[1] = -1.4681 1.083 h = 0.003 0.006 y[1] (numeric) = -19.490491578 1.11170238992 y[1] (closed_form) = -19.4905885106 1.11175291665 absolute error = 0.0001093 relative error = 0.0005599 % Correct digits = 5 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 x[1] = -1.4651 1.089 h = 0.0001 0.005 y[1] (numeric) = -19.4877406896 1.11802360926 y[1] (closed_form) = -19.4878383199 1.11807503167 absolute error = 0.0001103 relative error = 0.0005653 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.213 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.465 1.094 h = 0.0001 0.003 y[1] (numeric) = -19.4879127267 1.12316094065 y[1] (closed_form) = -19.4880109884 1.12321237722 absolute error = 0.0001109 relative error = 0.0005682 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.218 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4649 1.097 h = 0.001 0.001 y[1] (numeric) = -19.4879756514 1.12624556384 y[1] (closed_form) = -19.4880741403 1.12629701132 absolute error = 0.0001111 relative error = 0.0005692 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.221 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] = -1.4639 1.098 h = 0.001 0.003 y[1] (numeric) = -19.4870046195 1.12732727288 y[1] (closed_form) = -19.4871031094 1.12737877081 absolute error = 0.0001111 relative error = 0.0005694 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.222 Order of pole (given) = 0.5 0 NO 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=2458.8MB, alloc=52.3MB, time=30.35 x[1] = -1.4629 1.101 h = 0.0001 0.004 y[1] (numeric) = -19.4861443696 1.13046192267 y[1] (closed_form) = -19.4862430641 1.13051356827 absolute error = 0.0001114 relative error = 0.0005707 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.225 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4628 1.105 h = 0.003 0.006 y[1] (numeric) = -19.4862638917 1.13457334733 y[1] (closed_form) = -19.48636299 1.13462500575 absolute error = 0.0001118 relative error = 0.0005725 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.229 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4598 1.111 h = 0.0001 0.005 y[1] (numeric) = -19.4835189492 1.14089939346 y[1] (closed_form) = -19.4836187455 1.14095194738 absolute error = 0.0001128 relative error = 0.0005779 % Correct digits = 5 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] = -1.4597 1.116 h = 0.0001 0.003 y[1] (numeric) = -19.4836965349 1.14603807171 y[1] (closed_form) = -19.4837969627 1.14609063955 absolute error = 0.0001134 relative error = 0.0005808 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.24 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4596 1.119 h = 0.001 0.001 y[1] (numeric) = -19.4837627789 1.14912354733 y[1] (closed_form) = -19.4838634339 1.149176126 absolute error = 0.0001136 relative error = 0.0005818 % Correct digits = 5 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 x[1] = -1.4586 1.12 h = 0.001 0.003 y[1] (numeric) = -19.4827926148 1.15020661799 y[1] (closed_form) = -19.4828932709 1.15025924712 absolute error = 0.0001136 relative error = 0.000582 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.244 Order of pole (given) = 0.5 0 NO 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=2504.8MB, alloc=52.3MB, time=30.92 x[1] = -1.4576 1.123 h = 0.0001 0.004 y[1] (numeric) = -19.4819354621 1.15334312324 y[1] (closed_form) = -19.4820363228 1.15339589999 absolute error = 0.0001138 relative error = 0.0005833 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.247 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4575 1.127 h = 0.003 0.006 y[1] (numeric) = -19.4820594185 1.15745564685 y[1] (closed_form) = -19.482160683 1.15750843626 absolute error = 0.0001142 relative error = 0.0005851 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.251 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4545 1.133 h = 0.0001 0.005 y[1] (numeric) = -19.4793204242 1.16378651803 y[1] (closed_form) = -19.4794223872 1.16384020277 absolute error = 0.0001152 relative error = 0.0005905 % Correct digits = 5 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] = -1.4544 1.138 h = 0.0001 0.003 y[1] (numeric) = -19.4795035595 1.16892654124 y[1] (closed_form) = -19.479606154 1.16898023967 absolute error = 0.0001158 relative error = 0.0005934 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.262 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] = -1.4543 1.141 h = 0.001 0.001 y[1] (numeric) = -19.4795731234 1.17201286815 y[1] (closed_form) = -19.4796759452 1.17206657733 absolute error = 0.000116 relative error = 0.0005944 % Correct digits = 5 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 memory used=2550.7MB, alloc=52.3MB, time=31.48 x[1] = -1.4533 1.142 h = 0.001 0.003 y[1] (numeric) = -19.4786038277 1.17309730024 y[1] (closed_form) = -19.4787066504 1.17315105989 absolute error = 0.000116 relative error = 0.0005946 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.266 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] = -1.4523 1.145 h = 0.0001 0.004 y[1] (numeric) = -19.4777497732 1.17623566 y[1] (closed_form) = -19.4778528006 1.1762895672 absolute error = 0.0001163 relative error = 0.0005959 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.269 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] = -1.4522 1.149 h = 0.003 0.006 y[1] (numeric) = -19.4778781647 1.18034928103 y[1] (closed_form) = -19.477981596 1.18040320075 absolute error = 0.0001166 relative error = 0.0005977 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.273 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] = -1.4492 1.155 h = 0.0001 0.005 y[1] (numeric) = -19.4751451209 1.18668497552 y[1] (closed_form) = -19.475249251 1.1867397904 absolute error = 0.0001177 relative error = 0.0006031 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.28 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4491 1.16 h = 0.0001 0.003 y[1] (numeric) = -19.4753338068 1.1918263418 y[1] (closed_form) = -19.4754385685 1.19188117014 absolute error = 0.0001182 relative error = 0.000606 % Correct digits = 5 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 memory used=2596.8MB, alloc=52.3MB, time=32.05 x[1] = -1.449 1.163 h = 0.001 0.001 y[1] (numeric) = -19.4754066913 1.19491351886 y[1] (closed_form) = -19.4755116803 1.19496835787 absolute error = 0.0001184 relative error = 0.000607 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.287 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] = -1.448 1.164 h = 0.001 0.003 y[1] (numeric) = -19.4744382645 1.19599931219 y[1] (closed_form) = -19.4745432545 1.19605420167 absolute error = 0.0001185 relative error = 0.0006072 % Correct digits = 5 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] = -1.447 1.167 h = 0.0001 0.004 y[1] (numeric) = -19.4735873091 1.1991395255 y[1] (closed_form) = -19.4736925038 1.19919456247 absolute error = 0.0001187 relative error = 0.0006085 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.291 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4469 1.171 h = 0.003 0.006 y[1] (numeric) = -19.4737201365 1.20325424243 y[1] (closed_form) = -19.4738257352 1.20330929178 absolute error = 0.0001191 relative error = 0.0006104 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.295 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4439 1.177 h = 0.0001 0.005 y[1] (numeric) = -19.4709930455 1.20959475852 y[1] (closed_form) = -19.4710993434 1.20965070284 absolute error = 0.0001201 relative error = 0.0006157 % Correct digits = 5 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=2642.5MB, alloc=52.3MB, time=32.61 x[1] = -1.4438 1.182 h = 0.0001 0.003 y[1] (numeric) = -19.4711872829 1.21473746595 y[1] (closed_form) = -19.4712942125 1.2147934235 absolute error = 0.0001207 relative error = 0.0006186 % Correct digits = 5 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] = -1.4437 1.185 h = 0.001 0.001 y[1] (numeric) = -19.4712634886 1.21782549204 y[1] (closed_form) = -19.4713706454 1.21788146018 absolute error = 0.0001209 relative error = 0.0006197 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.309 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4427 1.186 h = 0.0001 0.004 y[1] (numeric) = -19.4702959313 1.21891264641 y[1] (closed_form) = -19.4704030892 1.21896866503 absolute error = 0.0001209 relative error = 0.0006198 % Correct digits = 5 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] = -1.4426 1.19 h = 0.003 0.006 y[1] (numeric) = -19.4704325908 1.22302825259 y[1] (closed_form) = -19.4705401525 1.22308428347 absolute error = 0.0001213 relative error = 0.0006217 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.314 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4396 1.196 h = 0.0001 0.005 y[1] (numeric) = -19.467710683 1.22937284661 y[1] (closed_form) = -19.4678189443 1.22942977231 absolute error = 0.0001223 relative error = 0.000627 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.321 Order of pole (given) = 0.5 0 NO 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=2688.5MB, alloc=52.3MB, time=33.18 x[1] = -1.4395 1.201 h = 0.0001 0.003 y[1] (numeric) = -19.4679097158 1.23451664079 y[1] (closed_form) = -19.4680186087 1.23457357952 absolute error = 0.0001229 relative error = 0.0006299 % Correct digits = 5 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] = -1.4394 1.204 h = 0.001 0.001 y[1] (numeric) = -19.4679887908 1.23760535722 y[1] (closed_form) = -19.468097911 1.23766230646 absolute error = 0.0001231 relative error = 0.000631 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.328 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4384 1.205 h = 0.001 0.003 y[1] (numeric) = -19.4670219985 1.23869367261 y[1] (closed_form) = -19.4671311199 1.23875067234 absolute error = 0.0001231 relative error = 0.0006311 % Correct digits = 5 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] = -1.4374 1.208 h = 0.0001 0.004 y[1] (numeric) = -19.4661768345 1.24183729543 y[1] (closed_form) = -19.4662861607 1.24189444252 absolute error = 0.0001234 relative error = 0.0006324 % Correct digits = 5 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] = -1.4373 1.212 h = 0.003 0.006 y[1] (numeric) = -19.4663179313 1.24595399468 y[1] (closed_form) = -19.4664276615 1.24601115388 absolute error = 0.0001237 relative error = 0.0006343 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.336 Order of pole (given) = 0.5 0 NO 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=2734.4MB, alloc=52.3MB, time=33.74 x[1] = -1.4343 1.218 h = 0.0001 0.005 y[1] (numeric) = -19.4636019806 1.25230340702 y[1] (closed_form) = -19.4637124107 1.25236146088 absolute error = 0.0001248 relative error = 0.0006397 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.343 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4342 1.223 h = 0.0001 0.003 y[1] (numeric) = -19.4638065668 1.25744853881 y[1] (closed_form) = -19.4639176286 1.25750660547 absolute error = 0.0001253 relative error = 0.0006425 % Correct digits = 5 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] = -1.4341 1.226 h = 0.001 0.001 y[1] (numeric) = -19.463888964 1.26053810215 y[1] (closed_form) = -19.4640002532 1.26059617924 absolute error = 0.0001255 relative error = 0.0006436 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.35 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4331 1.227 h = 0.001 0.003 y[1] (numeric) = -19.4629230424 1.26162777822 y[1] (closed_form) = -19.4630343326 1.2616859058 absolute error = 0.0001256 relative error = 0.0006437 % Correct digits = 5 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] = -1.4321 1.23 h = 0.0001 0.004 y[1] (numeric) = -19.4620809802 1.26477325182 y[1] (closed_form) = -19.4621924755 1.2648315267 absolute error = 0.0001258 relative error = 0.0006451 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.355 Order of pole (given) = 0.5 0 NO 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=2780.4MB, alloc=52.3MB, time=34.31 x[1] = -1.432 1.234 h = 0.003 0.006 y[1] (numeric) = -19.4622265152 1.26889104262 y[1] (closed_form) = -19.4623384144 1.26894932946 absolute error = 0.0001262 relative error = 0.0006469 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.358 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.429 1.24 h = 0.0001 0.005 y[1] (numeric) = -19.4595165239 1.27524527157 y[1] (closed_form) = -19.4596291234 1.27530445289 absolute error = 0.0001272 relative error = 0.0006523 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.365 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4289 1.245 h = 0.0001 0.003 y[1] (numeric) = -19.4597266644 1.28039173906 y[1] (closed_form) = -19.4598398957 1.28045093295 absolute error = 0.0001278 relative error = 0.0006552 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.37 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4288 1.248 h = 0.001 0.001 y[1] (numeric) = -19.4598123846 1.28348214816 y[1] (closed_form) = -19.4599258433 1.28354135242 absolute error = 0.000128 relative error = 0.0006562 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.373 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4278 1.249 h = 0.001 0.003 y[1] (numeric) = -19.458847334 1.28457318472 y[1] (closed_form) = -19.4589607938 1.28463243946 absolute error = 0.000128 relative error = 0.0006564 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.374 Order of pole (given) = 0.5 0 NO 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=2826.4MB, alloc=52.3MB, time=34.88 x[1] = -1.4268 1.252 h = 0.0001 0.004 y[1] (numeric) = -19.4580083747 1.28772050814 y[1] (closed_form) = -19.4581220396 1.28777991012 absolute error = 0.0001283 relative error = 0.0006577 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.377 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4267 1.256 h = 0.003 0.006 y[1] (numeric) = -19.4581583487 1.29183938897 y[1] (closed_form) = -19.4582724176 1.29189880277 absolute error = 0.0001286 relative error = 0.0006595 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.381 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4237 1.262 h = 0.0001 0.005 y[1] (numeric) = -19.455454319 1.29819843278 y[1] (closed_form) = -19.4555690886 1.29825874089 absolute error = 0.0001297 relative error = 0.0006649 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.387 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4236 1.267 h = 0.0001 0.003 y[1] (numeric) = -19.4556700149 1.30334623407 y[1] (closed_form) = -19.4557854163 1.30340655451 absolute error = 0.0001302 relative error = 0.0006678 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.392 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4235 1.27 h = 0.001 0.001 y[1] (numeric) = -19.4557590586 1.30643748782 y[1] (closed_form) = -19.4558746874 1.30649781854 absolute error = 0.0001304 relative error = 0.0006688 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.395 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4225 1.271 h = 0.001 0.003 y[1] (numeric) = -19.4547948798 1.30752988467 y[1] (closed_form) = -19.4549105097 1.30759026588 absolute error = 0.0001304 relative error = 0.000669 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.396 Order of pole (given) = 0.5 0 NO 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=2872.4MB, alloc=52.3MB, time=35.44 x[1] = -1.4215 1.274 h = 0.0001 0.004 y[1] (numeric) = -19.4539590242 1.31067905694 y[1] (closed_form) = -19.4540748593 1.31073958533 absolute error = 0.0001307 relative error = 0.0006703 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.399 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4214 1.278 h = 0.003 0.006 y[1] (numeric) = -19.454113438 1.31479902629 y[1] (closed_form) = -19.4542296771 1.31485956635 absolute error = 0.0001311 relative error = 0.0006721 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.403 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4184 1.284 h = 0.0001 0.005 y[1] (numeric) = -19.4514153723 1.32116288323 y[1] (closed_form) = -19.4515323125 1.32122431743 absolute error = 0.0001321 relative error = 0.0006775 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.41 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4183 1.289 h = 0.0001 0.003 y[1] (numeric) = -19.4516366245 1.32631201642 y[1] (closed_form) = -19.4517541966 1.32637346271 absolute error = 0.0001327 relative error = 0.0006804 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.414 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4182 1.292 h = 0.001 0.001 y[1] (numeric) = -19.4517289923 1.32940411367 y[1] (closed_form) = -19.4518467919 1.32946557016 absolute error = 0.0001329 relative error = 0.0006815 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.417 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 memory used=2918.3MB, alloc=52.3MB, time=36.00 x[1] = -1.4172 1.293 h = 0.0001 0.004 y[1] (numeric) = -19.4507656858 1.33049787061 y[1] (closed_form) = -19.4508834864 1.3305593776 absolute error = 0.0001329 relative error = 0.0006816 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.418 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4171 1.297 h = 0.003 0.006 y[1] (numeric) = -19.4509239348 1.3346187228 y[1] (closed_form) = -19.4510421395 1.33468024133 absolute error = 0.0001333 relative error = 0.0006835 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.422 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4141 1.303 h = 0.0001 0.005 y[1] (numeric) = -19.4482310619 1.34098665026 y[1] (closed_form) = -19.4483499679 1.34104906277 absolute error = 0.0001343 relative error = 0.0006889 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.429 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.414 1.308 h = 0.0001 0.003 y[1] (numeric) = -19.4484571135 1.34613686216 y[1] (closed_form) = -19.4485766514 1.34619928657 absolute error = 0.0001349 relative error = 0.0006917 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.433 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4139 1.311 h = 0.001 0.001 y[1] (numeric) = -19.4485523531 1.34922964496 y[1] (closed_form) = -19.4486721185 1.3492920795 absolute error = 0.0001351 relative error = 0.0006928 % Correct digits = 5 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=2964.2MB, alloc=52.3MB, time=36.57 x[1] = -1.4129 1.312 h = 0.001 0.003 y[1] (numeric) = -19.447589814 1.35032456207 y[1] (closed_form) = -19.4477095806 1.35038704711 absolute error = 0.0001351 relative error = 0.0006929 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.437 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4119 1.315 h = 0.0001 0.004 y[1] (numeric) = -19.4467597585 1.35347713507 y[1] (closed_form) = -19.4468797303 1.35353976718 absolute error = 0.0001353 relative error = 0.0006943 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.441 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] = -1.4118 1.319 h = 0.003 0.006 y[1] (numeric) = -19.4469224486 1.35759907294 y[1] (closed_form) = -19.4470428246 1.35766171644 absolute error = 0.0001357 relative error = 0.0006961 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.444 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] = -1.4088 1.325 h = 0.0001 0.005 y[1] (numeric) = -19.4442355439 1.36397181027 y[1] (closed_form) = -19.4443566217 1.36403534758 absolute error = 0.0001367 relative error = 0.0007015 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.451 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4087 1.33 h = 0.0001 0.003 y[1] (numeric) = -19.4444671537 1.36912335051 y[1] (closed_form) = -19.4445888634 1.36918689949 absolute error = 0.0001373 relative error = 0.0007044 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.456 Order of pole (given) = 0.5 0 NO 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=3010.1MB, alloc=52.3MB, time=37.13 x[1] = -1.4086 1.333 h = 0.001 0.001 y[1] (numeric) = -19.4445657186 1.37221697469 y[1] (closed_form) = -19.4446876558 1.37228053372 absolute error = 0.0001375 relative error = 0.0007054 % Correct digits = 5 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] = -1.4076 1.334 h = 0.001 0.003 y[1] (numeric) = -19.4436040529 1.37331325154 y[1] (closed_form) = -19.4437259912 1.37337686107 absolute error = 0.0001375 relative error = 0.0007056 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.46 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4066 1.337 h = 0.0001 0.004 y[1] (numeric) = -19.4427771038 1.37646767062 y[1] (closed_form) = -19.4428992475 1.37653142716 absolute error = 0.0001378 relative error = 0.0007069 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.463 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] = -1.4065 1.341 h = 0.003 0.006 y[1] (numeric) = -19.442944236 1.38059069264 y[1] (closed_form) = -19.4430667839 1.38065446043 absolute error = 0.0001381 relative error = 0.0007087 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.466 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] = -1.4035 1.347 h = 0.0001 0.005 y[1] (numeric) = -19.4402633018 1.38696823811 y[1] (closed_form) = -19.4403865519 1.38703289953 absolute error = 0.0001392 relative error = 0.0007141 % Correct digits = 5 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 memory used=3056.0MB, alloc=52.3MB, time=37.70 x[1] = -1.4034 1.352 h = 0.0001 0.003 y[1] (numeric) = -19.4405004707 1.39212110479 y[1] (closed_form) = -19.4406243528 1.39218577764 absolute error = 0.0001397 relative error = 0.000717 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.478 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.4033 1.355 h = 0.001 0.001 y[1] (numeric) = -19.4406023615 1.39521556922 y[1] (closed_form) = -19.4407264711 1.39528025205 absolute error = 0.00014 relative error = 0.0007181 % Correct digits = 5 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] = -1.4023 1.356 h = 0.001 0.003 y[1] (numeric) = -19.4396415697 1.3963132056 y[1] (closed_form) = -19.4397656804 1.39637793893 absolute error = 0.00014 relative error = 0.0007182 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.482 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] = -1.4013 1.359 h = 0.0001 0.004 y[1] (numeric) = -19.4388177281 1.39946946981 y[1] (closed_form) = -19.4389420442 1.39953435009 absolute error = 0.0001402 relative error = 0.0007195 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.485 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] = -1.4012 1.363 h = 0.003 0.006 y[1] (numeric) = -19.4389893032 1.40359357447 y[1] (closed_form) = -19.4391140236 1.40365846585 absolute error = 0.0001406 relative error = 0.0007214 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.489 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 memory used=3101.9MB, alloc=52.3MB, time=38.27 x[1] = -1.3982 1.369 h = 0.0001 0.005 y[1] (numeric) = -19.4363143418 1.40997592633 y[1] (closed_form) = -19.4364397647 1.41004171117 absolute error = 0.0001416 relative error = 0.0007268 % Correct digits = 5 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 x[1] = -1.3981 1.374 h = 0.0001 0.003 y[1] (numeric) = -19.4365570709 1.41513011754 y[1] (closed_form) = -19.4366831259 1.41519591358 absolute error = 0.0001422 relative error = 0.0007296 % Correct digits = 5 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] = -1.398 1.377 h = 0.001 0.001 y[1] (numeric) = -19.4366622881 1.41822542109 y[1] (closed_form) = -19.4367885706 1.41829122702 absolute error = 0.0001424 relative error = 0.0007307 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.503 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.397 1.378 h = 0.001 0.003 y[1] (numeric) = -19.4357023708 1.41932441681 y[1] (closed_form) = -19.4358286545 1.41939027325 absolute error = 0.0001424 relative error = 0.0007308 % Correct digits = 5 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] = -1.396 1.381 h = 0.0001 0.004 y[1] (numeric) = -19.4348816376 1.42248252518 y[1] (closed_form) = -19.4350081268 1.4225485285 absolute error = 0.0001427 relative error = 0.0007322 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.507 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 memory used=3148.0MB, alloc=52.3MB, time=38.84 x[1] = -1.3959 1.385 h = 0.003 0.006 y[1] (numeric) = -19.4350576563 1.42660771095 y[1] (closed_form) = -19.4351845498 1.42667372523 absolute error = 0.000143 relative error = 0.000734 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.511 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3929 1.391 h = 0.0001 0.005 y[1] (numeric) = -19.43238867 1.43299486748 y[1] (closed_form) = -19.4325162665 1.43306177504 absolute error = 0.0001441 relative error = 0.0007394 % Correct digits = 5 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] = -1.3928 1.396 h = 0.0001 0.003 y[1] (numeric) = -19.4326369603 1.43815038131 y[1] (closed_form) = -19.4327651888 1.43821729984 absolute error = 0.0001446 relative error = 0.0007423 % Correct digits = 5 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] = -1.3927 1.399 h = 0.001 0.001 y[1] (numeric) = -19.4327455046 1.44124652284 y[1] (closed_form) = -19.4328739607 1.44131345119 absolute error = 0.0001448 relative error = 0.0007433 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.525 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3917 1.4 h = 0.003 0.006 y[1] (numeric) = -19.4317864624 1.4423468777 y[1] (closed_form) = -19.4319149196 1.44241385656 absolute error = 0.0001449 relative error = 0.0007435 % Correct digits = 5 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 memory used=3193.9MB, alloc=52.3MB, time=39.40 x[1] = -1.3887 1.406 h = 0.0001 0.005 y[1] (numeric) = -19.4291214669 1.44873748885 y[1] (closed_form) = -19.4292506271 1.4488053609 absolute error = 0.0001459 relative error = 0.0007489 % Correct digits = 5 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 x[1] = -1.3886 1.411 h = 0.0001 0.003 y[1] (numeric) = -19.4293735499 1.45389405152 y[1] (closed_form) = -19.4295033423 1.45396193437 absolute error = 0.0001465 relative error = 0.0007518 % Correct digits = 5 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] = -1.3885 1.414 h = 0.001 0.001 y[1] (numeric) = -19.4294843621 1.45699085265 y[1] (closed_form) = -19.4296143821 1.45705874526 absolute error = 0.0001467 relative error = 0.0007528 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.541 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] = -1.3875 1.415 h = 0.001 0.003 y[1] (numeric) = -19.428525888 1.4580921644 y[1] (closed_form) = -19.4286559091 1.45816010753 absolute error = 0.0001467 relative error = 0.000753 % Correct digits = 5 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] = -1.3865 1.418 h = 0.0001 0.004 y[1] (numeric) = -19.4277103572 1.46125346167 y[1] (closed_form) = -19.4278405839 1.46132155158 absolute error = 0.000147 relative error = 0.0007543 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.545 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3864 1.422 h = 0.003 0.006 y[1] (numeric) = -19.427893851 1.46538058078 y[1] (closed_form) = -19.4280244821 1.46544868141 absolute error = 0.0001473 relative error = 0.0007561 % Correct digits = 5 memory used=3239.9MB, alloc=52.3MB, time=39.97 Radius of convergence (given) for eq 1 = 1.549 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] = -1.3834 1.428 h = 0.0001 0.005 y[1] (numeric) = -19.4252348343 1.47177599373 y[1] (closed_form) = -19.4253661689 1.47184498735 absolute error = 0.0001484 relative error = 0.0007615 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.555 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3833 1.433 h = 0.0001 0.003 y[1] (numeric) = -19.4254924801 1.47693387583 y[1] (closed_form) = -19.425624447 1.47700288003 absolute error = 0.0001489 relative error = 0.0007644 % Correct digits = 5 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] = -1.3832 1.436 h = 0.001 0.001 y[1] (numeric) = -19.4256066205 1.48003151304 y[1] (closed_form) = -19.425738815 1.48010052692 absolute error = 0.0001491 relative error = 0.0007654 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.563 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3822 1.437 h = 0.001 0.003 y[1] (numeric) = -19.4246490224 1.48113418362 y[1] (closed_form) = -19.4247812181 1.48120324801 absolute error = 0.0001491 relative error = 0.0007656 % Correct digits = 5 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] = -1.3812 1.44 h = 0.0001 0.004 y[1] (numeric) = -19.4238366026 1.48429732248 y[1] (closed_form) = -19.423969004 1.4843665336 absolute error = 0.0001494 relative error = 0.0007669 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.567 Order of pole (given) = 0.5 0 NO 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=3285.8MB, alloc=52.3MB, time=40.53 x[1] = -1.3811 1.444 h = 0.003 0.006 y[1] (numeric) = -19.4240245423 1.48842551864 y[1] (closed_form) = -19.424157348 1.48849474033 absolute error = 0.0001498 relative error = 0.0007688 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.571 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3781 1.45 h = 0.0001 0.005 y[1] (numeric) = -19.4213715068 1.49482573163 y[1] (closed_form) = -19.4215050166 1.49489584614 absolute error = 0.0001508 relative error = 0.0007742 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.578 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.378 1.455 h = 0.0001 0.003 y[1] (numeric) = -19.4216347166 1.49998493126 y[1] (closed_form) = -19.4217688586 1.50005505611 absolute error = 0.0001514 relative error = 0.000777 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.582 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3779 1.458 h = 0.001 0.001 y[1] (numeric) = -19.4217521857 1.50308340342 y[1] (closed_form) = -19.4218865553 1.50315353786 absolute error = 0.0001516 relative error = 0.0007781 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.585 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3769 1.459 h = 0.001 0.003 y[1] (numeric) = -19.4207954642 1.50418743263 y[1] (closed_form) = -19.420929835 1.5042576176 absolute error = 0.0001516 relative error = 0.0007783 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.586 Order of pole (given) = 0.5 0 NO 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=3331.7MB, alloc=52.3MB, time=41.10 x[1] = -1.3759 1.462 h = 0.0001 0.004 y[1] (numeric) = -19.4199861564 1.50735241212 y[1] (closed_form) = -19.420120733 1.50742274375 absolute error = 0.0001518 relative error = 0.0007796 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.59 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3758 1.466 h = 0.003 0.006 y[1] (numeric) = -19.4201785427 1.51148168381 y[1] (closed_form) = -19.4203135237 1.51155202586 absolute error = 0.0001522 relative error = 0.0007814 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.593 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3728 1.472 h = 0.0001 0.005 y[1] (numeric) = -19.4175314909 1.5178866951 y[1] (closed_form) = -19.4176671763 1.5179579298 absolute error = 0.0001532 relative error = 0.0007868 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.6 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3727 1.477 h = 0.0001 0.003 y[1] (numeric) = -19.4178002654 1.52304721034 y[1] (closed_form) = -19.4179365832 1.52311845515 absolute error = 0.0001538 relative error = 0.0007897 % Correct digits = 5 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] = -1.3726 1.48 h = 0.001 0.001 y[1] (numeric) = -19.4179210639 1.52614651631 y[1] (closed_form) = -19.4180576092 1.52621777063 absolute error = 0.000154 relative error = 0.0007907 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.607 Order of pole (given) = 0.5 0 NO 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=3377.8MB, alloc=52.3MB, time=41.67 x[1] = -1.3716 1.481 h = 0.0001 0.004 y[1] (numeric) = -19.4169652196 1.52725190396 y[1] (closed_form) = -19.4171017662 1.52732320881 absolute error = 0.000154 relative error = 0.0007909 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.609 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 x[1] = -1.3715 1.485 h = 0.003 0.006 y[1] (numeric) = -19.4171614469 1.53138204723 y[1] (closed_form) = -19.4172983979 1.53145336237 absolute error = 0.0001544 relative error = 0.0007927 % Correct digits = 5 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] = -1.3685 1.491 h = 0.0001 0.005 y[1] (numeric) = -19.4145196046 1.53779111603 y[1] (closed_form) = -19.4146572603 1.53786332367 absolute error = 0.0001554 relative error = 0.0007982 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.619 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3684 1.496 h = 0.0001 0.003 y[1] (numeric) = -19.4147931856 1.54295269589 y[1] (closed_form) = -19.4149314737 1.54302491344 absolute error = 0.000156 relative error = 0.000801 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.624 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3683 1.499 h = 0.001 0.001 y[1] (numeric) = -19.4149168602 1.54605267899 y[1] (closed_form) = -19.4150553759 1.54612490598 absolute error = 0.0001562 relative error = 0.0008021 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.627 Order of pole (given) = 0.5 0 NO 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=3423.8MB, alloc=52.3MB, time=42.24 x[1] = -1.3673 1.5 h = 0.001 0.003 y[1] (numeric) = -19.4139617876 1.54715922532 y[1] (closed_form) = -19.4141003046 1.54723150285 absolute error = 0.0001562 relative error = 0.0008022 % Correct digits = 5 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] = -1.3663 1.503 h = 0.0001 0.004 y[1] (numeric) = -19.4131582949 1.55032759012 y[1] (closed_form) = -19.4132970178 1.55040001419 absolute error = 0.0001565 relative error = 0.0008035 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.631 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3662 1.507 h = 0.003 0.006 y[1] (numeric) = -19.4133589703 1.55445880608 y[1] (closed_form) = -19.4134980976 1.55453124029 absolute error = 0.0001569 relative error = 0.0008054 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.635 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3632 1.513 h = 0.0001 0.005 y[1] (numeric) = -19.4107231158 1.56087266992 y[1] (closed_form) = -19.4108629483 1.56094599645 absolute error = 0.0001579 relative error = 0.0008108 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.642 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3631 1.518 h = 0.0001 0.003 y[1] (numeric) = -19.4110022635 1.56603556183 y[1] (closed_form) = -19.4111427284 1.56610889805 absolute error = 0.0001585 relative error = 0.0008137 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.646 Order of pole (given) = 0.5 0 NO 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=3469.9MB, alloc=52.3MB, time=42.80 x[1] = -1.363 1.521 h = 0.001 0.001 y[1] (numeric) = -19.4111292686 1.56913637661 y[1] (closed_form) = -19.4112699611 1.56920972219 absolute error = 0.0001587 relative error = 0.0008147 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.649 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.362 1.522 h = 0.001 0.003 y[1] (numeric) = -19.4101750743 1.57024428102 y[1] (closed_form) = -19.4103157681 1.57031767713 absolute error = 0.0001587 relative error = 0.0008149 % Correct digits = 5 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 x[1] = -1.361 1.525 h = 0.0001 0.004 y[1] (numeric) = -19.4093746963 1.57341448367 y[1] (closed_form) = -19.409515596 1.57348802627 absolute error = 0.0001589 relative error = 0.0008162 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.653 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3609 1.529 h = 0.003 0.006 y[1] (numeric) = -19.4095798205 1.57754677079 y[1] (closed_form) = -19.4097211248 1.57762032339 absolute error = 0.0001593 relative error = 0.000818 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.657 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3579 1.535 h = 0.0001 0.005 y[1] (numeric) = -19.4069499562 1.58396542792 y[1] (closed_form) = -19.407091966 1.58403987267 absolute error = 0.0001603 relative error = 0.0008235 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.664 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 memory used=3515.7MB, alloc=52.3MB, time=43.37 x[1] = -1.3578 1.54 h = 0.0001 0.003 y[1] (numeric) = -19.4072346715 1.58912962999 y[1] (closed_form) = -19.4073773138 1.58920408418 absolute error = 0.0001609 relative error = 0.0008263 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.669 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3577 1.543 h = 0.001 0.001 y[1] (numeric) = -19.4073650077 1.59223127532 y[1] (closed_form) = -19.4075078776 1.59230573879 absolute error = 0.0001611 relative error = 0.0008274 % Correct digits = 5 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] = -1.3567 1.544 h = 0.001 0.003 y[1] (numeric) = -19.4064116922 1.5933405376 y[1] (closed_form) = -19.4065545635 1.59341505161 absolute error = 0.0001611 relative error = 0.0008275 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.673 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3557 1.547 h = 0.0001 0.004 y[1] (numeric) = -19.4056144298 1.59651257714 y[1] (closed_form) = -19.4057575071 1.59658723757 absolute error = 0.0001614 relative error = 0.0008288 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.676 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3556 1.551 h = 0.003 0.006 y[1] (numeric) = -19.4058240038 1.6006459339 y[1] (closed_form) = -19.4059674856 1.60072060419 absolute error = 0.0001617 relative error = 0.0008307 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.68 Order of pole (given) = 0.5 0 NO 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=3561.8MB, alloc=52.3MB, time=43.93 x[1] = -1.3526 1.557 h = 0.0001 0.005 y[1] (numeric) = -19.4032001319 1.60706938258 y[1] (closed_form) = -19.4033443196 1.60714494484 absolute error = 0.0001628 relative error = 0.0008361 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.686 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 x[1] = -1.3525 1.562 h = 0.0001 0.003 y[1] (numeric) = -19.4034904159 1.61223489289 y[1] (closed_form) = -19.4036352361 1.61231046437 absolute error = 0.0001634 relative error = 0.000839 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.691 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3524 1.565 h = 0.001 0.001 y[1] (numeric) = -19.4036240837 1.61533736763 y[1] (closed_form) = -19.4037691317 1.61541294831 absolute error = 0.0001636 relative error = 0.00084 % Correct digits = 5 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] = -1.3514 1.566 h = 0.001 0.003 y[1] (numeric) = -19.4026716477 1.61644798759 y[1] (closed_form) = -19.402816697 1.61652361881 absolute error = 0.0001636 relative error = 0.0008402 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.695 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3504 1.569 h = 0.0001 0.004 y[1] (numeric) = -19.4018775019 1.61962186305 y[1] (closed_form) = -19.4020227573 1.61969764062 absolute error = 0.0001638 relative error = 0.0008415 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.698 Order of pole (given) = 0.5 0 NO 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=3607.7MB, alloc=52.3MB, time=44.50 x[1] = -1.3503 1.573 h = 0.003 0.006 y[1] (numeric) = -19.4020915263 1.62375628793 y[1] (closed_form) = -19.4022371863 1.62383207522 absolute error = 0.0001642 relative error = 0.0008433 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.702 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] = -1.3473 1.579 h = 0.0001 0.005 y[1] (numeric) = -19.3994736492 1.63018452642 y[1] (closed_form) = -19.3996200155 1.6302612055 absolute error = 0.0001652 relative error = 0.0008488 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.709 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] = -1.3472 1.584 h = 0.0001 0.003 y[1] (numeric) = -19.3997695028 1.63535134307 y[1] (closed_form) = -19.3999165016 1.63542803113 absolute error = 0.0001658 relative error = 0.0008516 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.713 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] = -1.3471 1.587 h = 0.001 0.001 y[1] (numeric) = -19.399906503 1.63845464608 y[1] (closed_form) = -19.4000537295 1.63853134326 absolute error = 0.000166 relative error = 0.0008527 % Correct digits = 5 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] = -1.3461 1.588 h = 0.0001 0.004 y[1] (numeric) = -19.3989549469 1.63956662352 y[1] (closed_form) = -19.3991021748 1.63964337125 absolute error = 0.000166 relative error = 0.0008528 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.717 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.346 1.592 h = 0.003 0.006 y[1] (numeric) = -19.3991728156 1.64370191357 y[1] (closed_form) = -19.3993204481 1.64377867087 absolute error = 0.0001664 relative error = 0.0008547 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.721 Order of pole (given) = 0.5 0 NO 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=3653.7MB, alloc=52.3MB, time=45.06 x[1] = -1.343 1.598 h = 0.0001 0.005 y[1] (numeric) = -19.3965601574 1.65013420212 y[1] (closed_form) = -19.3967084965 1.65021185107 absolute error = 0.0001674 relative error = 0.0008601 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.728 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] = -1.3429 1.603 h = 0.0001 0.003 y[1] (numeric) = -19.3968608215 1.65530207533 y[1] (closed_form) = -19.3970097932 1.65537973306 absolute error = 0.000168 relative error = 0.000863 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.732 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3428 1.606 h = 0.001 0.001 y[1] (numeric) = -19.3970007003 1.65840605067 y[1] (closed_form) = -19.3971498997 1.65848371746 absolute error = 0.0001682 relative error = 0.000864 % Correct digits = 5 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] = -1.3418 1.607 h = 0.001 0.003 y[1] (numeric) = -19.3960499183 1.65951918594 y[1] (closed_form) = -19.3961991191 1.65959690328 absolute error = 0.0001682 relative error = 0.0008642 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.737 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3408 1.61 h = 0.0001 0.004 y[1] (numeric) = -19.3952615962 1.66269643789 y[1] (closed_form) = -19.3954110032 1.66277430147 absolute error = 0.0001685 relative error = 0.0008655 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.74 Order of pole (given) = 0.5 0 NO 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=3699.6MB, alloc=52.3MB, time=45.62 x[1] = -1.3407 1.614 h = 0.003 0.006 y[1] (numeric) = -19.3954839167 1.66683279321 y[1] (closed_form) = -19.3956337285 1.66691066622 absolute error = 0.0001688 relative error = 0.0008673 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.743 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3377 1.62 h = 0.0001 0.005 y[1] (numeric) = -19.3928772576 1.6732698683 y[1] (closed_form) = -19.3930277763 1.67334863277 absolute error = 0.0001699 relative error = 0.0008727 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.75 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] = -1.3376 1.625 h = 0.0001 0.003 y[1] (numeric) = -19.393183493 1.67843904428 y[1] (closed_form) = -19.3933346444 1.67851781731 absolute error = 0.0001704 relative error = 0.0008756 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.755 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] = -1.3375 1.628 h = 0.001 0.001 y[1] (numeric) = -19.3933267053 1.68154384578 y[1] (closed_form) = -19.3934780844 1.68162262777 absolute error = 0.0001707 relative error = 0.0008767 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.758 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3365 1.629 h = 0.001 0.003 y[1] (numeric) = -19.3923768044 1.68265833815 y[1] (closed_form) = -19.3925281849 1.68273717071 absolute error = 0.0001707 relative error = 0.0008768 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.759 Order of pole (given) = 0.5 0 NO 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=3745.6MB, alloc=52.3MB, time=46.19 x[1] = -1.3355 1.632 h = 0.0001 0.004 y[1] (numeric) = -19.3915916015 1.68583742325 y[1] (closed_form) = -19.3917431883 1.68591640198 absolute error = 0.0001709 relative error = 0.0008781 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.762 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3354 1.636 h = 0.003 0.006 y[1] (numeric) = -19.3918183748 1.68997484232 y[1] (closed_form) = -19.3919703664 1.69005383034 absolute error = 0.0001713 relative error = 0.00088 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.766 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 x[1] = -1.3324 1.642 h = 0.0001 0.005 y[1] (numeric) = -19.389217717 1.6964167022 y[1] (closed_form) = -19.3893704159 1.69649658151 absolute error = 0.0001723 relative error = 0.0008854 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.773 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3323 1.647 h = 0.0001 0.003 y[1] (numeric) = -19.3895295249 1.70158717905 y[1] (closed_form) = -19.3896828565 1.70166706667 absolute error = 0.0001729 relative error = 0.0008883 % Correct digits = 5 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] = -1.3322 1.65 h = 0.001 0.001 y[1] (numeric) = -19.3896760711 1.70469280555 y[1] (closed_form) = -19.3898296305 1.70477270207 absolute error = 0.0001731 relative error = 0.0008893 % Correct digits = 5 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 memory used=3791.5MB, alloc=52.3MB, time=46.76 x[1] = -1.3312 1.651 h = 0.001 0.003 y[1] (numeric) = -19.3887270518 1.70580865484 y[1] (closed_form) = -19.3888806127 1.70588860192 absolute error = 0.0001731 relative error = 0.0008895 % Correct digits = 5 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 x[1] = -1.3302 1.654 h = 0.0001 0.004 y[1] (numeric) = -19.3879449693 1.70898957212 y[1] (closed_form) = -19.3880987365 1.70906966531 absolute error = 0.0001734 relative error = 0.0008908 % Correct digits = 5 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] = -1.3301 1.658 h = 0.003 0.006 y[1] (numeric) = -19.3881761961 1.71312805342 y[1] (closed_form) = -19.3883303681 1.71320815575 absolute error = 0.0001737 relative error = 0.0008926 % Correct digits = 5 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] = -1.3271 1.664 h = 0.0001 0.005 y[1] (numeric) = -19.3855815418 1.71957469634 y[1] (closed_form) = -19.3857364216 1.71965568979 absolute error = 0.0001748 relative error = 0.0008981 % Correct digits = 5 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] = -1.327 1.669 h = 0.0001 0.003 y[1] (numeric) = -19.3858989231 1.72474647214 y[1] (closed_form) = -19.3860544356 1.72482747367 absolute error = 0.0001753 relative error = 0.0009009 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.8 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=3837.4MB, alloc=52.3MB, time=47.32 x[1] = -1.3269 1.672 h = 0.001 0.001 y[1] (numeric) = -19.386048804 1.72785292252 y[1] (closed_form) = -19.3862045443 1.72793393286 absolute error = 0.0001755 relative error = 0.000902 % Correct digits = 5 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 x[1] = -1.3259 1.673 h = 0.001 0.003 y[1] (numeric) = -19.3851006669 1.72897012853 y[1] (closed_form) = -19.3852564087 1.72905118944 absolute error = 0.0001756 relative error = 0.0009021 % Correct digits = 5 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] = -1.3249 1.676 h = 0.0001 0.004 y[1] (numeric) = -19.3843217056 1.73215287701 y[1] (closed_form) = -19.3844776538 1.73223408397 absolute error = 0.0001758 relative error = 0.0009034 % Correct digits = 5 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] = -1.3248 1.68 h = 0.003 0.006 y[1] (numeric) = -19.3845573868 1.73629241902 y[1] (closed_form) = -19.3847137398 1.73637363497 absolute error = 0.0001762 relative error = 0.0009053 % Correct digits = 5 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] = -1.3218 1.686 h = 0.0001 0.005 y[1] (numeric) = -19.3819687384 1.74274384324 y[1] (closed_form) = -19.3821257995 1.74282595013 absolute error = 0.0001772 relative error = 0.0009107 % Correct digits = 5 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 memory used=3883.3MB, alloc=52.3MB, time=47.88 x[1] = -1.3217 1.691 h = 0.0001 0.003 y[1] (numeric) = -19.3822916941 1.74791691609 y[1] (closed_form) = -19.382449388 1.74799903083 absolute error = 0.0001778 relative error = 0.0009136 % Correct digits = 5 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 x[1] = -1.3216 1.694 h = 0.001 0.001 y[1] (numeric) = -19.3824449101 1.7510241892 y[1] (closed_form) = -19.3826028319 1.75110631267 absolute error = 0.000178 relative error = 0.0009146 % Correct digits = 5 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] = -1.3206 1.695 h = 0.0001 0.004 y[1] (numeric) = -19.3814976559 1.75214275173 y[1] (closed_form) = -19.3816555791 1.75222492578 absolute error = 0.000178 relative error = 0.0009148 % Correct digits = 5 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] = -1.3205 1.699 h = 0.003 0.006 y[1] (numeric) = -19.3817371846 1.75628315247 y[1] (closed_form) = -19.3818955126 1.75636533538 absolute error = 0.0001784 relative error = 0.0009166 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.83 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3175 1.705 h = 0.0001 0.005 y[1] (numeric) = -19.3791537646 1.7627386193 y[1] (closed_form) = -19.379312801 1.76282169299 absolute error = 0.0001794 relative error = 0.0009221 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.837 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 memory used=3929.1MB, alloc=52.3MB, time=48.45 x[1] = -1.3174 1.71 h = 0.0001 0.003 y[1] (numeric) = -19.3794815347 1.76791274065 y[1] (closed_form) = -19.3796412041 1.76799582199 absolute error = 0.00018 relative error = 0.0009249 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.841 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] = -1.3173 1.713 h = 0.001 0.001 y[1] (numeric) = -19.3796376319 1.7710206813 y[1] (closed_form) = -19.3797975291 1.7711037713 absolute error = 0.0001802 relative error = 0.000926 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.844 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3163 1.714 h = 0.001 0.003 y[1] (numeric) = -19.3786911541 1.7721404008 y[1] (closed_form) = -19.3788510528 1.77222354137 absolute error = 0.0001802 relative error = 0.0009261 % Correct digits = 5 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] = -1.3153 1.717 h = 0.0001 0.004 y[1] (numeric) = -19.377918025 1.77532651694 y[1] (closed_form) = -19.3780781302 1.77540980345 absolute error = 0.0001805 relative error = 0.0009274 % Correct digits = 5 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] = -1.3152 1.721 h = 0.003 0.006 y[1] (numeric) = -19.3781620094 1.77946797554 y[1] (closed_form) = -19.3783225195 1.77955127077 absolute error = 0.0001808 relative error = 0.0009293 % Correct digits = 5 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 memory used=3975.1MB, alloc=52.3MB, time=49.01 x[1] = -1.3122 1.727 h = 0.0001 0.005 y[1] (numeric) = -19.3755845995 1.78592822038 y[1] (closed_form) = -19.3757458185 1.78601240622 absolute error = 0.0001819 relative error = 0.0009347 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.859 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3121 1.732 h = 0.0001 0.003 y[1] (numeric) = -19.3759179458 1.79110363522 y[1] (closed_form) = -19.3760797978 1.79118782848 absolute error = 0.0001824 relative error = 0.0009376 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.864 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.312 1.735 h = 0.001 0.001 y[1] (numeric) = -19.3760773794 1.79421239647 y[1] (closed_form) = -19.3762394592 1.79429659831 absolute error = 0.0001826 relative error = 0.0009386 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.866 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.311 1.736 h = 0.001 0.003 y[1] (numeric) = -19.3751317854 1.79533347212 y[1] (closed_form) = -19.3752938667 1.79541772453 absolute error = 0.0001827 relative error = 0.0009388 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.868 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.31 1.739 h = 0.0001 0.004 y[1] (numeric) = -19.3743617802 1.79852141669 y[1] (closed_form) = -19.3745240681 1.79860581498 absolute error = 0.0001829 relative error = 0.0009401 % Correct digits = 5 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] = -1.3099 1.743 h = 0.003 0.006 y[1] (numeric) = -19.3746102213 1.80266393163 y[1] (closed_form) = -19.3747729141 1.80274833849 absolute error = 0.0001833 relative error = 0.0009419 % Correct digits = 5 memory used=4021.1MB, alloc=52.3MB, time=49.58 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 x[1] = -1.3069 1.749 h = 0.0001 0.005 y[1] (numeric) = -19.3720388238 1.80912895274 y[1] (closed_form) = -19.3722022259 1.80921425003 absolute error = 0.0001843 relative error = 0.0009474 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.881 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3068 1.754 h = 0.0001 0.003 y[1] (numeric) = -19.3723777473 1.81430565915 y[1] (closed_form) = -19.3725417824 1.81439096363 absolute error = 0.0001849 relative error = 0.0009502 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.886 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3067 1.757 h = 0.001 0.001 y[1] (numeric) = -19.3725405178 1.81741523987 y[1] (closed_form) = -19.3727047808 1.81750055285 absolute error = 0.0001851 relative error = 0.0009513 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.889 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3057 1.758 h = 0.001 0.003 y[1] (numeric) = -19.3715958083 1.81853767147 y[1] (closed_form) = -19.3717600727 1.81862303503 absolute error = 0.0001851 relative error = 0.0009514 % Correct digits = 5 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] = -1.3047 1.761 h = 0.0001 0.004 y[1] (numeric) = -19.3708289279 1.8217274435 y[1] (closed_form) = -19.3709933991 1.82181295287 absolute error = 0.0001854 relative error = 0.0009527 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.893 Order of pole (given) = 0.5 0 NO 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=4067.0MB, alloc=52.3MB, time=50.14 x[1] = -1.3046 1.765 h = 0.003 0.006 y[1] (numeric) = -19.3710818264 1.82587101325 y[1] (closed_form) = -19.3712467025 1.82595653104 absolute error = 0.0001857 relative error = 0.0009546 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.897 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3016 1.771 h = 0.0001 0.005 y[1] (numeric) = -19.3685164436 1.83234080889 y[1] (closed_form) = -19.3686820294 1.83242721694 absolute error = 0.0001868 relative error = 0.00096 % Correct digits = 5 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] = -1.3015 1.776 h = 0.0001 0.003 y[1] (numeric) = -19.3688609453 1.83751880495 y[1] (closed_form) = -19.3690271641 1.83760521996 absolute error = 0.0001873 relative error = 0.0009629 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.908 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3014 1.779 h = 0.001 0.001 y[1] (numeric) = -19.3690270533 1.840629204 y[1] (closed_form) = -19.3691935001 1.84071562743 absolute error = 0.0001875 relative error = 0.0009639 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.911 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.3004 1.78 h = 0.001 0.003 y[1] (numeric) = -19.3680832288 1.84175299136 y[1] (closed_form) = -19.3682496771 1.84183946537 absolute error = 0.0001876 relative error = 0.0009641 % Correct digits = 5 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 memory used=4112.9MB, alloc=52.3MB, time=50.70 x[1] = -1.2994 1.783 h = 0.0001 0.004 y[1] (numeric) = -19.3673194743 1.84494458988 y[1] (closed_form) = -19.3674861293 1.84503120964 absolute error = 0.0001878 relative error = 0.0009654 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.916 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2993 1.787 h = 0.003 0.006 y[1] (numeric) = -19.367576831 1.84908921291 y[1] (closed_form) = -19.367743891 1.84917584095 absolute error = 0.0001882 relative error = 0.0009672 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.919 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2963 1.793 h = 0.0001 0.005 y[1] (numeric) = -19.3650174652 1.85556378132 y[1] (closed_form) = -19.3651852352 1.85565129945 absolute error = 0.0001892 relative error = 0.0009727 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.926 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] = -1.2962 1.798 h = 0.0001 0.003 y[1] (numeric) = -19.365367546 1.86074306513 y[1] (closed_form) = -19.3655359491 1.86083058998 absolute error = 0.0001898 relative error = 0.0009755 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.931 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2961 1.801 h = 0.001 0.001 y[1] (numeric) = -19.3655369922 1.86385428138 y[1] (closed_form) = -19.3657056233 1.86394181456 absolute error = 0.00019 relative error = 0.0009766 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.934 Order of pole (given) = 0.5 0 NO 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=4158.8MB, alloc=52.3MB, time=51.27 x[1] = -1.2951 1.802 h = 0.0001 0.004 y[1] (numeric) = -19.3645940533 1.8649794243 y[1] (closed_form) = -19.3647626859 1.86506700807 absolute error = 0.00019 relative error = 0.0009768 % Correct digits = 5 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] = -1.295 1.806 h = 0.003 0.006 y[1] (numeric) = -19.3648552606 1.86912489963 y[1] (closed_form) = -19.3650242982 1.86921249155 absolute error = 0.0001904 relative error = 0.0009786 % Correct digits = 5 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] = -1.292 1.812 h = 0.0001 0.005 y[1] (numeric) = -19.3623011327 1.87560350318 y[1] (closed_form) = -19.3624708806 1.87569198502 absolute error = 0.0001914 relative error = 0.000984 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.945 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2919 1.817 h = 0.0001 0.003 y[1] (numeric) = -19.362656032 1.88078382743 y[1] (closed_form) = -19.362826413 1.88087231579 absolute error = 0.000192 relative error = 0.0009869 % Correct digits = 5 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] = -1.2918 1.82 h = 0.001 0.001 y[1] (numeric) = -19.3628283618 1.88389570641 y[1] (closed_form) = -19.3629989708 1.88398420303 absolute error = 0.0001922 relative error = 0.0009879 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.953 Order of pole (given) = 0.5 0 NO 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=4204.7MB, alloc=52.3MB, time=51.84 x[1] = -1.2908 1.821 h = 0.001 0.003 y[1] (numeric) = -19.3618862017 1.88502200543 y[1] (closed_form) = -19.3620568123 1.88511055264 absolute error = 0.0001922 relative error = 0.0009881 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.954 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2898 1.824 h = 0.0001 0.004 y[1] (numeric) = -19.3611282879 1.88821696277 y[1] (closed_form) = -19.3612991054 1.88830565562 absolute error = 0.0001925 relative error = 0.0009894 % Correct digits = 5 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 x[1] = -1.2897 1.828 h = 0.003 0.006 y[1] (numeric) = -19.3613939549 1.89236348854 y[1] (closed_form) = -19.3615651774 1.8924521894 absolute error = 0.0001928 relative error = 0.0009912 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.961 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2867 1.834 h = 0.0001 0.005 y[1] (numeric) = -19.3588458482 1.89884686157 y[1] (closed_form) = -19.3590177815 1.89893645218 absolute error = 0.0001939 relative error = 0.0009967 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.968 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2866 1.839 h = 0.0001 0.003 y[1] (numeric) = -19.3592063284 1.90402847001 y[1] (closed_form) = -19.3593788949 1.9041180669 absolute error = 0.0001944 relative error = 0.0009995 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.973 Order of pole (given) = 0.5 0 NO 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=4250.7MB, alloc=52.3MB, time=52.40 x[1] = -1.2865 1.842 h = 0.001 0.001 y[1] (numeric) = -19.3593819975 1.90714116405 y[1] (closed_form) = -19.3595547919 1.90723076913 absolute error = 0.0001946 relative error = 0.001001 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.975 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2855 1.843 h = 0.001 0.003 y[1] (numeric) = -19.358440724 1.90826881825 y[1] (closed_form) = -19.3586135201 1.90835847392 absolute error = 0.0001947 relative error = 0.001001 % Correct digits = 5 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 x[1] = -1.2845 1.846 h = 0.0001 0.004 y[1] (numeric) = -19.3576859388 1.9114655993 y[1] (closed_form) = -19.3578589418 1.91155540055 absolute error = 0.0001949 relative error = 0.001002 % Correct digits = 5 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] = -1.2844 1.85 h = 0.003 0.006 y[1] (numeric) = -19.3579560662 1.91561317398 y[1] (closed_form) = -19.3581294744 1.91570298309 absolute error = 0.0001953 relative error = 0.001004 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.984 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2814 1.856 h = 0.0001 0.005 y[1] (numeric) = -19.3554139831 1.92210131475 y[1] (closed_form) = -19.3555881023 1.92219201343 absolute error = 0.0001963 relative error = 0.001009 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.99 Order of pole (given) = 0.5 0 NO 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=4296.6MB, alloc=52.3MB, time=52.96 x[1] = -1.2813 1.861 h = 0.0001 0.003 y[1] (numeric) = -19.3557800452 1.92728420545 y[1] (closed_form) = -19.3559547977 1.92737491019 absolute error = 0.0001969 relative error = 0.001012 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.995 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2812 1.864 h = 0.001 0.001 y[1] (numeric) = -19.3559590541 1.93039771342 y[1] (closed_form) = -19.3561340346 1.93048842626 absolute error = 0.0001971 relative error = 0.001013 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.998 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2802 1.865 h = 0.001 0.003 y[1] (numeric) = -19.3550186679 1.93152672261 y[1] (closed_form) = -19.35519365 1.93161748605 absolute error = 0.0001971 relative error = 0.001013 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.999 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2792 1.868 h = 0.0001 0.004 y[1] (numeric) = -19.3542670122 1.93472532639 y[1] (closed_form) = -19.3544422014 1.93481623534 absolute error = 0.0001974 relative error = 0.001015 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.002 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2791 1.872 h = 0.003 0.006 y[1] (numeric) = -19.3545416009 1.93887394846 y[1] (closed_form) = -19.3547171952 1.93896486512 absolute error = 0.0001977 relative error = 0.001017 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.006 Order of pole (given) = 0.5 0 NO 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=4342.4MB, alloc=52.3MB, time=53.53 x[1] = -1.2761 1.878 h = 0.0001 0.005 y[1] (numeric) = -19.3520055436 1.94536685522 y[1] (closed_form) = -19.3521818493 1.94545866128 absolute error = 0.0001988 relative error = 0.001022 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.013 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.276 1.883 h = 0.0001 0.003 y[1] (numeric) = -19.3523771886 1.95055102628 y[1] (closed_form) = -19.3525541277 1.95064283816 absolute error = 0.0001993 relative error = 0.001025 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.017 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2759 1.886 h = 0.001 0.001 y[1] (numeric) = -19.352559538 1.95366534703 y[1] (closed_form) = -19.3527367051 1.95375716693 absolute error = 0.0001995 relative error = 0.001026 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.02 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2749 1.887 h = 0.001 0.003 y[1] (numeric) = -19.3516200396 1.95479571101 y[1] (closed_form) = -19.3517972083 1.95488758152 absolute error = 0.0001996 relative error = 0.001026 % Correct digits = 5 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] = -1.2739 1.89 h = 0.0001 0.004 y[1] (numeric) = -19.3508715143 1.95799613655 y[1] (closed_form) = -19.3510488902 1.95808815251 absolute error = 0.0001998 relative error = 0.001027 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.025 Order of pole (given) = 0.5 0 NO 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=4388.2MB, alloc=52.3MB, time=54.09 x[1] = -1.2738 1.894 h = 0.003 0.006 y[1] (numeric) = -19.351150565 1.96214580448 y[1] (closed_form) = -19.3513283461 1.96223782801 absolute error = 0.0002002 relative error = 0.001029 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.028 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2708 1.9 h = 0.0001 0.005 y[1] (numeric) = -19.3486205358 1.96864347549 y[1] (closed_form) = -19.3487990288 1.96873638823 absolute error = 0.0002012 relative error = 0.001035 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.035 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2707 1.905 h = 0.0001 0.003 y[1] (numeric) = -19.3489977647 1.97382892498 y[1] (closed_form) = -19.3491768911 1.97392184332 absolute error = 0.0002018 relative error = 0.001038 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.04 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2706 1.908 h = 0.001 0.001 y[1] (numeric) = -19.3491834552 1.97694405738 y[1] (closed_form) = -19.3493628096 1.97703698365 absolute error = 0.000202 relative error = 0.001039 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.043 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2696 1.909 h = 0.0001 0.004 y[1] (numeric) = -19.3482448452 1.97807577595 y[1] (closed_form) = -19.3484242012 1.97816875283 absolute error = 0.000202 relative error = 0.001039 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.044 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2695 1.913 h = 0.003 0.006 y[1] (numeric) = -19.3485277498 1.98222628974 y[1] (closed_form) = -19.3487075109 1.98231927405 absolute error = 0.0002024 relative error = 0.001041 % Correct digits = 5 memory used=4434.1MB, alloc=52.3MB, time=54.66 Radius of convergence (given) for eq 1 = 2.048 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2665 1.919 h = 0.0001 0.005 y[1] (numeric) = -19.3460029679 1.98872798839 y[1] (closed_form) = -19.3461834413 1.98882186176 absolute error = 0.0002034 relative error = 0.001046 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.054 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2664 1.924 h = 0.0001 0.003 y[1] (numeric) = -19.3463850193 1.99391447026 y[1] (closed_form) = -19.3465661261 1.99400834903 absolute error = 0.000204 relative error = 0.001049 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.059 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2663 1.927 h = 0.001 0.001 y[1] (numeric) = -19.3465735958 1.99703026057 y[1] (closed_form) = -19.3467549306 1.99712414721 absolute error = 0.0002042 relative error = 0.00105 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.062 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2653 1.928 h = 0.001 0.003 y[1] (numeric) = -19.345635767 1.99816313438 y[1] (closed_form) = -19.3458171035 1.99825707163 absolute error = 0.0002042 relative error = 0.00105 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.063 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2643 1.931 h = 0.0001 0.004 y[1] (numeric) = -19.344893091 2.0013669099 y[1] (closed_form) = -19.3450746348 2.00146099249 absolute error = 0.0002045 relative error = 0.001051 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.066 Order of pole (given) = 0.5 0 NO 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=4480.0MB, alloc=52.3MB, time=55.22 x[1] = -1.2642 1.935 h = 0.003 0.006 y[1] (numeric) = -19.345180459 2.0055184667 y[1] (closed_form) = -19.3453624081 2.00561255658 absolute error = 0.0002048 relative error = 0.001053 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.07 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2612 1.941 h = 0.0001 0.005 y[1] (numeric) = -19.3426617095 2.0120249263 y[1] (closed_form) = -19.3428443711 2.01211990506 absolute error = 0.0002059 relative error = 0.001059 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.077 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2611 1.946 h = 0.0001 0.003 y[1] (numeric) = -19.3430493466 2.01721268304 y[1] (closed_form) = -19.3432326417 2.01730766696 absolute error = 0.0002064 relative error = 0.001062 % Correct digits = 5 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] = -1.261 1.949 h = 0.001 0.001 y[1] (numeric) = -19.3432412653 2.02032928287 y[1] (closed_form) = -19.3434247884 2.02042427458 absolute error = 0.0002066 relative error = 0.001063 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.084 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] = -1.26 1.95 h = 0.001 0.003 y[1] (numeric) = -19.3423043259 2.02146351089 y[1] (closed_form) = -19.3424878508 2.02155855321 absolute error = 0.0002067 relative error = 0.001063 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.086 Order of pole (given) = 0.5 0 NO 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=4526.0MB, alloc=52.3MB, time=55.78 x[1] = -1.259 1.953 h = 0.0001 0.004 y[1] (numeric) = -19.3415647831 2.02466910539 y[1] (closed_form) = -19.3417485153 2.02476429298 absolute error = 0.0002069 relative error = 0.001064 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.089 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2589 1.957 h = 0.003 0.006 y[1] (numeric) = -19.3418566154 2.02882170367 y[1] (closed_form) = -19.3420407529 2.02891689841 absolute error = 0.0002073 relative error = 0.001066 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.093 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2559 1.963 h = 0.0001 0.005 y[1] (numeric) = -19.3393439005 2.03533292246 y[1] (closed_form) = -19.339528751 2.03542900591 absolute error = 0.0002083 relative error = 0.001071 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.099 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2558 1.968 h = 0.0001 0.003 y[1] (numeric) = -19.3397371242 2.04052195216 y[1] (closed_form) = -19.3399226083 2.04061804054 absolute error = 0.0002089 relative error = 0.001074 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.104 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2557 1.971 h = 0.001 0.001 y[1] (numeric) = -19.3399323857 2.04363936037 y[1] (closed_form) = -19.3401180979 2.04373545645 absolute error = 0.0002091 relative error = 0.001075 % Correct digits = 5 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 memory used=4571.9MB, alloc=52.3MB, time=56.35 x[1] = -1.2547 1.972 h = 0.001 0.003 y[1] (numeric) = -19.3389963364 2.04477494241 y[1] (closed_form) = -19.3391820502 2.04487108911 absolute error = 0.0002091 relative error = 0.001075 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.108 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2537 1.975 h = 0.0001 0.004 y[1] (numeric) = -19.3382599277 2.04798235491 y[1] (closed_form) = -19.3384458489 2.04807864682 absolute error = 0.0002094 relative error = 0.001077 % Correct digits = 5 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] = -1.2536 1.979 h = 0.003 0.006 y[1] (numeric) = -19.3385562251 2.05213599315 y[1] (closed_form) = -19.3387425516 2.05223229206 absolute error = 0.0002097 relative error = 0.001079 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.115 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2506 1.985 h = 0.0001 0.005 y[1] (numeric) = -19.3360495471 2.05865196938 y[1] (closed_form) = -19.336236587 2.05874915682 absolute error = 0.0002108 relative error = 0.001084 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.122 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2505 1.99 h = 0.0001 0.003 y[1] (numeric) = -19.3364483585 2.06384227012 y[1] (closed_form) = -19.336636032 2.06393946226 absolute error = 0.0002113 relative error = 0.001087 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.126 Order of pole (given) = 0.5 0 NO 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=4617.9MB, alloc=52.3MB, time=56.92 x[1] = -1.2504 1.993 h = 0.001 0.001 y[1] (numeric) = -19.3366469634 2.06696048556 y[1] (closed_form) = -19.336834865 2.06705768532 absolute error = 0.0002116 relative error = 0.001088 % Correct digits = 5 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 x[1] = -1.2494 1.994 h = 0.001 0.003 y[1] (numeric) = -19.3357118047 2.06809742142 y[1] (closed_form) = -19.335899708 2.0681946718 absolute error = 0.0002116 relative error = 0.001088 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.131 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2484 1.997 h = 0.0001 0.004 y[1] (numeric) = -19.334978531 2.07130665096 y[1] (closed_form) = -19.3351666419 2.07140404649 absolute error = 0.0002118 relative error = 0.001089 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.134 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2483 2.001 h = 0.003 0.006 y[1] (numeric) = -19.3352792943 2.07546132762 y[1] (closed_form) = -19.3354678105 2.07555873001 absolute error = 0.0002122 relative error = 0.001091 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.138 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2453 2.007 h = 0.0001 0.005 y[1] (numeric) = -19.3327786555 2.08198205954 y[1] (closed_form) = -19.3329678855 2.08208035028 absolute error = 0.0002132 relative error = 0.001097 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.144 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 memory used=4663.8MB, alloc=52.3MB, time=57.48 x[1] = -1.2452 2.012 h = 0.0001 0.003 y[1] (numeric) = -19.3331830556 2.08717362941 y[1] (closed_form) = -19.3333729192 2.08727192461 absolute error = 0.0002138 relative error = 0.001099 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.149 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2451 2.015 h = 0.001 0.001 y[1] (numeric) = -19.3333850045 2.09029265094 y[1] (closed_form) = -19.3335750962 2.09039095369 absolute error = 0.000214 relative error = 0.0011 % Correct digits = 5 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] = -1.2441 2.016 h = 0.0001 0.004 y[1] (numeric) = -19.3324507369 2.09143094042 y[1] (closed_form) = -19.3326408304 2.09152929379 absolute error = 0.000214 relative error = 0.001101 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.153 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.244 2.02 h = 0.003 0.006 y[1] (numeric) = -19.3327553573 2.09558645651 y[1] (closed_form) = -19.3329458561 2.0956848166 absolute error = 0.0002144 relative error = 0.001102 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.157 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.241 2.026 h = 0.0001 0.005 y[1] (numeric) = -19.3302599753 2.10211120858 y[1] (closed_form) = -19.3304511882 2.10221045687 absolute error = 0.0002154 relative error = 0.001108 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.164 Order of pole (given) = 0.5 0 NO 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=4709.6MB, alloc=52.3MB, time=58.04 x[1] = -1.2409 2.031 h = 0.0001 0.003 y[1] (numeric) = -19.3306692017 2.10730380275 y[1] (closed_form) = -19.3308610483 2.1074030553 absolute error = 0.000216 relative error = 0.001111 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.168 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2408 2.034 h = 0.001 0.001 y[1] (numeric) = -19.3308740391 2.11042347738 y[1] (closed_form) = -19.3310661139 2.11052273741 absolute error = 0.0002162 relative error = 0.001112 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.171 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] = -1.2398 2.035 h = 0.001 0.003 y[1] (numeric) = -19.3299405552 2.11156292123 y[1] (closed_form) = -19.3301326317 2.11166223189 absolute error = 0.0002162 relative error = 0.001112 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.172 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2388 2.038 h = 0.0001 0.004 y[1] (numeric) = -19.3292131393 2.11477549189 y[1] (closed_form) = -19.3294054234 2.11487494757 absolute error = 0.0002165 relative error = 0.001113 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.176 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2387 2.042 h = 0.003 0.006 y[1] (numeric) = -19.329522227 2.11893204354 y[1] (closed_form) = -19.3297149165 2.11903150581 absolute error = 0.0002168 relative error = 0.001115 % Correct digits = 5 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 memory used=4755.6MB, alloc=52.3MB, time=58.61 x[1] = -1.2357 2.048 h = 0.0001 0.005 y[1] (numeric) = -19.3270328885 2.125461548 y[1] (closed_form) = -19.3272262925 2.12556189829 absolute error = 0.0002179 relative error = 0.001121 % Correct digits = 5 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 x[1] = -1.2356 2.053 h = 0.0001 0.003 y[1] (numeric) = -19.3274477053 2.13065540773 y[1] (closed_form) = -19.3276417431 2.13075576204 absolute error = 0.0002185 relative error = 0.001123 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.191 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2355 2.056 h = 0.001 0.001 y[1] (numeric) = -19.3276558878 2.13377588633 y[1] (closed_form) = -19.3278501538 2.13387624803 absolute error = 0.0002187 relative error = 0.001124 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.194 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2345 2.057 h = 0.001 0.003 y[1] (numeric) = -19.3267232961 2.13491668342 y[1] (closed_form) = -19.3269175638 2.13501709576 absolute error = 0.0002187 relative error = 0.001125 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.195 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2335 2.06 h = 0.0001 0.004 y[1] (numeric) = -19.325999018 2.13813106831 y[1] (closed_form) = -19.3261934935 2.13823162562 absolute error = 0.0002189 relative error = 0.001126 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.198 Order of pole (given) = 0.5 0 NO 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=4801.6MB, alloc=52.3MB, time=59.18 x[1] = -1.2334 2.064 h = 0.003 0.006 y[1] (numeric) = -19.3263125738 2.14228865402 y[1] (closed_form) = -19.3265074547 2.14238921776 absolute error = 0.0002193 relative error = 0.001128 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.202 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2304 2.07 h = 0.0001 0.005 y[1] (numeric) = -19.323829281 2.14882290911 y[1] (closed_form) = -19.3240248768 2.1489243607 absolute error = 0.0002203 relative error = 0.001133 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.208 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2303 2.075 h = 0.0001 0.003 y[1] (numeric) = -19.3242496893 2.15401803247 y[1] (closed_form) = -19.3244459189 2.15411948786 absolute error = 0.0002209 relative error = 0.001136 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.213 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2302 2.078 h = 0.001 0.001 y[1] (numeric) = -19.3244612175 2.1571393139 y[1] (closed_form) = -19.3246576753 2.15724077659 absolute error = 0.0002211 relative error = 0.001137 % Correct digits = 5 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] = -1.2292 2.079 h = 0.001 0.003 y[1] (numeric) = -19.3235295186 2.15828146404 y[1] (closed_form) = -19.3237259782 2.15838297737 absolute error = 0.0002211 relative error = 0.001137 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.217 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] = -1.2282 2.082 h = 0.0001 0.004 y[1] (numeric) = -19.3228083792 2.1614976622 y[1] (closed_form) = -19.3230050466 2.16159932043 absolute error = 0.0002214 relative error = 0.001139 % Correct digits = 5 memory used=4847.4MB, alloc=52.3MB, time=59.75 Radius of convergence (given) for eq 1 = 2.22 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2281 2.086 h = 0.003 0.006 y[1] (numeric) = -19.3231264039 2.16565628042 y[1] (closed_form) = -19.3233234767 2.16575794495 absolute error = 0.0002218 relative error = 0.00114 % Correct digits = 5 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 x[1] = -1.2251 2.092 h = 0.0001 0.005 y[1] (numeric) = -19.3206491592 2.17219528439 y[1] (closed_form) = -19.3208469473 2.17229783658 absolute error = 0.0002228 relative error = 0.001146 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.231 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.225 2.097 h = 0.0001 0.003 y[1] (numeric) = -19.3210751598 2.17739166948 y[1] (closed_form) = -19.3212735818 2.17749422524 absolute error = 0.0002234 relative error = 0.001149 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.236 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2249 2.1 h = 0.001 0.001 y[1] (numeric) = -19.3212900343 2.18051375258 y[1] (closed_form) = -19.3214886845 2.18061631556 absolute error = 0.0002236 relative error = 0.00115 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.238 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2239 2.101 h = 0.001 0.003 y[1] (numeric) = -19.3203592288 2.18165725557 y[1] (closed_form) = -19.3205578808 2.18175986919 absolute error = 0.0002236 relative error = 0.00115 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.24 Order of pole (given) = 0.5 0 NO 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=4893.3MB, alloc=52.3MB, time=60.31 x[1] = -1.2229 2.104 h = 0.0001 0.004 y[1] (numeric) = -19.3196412292 2.18487526602 y[1] (closed_form) = -19.319840089 2.18497802449 absolute error = 0.0002238 relative error = 0.001151 % Correct digits = 5 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 x[1] = -1.2228 2.108 h = 0.003 0.006 y[1] (numeric) = -19.3199637235 2.18903491524 y[1] (closed_form) = -19.3201629889 2.18913767985 absolute error = 0.0002242 relative error = 0.001153 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.247 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2198 2.114 h = 0.0001 0.005 y[1] (numeric) = -19.3174925291 2.19557866633 y[1] (closed_form) = -19.3176925101 2.19568231842 absolute error = 0.0002252 relative error = 0.001159 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.253 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2197 2.119 h = 0.0001 0.003 y[1] (numeric) = -19.3179241231 2.20077631122 y[1] (closed_form) = -19.3181247381 2.20087996665 absolute error = 0.0002258 relative error = 0.001161 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.258 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] = -1.2196 2.122 h = 0.001 0.001 y[1] (numeric) = -19.3181423445 2.20389919486 y[1] (closed_form) = -19.3183431877 2.20400285744 absolute error = 0.000226 relative error = 0.001162 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.261 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=4939.2MB, alloc=52.3MB, time=60.88 x[1] = -1.2186 2.123 h = 0.0001 0.004 y[1] (numeric) = -19.317212433 2.2050440505 y[1] (closed_form) = -19.317413278 2.20514776372 absolute error = 0.000226 relative error = 0.001163 % Correct digits = 5 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] = -1.2185 2.127 h = 0.003 0.006 y[1] (numeric) = -19.3175387876 2.20920453269 y[1] (closed_form) = -19.3177400382 2.20930825191 absolute error = 0.0002264 relative error = 0.001164 % Correct digits = 5 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] = -1.2155 2.133 h = 0.0001 0.005 y[1] (numeric) = -19.3150728595 2.21575229642 y[1] (closed_form) = -19.315274826 2.21585690298 absolute error = 0.0002274 relative error = 0.00117 % Correct digits = 5 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] = -1.2154 2.138 h = 0.0001 0.003 y[1] (numeric) = -19.3155092838 2.22095095753 y[1] (closed_form) = -19.3157118843 2.22105556723 absolute error = 0.000228 relative error = 0.001173 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.277 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] = -1.2153 2.141 h = 0.001 0.001 y[1] (numeric) = -19.3157303962 2.22407448946 y[1] (closed_form) = -19.3159332249 2.22417910622 absolute error = 0.0002282 relative error = 0.001174 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.28 Order of pole (given) = 0.5 0 NO 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=4985.1MB, alloc=52.3MB, time=61.44 x[1] = -1.2143 2.142 h = 0.001 0.003 y[1] (numeric) = -19.3148012707 2.22522049859 y[1] (closed_form) = -19.3150041013 2.225325166 absolute error = 0.0002282 relative error = 0.001174 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.282 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2133 2.145 h = 0.0001 0.004 y[1] (numeric) = -19.3140891373 2.22844184129 y[1] (closed_form) = -19.3142921759 2.22854665343 absolute error = 0.0002285 relative error = 0.001175 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.285 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2132 2.149 h = 0.003 0.006 y[1] (numeric) = -19.314419963 2.23260335161 y[1] (closed_form) = -19.3146234072 2.23270816961 absolute error = 0.0002289 relative error = 0.001177 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.289 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2102 2.155 h = 0.0001 0.005 y[1] (numeric) = -19.3119600895 2.23915585916 y[1] (closed_form) = -19.31216425 2.23926156432 absolute error = 0.0002299 relative error = 0.001183 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.295 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2101 2.16 h = 0.0001 0.003 y[1] (numeric) = -19.312402109 2.2443557765 y[1] (closed_form) = -19.3126069036 2.24446148457 absolute error = 0.0002305 relative error = 0.001185 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.3 Order of pole (given) = 0.5 0 NO 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=5031.1MB, alloc=52.3MB, time=62.01 x[1] = -1.21 2.163 h = 0.001 0.001 y[1] (numeric) = -19.3126265693 2.24748010683 y[1] (closed_form) = -19.3128315922 2.24758582189 absolute error = 0.0002307 relative error = 0.001186 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.303 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] = -1.209 2.164 h = 0.001 0.003 y[1] (numeric) = -19.3116983389 2.24862746823 y[1] (closed_form) = -19.3119033636 2.24873323394 absolute error = 0.0002307 relative error = 0.001187 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.304 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.208 2.167 h = 0.0001 0.004 y[1] (numeric) = -19.3109893479 2.25185062043 y[1] (closed_form) = -19.3111945806 2.25195653081 absolute error = 0.0002309 relative error = 0.001188 % Correct digits = 5 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] = -1.2079 2.171 h = 0.003 0.006 y[1] (numeric) = -19.3113246456 2.25601315736 y[1] (closed_form) = -19.311530284 2.25611907345 absolute error = 0.0002313 relative error = 0.00119 % Correct digits = 5 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] = -1.2049 2.177 h = 0.0001 0.005 y[1] (numeric) = -19.3088708288 2.26257040697 y[1] (closed_form) = -19.309077184 2.26267721004 absolute error = 0.0002324 relative error = 0.001195 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.318 Order of pole (given) = 0.5 0 NO 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=5077.1MB, alloc=52.3MB, time=62.57 x[1] = -1.2048 2.182 h = 0.0001 0.003 y[1] (numeric) = -19.3093184445 2.26777157863 y[1] (closed_form) = -19.3095254337 2.26787838437 absolute error = 0.0002329 relative error = 0.001198 % Correct digits = 5 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 x[1] = -1.2047 2.185 h = 0.001 0.001 y[1] (numeric) = -19.3095462535 2.27089670622 y[1] (closed_form) = -19.309753471 2.27100351887 absolute error = 0.0002331 relative error = 0.001199 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.325 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] = -1.2037 2.186 h = 0.001 0.003 y[1] (numeric) = -19.3086189186 2.27204541969 y[1] (closed_form) = -19.308826138 2.272152283 absolute error = 0.0002332 relative error = 0.001199 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.327 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2027 2.189 h = 0.0001 0.004 y[1] (numeric) = -19.307913071 2.27527038042 y[1] (closed_form) = -19.3081204985 2.27537738833 absolute error = 0.0002334 relative error = 0.001201 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.33 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.2026 2.193 h = 0.003 0.006 y[1] (numeric) = -19.3082528413 2.27943394242 y[1] (closed_form) = -19.3084606746 2.2795409559 absolute error = 0.0002338 relative error = 0.001202 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.333 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 memory used=5123.1MB, alloc=52.3MB, time=63.15 x[1] = -1.1996 2.199 h = 0.0001 0.005 y[1] (numeric) = -19.3058050837 2.28599593234 y[1] (closed_form) = -19.3060136341 2.28610383261 absolute error = 0.0002348 relative error = 0.001208 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.34 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 x[1] = -1.1995 2.204 h = 0.0001 0.003 y[1] (numeric) = -19.3062582965 2.29119835639 y[1] (closed_form) = -19.306467481 2.29130625911 absolute error = 0.0002354 relative error = 0.001211 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.345 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1994 2.207 h = 0.001 0.001 y[1] (numeric) = -19.3064894547 2.2943242801 y[1] (closed_form) = -19.3066988676 2.29443218965 absolute error = 0.0002356 relative error = 0.001212 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.348 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] = -1.1984 2.208 h = 0.001 0.003 y[1] (numeric) = -19.305563016 2.29547434544 y[1] (closed_form) = -19.3057724307 2.29558230565 absolute error = 0.0002356 relative error = 0.001212 % Correct digits = 5 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] = -1.1974 2.211 h = 0.0001 0.004 y[1] (numeric) = -19.3048603126 2.29870111372 y[1] (closed_form) = -19.3050699356 2.29880921847 absolute error = 0.0002359 relative error = 0.001213 % Correct digits = 5 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 memory used=5169.0MB, alloc=52.3MB, time=63.71 x[1] = -1.1973 2.215 h = 0.003 0.006 y[1] (numeric) = -19.3052045565 2.30286569928 y[1] (closed_form) = -19.3054145852 2.30297380945 absolute error = 0.0002362 relative error = 0.001215 % Correct digits = 5 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 x[1] = -1.1943 2.221 h = 0.0001 0.005 y[1] (numeric) = -19.3027628603 2.30943242773 y[1] (closed_form) = -19.3029736065 2.30954142452 absolute error = 0.0002373 relative error = 0.00122 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.363 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1942 2.226 h = 0.0001 0.003 y[1] (numeric) = -19.3032216712 2.31463610226 y[1] (closed_form) = -19.3034330516 2.31474510126 absolute error = 0.0002378 relative error = 0.001223 % Correct digits = 5 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] = -1.1941 2.229 h = 0.001 0.001 y[1] (numeric) = -19.3034561792 2.31776282095 y[1] (closed_form) = -19.303667788 2.31787182669 absolute error = 0.000238 relative error = 0.001224 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.37 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1931 2.23 h = 0.0001 0.004 y[1] (numeric) = -19.3025306373 2.31891423796 y[1] (closed_form) = -19.3027422479 2.31902329437 absolute error = 0.0002381 relative error = 0.001224 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.371 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 memory used=5215.0MB, alloc=52.3MB, time=64.28 x[1] = -1.193 2.234 h = 0.003 0.006 y[1] (numeric) = -19.3028787447 2.32307965003 y[1] (closed_form) = -19.303090761 2.32318871173 absolute error = 0.0002384 relative error = 0.001226 % Correct digits = 5 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] = -1.19 2.24 h = 0.0001 0.005 y[1] (numeric) = -19.3004423242 2.32965038361 y[1] (closed_form) = -19.3006550584 2.32976033177 absolute error = 0.0002395 relative error = 0.001232 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.382 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 x[1] = -1.1899 2.245 h = 0.0001 0.003 y[1] (numeric) = -19.3009059693 2.33485506627 y[1] (closed_form) = -19.3011193378 2.33496501645 absolute error = 0.00024 relative error = 0.001235 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.387 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1898 2.248 h = 0.001 0.001 y[1] (numeric) = -19.3011433707 2.33798242843 y[1] (closed_form) = -19.3013569676 2.33809238527 absolute error = 0.0002402 relative error = 0.001236 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.39 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1888 2.249 h = 0.001 0.003 y[1] (numeric) = -19.3002186172 2.33913499806 y[1] (closed_form) = -19.3004322159 2.33924500557 absolute error = 0.0002403 relative error = 0.001236 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.391 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] = -1.1878 2.252 h = 0.0001 0.004 y[1] (numeric) = -19.2995217887 2.3423650897 y[1] (closed_form) = -19.2997355957 2.34247524163 absolute error = 0.0002405 relative error = 0.001237 % Correct digits = 5 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 memory used=5261.0MB, alloc=52.3MB, time=64.84 x[1] = -1.1877 2.256 h = 0.003 0.006 y[1] (numeric) = -19.299874371 2.34653152245 y[1] (closed_form) = -19.3000885839 2.34664167954 absolute error = 0.0002409 relative error = 0.001239 % Correct digits = 5 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] = -1.1847 2.262 h = 0.0001 0.005 y[1] (numeric) = -19.2974440161 2.35310699127 y[1] (closed_form) = -19.2976589472 2.35321803463 absolute error = 0.0002419 relative error = 0.001244 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.404 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] = -1.1846 2.267 h = 0.0001 0.003 y[1] (numeric) = -19.2979132612 2.35831292083 y[1] (closed_form) = -19.2981288266 2.35842396598 absolute error = 0.0002425 relative error = 0.001247 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.409 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] = -1.1845 2.27 h = 0.001 0.001 y[1] (numeric) = -19.2981540135 2.36144107582 y[1] (closed_form) = -19.2983698073 2.36155212756 absolute error = 0.0002427 relative error = 0.001248 % Correct digits = 5 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] = -1.1835 2.271 h = 0.001 0.003 y[1] (numeric) = -19.2972301578 2.36259499675 y[1] (closed_form) = -19.2974459535 2.36270609916 absolute error = 0.0002427 relative error = 0.001248 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.413 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 memory used=5306.9MB, alloc=52.3MB, time=65.40 x[1] = -1.1825 2.274 h = 0.0001 0.004 y[1] (numeric) = -19.2965364762 2.36582689314 y[1] (closed_form) = -19.2967524804 2.36593813991 absolute error = 0.000243 relative error = 0.00125 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.416 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 x[1] = -1.1824 2.278 h = 0.003 0.006 y[1] (numeric) = -19.2968935343 2.36999434505 y[1] (closed_form) = -19.2971099443 2.37010559683 absolute error = 0.0002433 relative error = 0.001252 % Correct digits = 5 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 x[1] = -1.1794 2.284 h = 0.0001 0.005 y[1] (numeric) = -19.2944692474 2.37657454734 y[1] (closed_form) = -19.294686376 2.37668668522 absolute error = 0.0002444 relative error = 0.001257 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.427 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] = -1.1793 2.289 h = 0.0001 0.003 y[1] (numeric) = -19.2949440933 2.38178172188 y[1] (closed_form) = -19.2951618563 2.38189386131 absolute error = 0.0002449 relative error = 0.00126 % Correct digits = 5 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] = -1.1792 2.292 h = 0.001 0.001 y[1] (numeric) = -19.2951881971 2.38491066858 y[1] (closed_form) = -19.2954061885 2.38502281452 absolute error = 0.0002451 relative error = 0.001261 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.435 Order of pole (given) = 0.5 0 NO 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=5352.9MB, alloc=52.3MB, time=65.97 x[1] = -1.1782 2.293 h = 0.001 0.003 y[1] (numeric) = -19.2942652398 2.38606594059 y[1] (closed_form) = -19.2944832332 2.38617813721 absolute error = 0.0002452 relative error = 0.001261 % Correct digits = 5 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] = -1.1772 2.296 h = 0.0001 0.004 y[1] (numeric) = -19.2935747062 2.38929964076 y[1] (closed_form) = -19.293792908 2.38941198168 absolute error = 0.0002454 relative error = 0.001262 % Correct digits = 5 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 x[1] = -1.1771 2.3 h = 0.003 0.006 y[1] (numeric) = -19.2939362408 2.39346811031 y[1] (closed_form) = -19.2941548485 2.39358045608 absolute error = 0.0002458 relative error = 0.001264 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.443 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] = -1.1741 2.306 h = 0.0001 0.005 y[1] (numeric) = -19.2915180241 2.4000530443 y[1] (closed_form) = -19.2917373508 2.40016627599 absolute error = 0.0002468 relative error = 0.00127 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.449 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] = -1.174 2.311 h = 0.0001 0.003 y[1] (numeric) = -19.2919984718 2.40526146191 y[1] (closed_form) = -19.292218433 2.40537469492 absolute error = 0.0002474 relative error = 0.001273 % Correct digits = 5 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 memory used=5398.8MB, alloc=52.3MB, time=66.54 x[1] = -1.1739 2.314 h = 0.001 0.001 y[1] (numeric) = -19.2922459278 2.40839119916 y[1] (closed_form) = -19.2924661174 2.4085044386 absolute error = 0.0002476 relative error = 0.001274 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.457 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 x[1] = -1.1729 2.315 h = 0.001 0.003 y[1] (numeric) = -19.2913238694 2.40954782207 y[1] (closed_form) = -19.291544061 2.40966111218 absolute error = 0.0002476 relative error = 0.001274 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.458 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] = -1.1719 2.318 h = 0.0001 0.004 y[1] (numeric) = -19.2906364847 2.41278332504 y[1] (closed_form) = -19.2908568848 2.41289675939 absolute error = 0.0002479 relative error = 0.001275 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.461 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1718 2.322 h = 0.003 0.006 y[1] (numeric) = -19.2910024966 2.41695281068 y[1] (closed_form) = -19.2912233027 2.41706624974 absolute error = 0.0002482 relative error = 0.001277 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.465 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] = -1.1688 2.328 h = 0.0001 0.005 y[1] (numeric) = -19.2885903524 2.42354247462 y[1] (closed_form) = -19.2888118779 2.42365679943 absolute error = 0.0002493 relative error = 0.001282 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.472 Order of pole (given) = 0.5 0 NO 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=5444.8MB, alloc=52.3MB, time=67.12 x[1] = -1.1687 2.333 h = 0.0001 0.003 y[1] (numeric) = -19.289076403 2.42875213337 y[1] (closed_form) = -19.2892985629 2.42886645926 absolute error = 0.0002499 relative error = 0.001285 % Correct digits = 5 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 x[1] = -1.1686 2.336 h = 0.001 0.001 y[1] (numeric) = -19.2893272117 2.43188266003 y[1] (closed_form) = -19.2895496001 2.43199699227 absolute error = 0.0002501 relative error = 0.001286 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.48 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1676 2.337 h = 0.0001 0.004 y[1] (numeric) = -19.2884060529 2.43304063363 y[1] (closed_form) = -19.2886284432 2.43315501655 absolute error = 0.0002501 relative error = 0.001286 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.481 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] = -1.1675 2.341 h = 0.003 0.006 y[1] (numeric) = -19.2887759315 2.43721093933 y[1] (closed_form) = -19.2889987277 2.43732532683 absolute error = 0.0002504 relative error = 0.001288 % Correct digits = 5 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] = -1.1645 2.347 h = 0.0001 0.005 y[1] (numeric) = -19.2863690724 2.44380460087 y[1] (closed_form) = -19.2865925884 2.44391987395 absolute error = 0.0002515 relative error = 0.001294 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.491 Order of pole (given) = 0.5 0 NO 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=5490.7MB, alloc=52.3MB, time=67.68 x[1] = -1.1644 2.352 h = 0.0001 0.003 y[1] (numeric) = -19.2868599612 2.44901525966 y[1] (closed_form) = -19.2870841117 2.44913053362 absolute error = 0.0002521 relative error = 0.001296 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.496 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1643 2.355 h = 0.001 0.001 y[1] (numeric) = -19.2871136657 2.45214642495 y[1] (closed_form) = -19.2873380447 2.4522617052 absolute error = 0.0002523 relative error = 0.001297 % Correct digits = 5 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] = -1.1633 2.356 h = 0.001 0.003 y[1] (numeric) = -19.2861932977 2.4533055503 y[1] (closed_form) = -19.2864176787 2.45342088123 absolute error = 0.0002523 relative error = 0.001298 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.5 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] = -1.1623 2.359 h = 0.0001 0.004 y[1] (numeric) = -19.2855117963 2.45654436773 y[1] (closed_form) = -19.285736386 2.45665984278 absolute error = 0.0002525 relative error = 0.001299 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.503 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1622 2.363 h = 0.003 0.006 y[1] (numeric) = -19.2858861536 2.46071568667 y[1] (closed_form) = -19.2861111493 2.46083116615 absolute error = 0.0002529 relative error = 0.001301 % Correct digits = 5 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 memory used=5536.7MB, alloc=52.3MB, time=68.25 x[1] = -1.1592 2.369 h = 0.0001 0.005 y[1] (numeric) = -19.2834853713 2.46731407483 y[1] (closed_form) = -19.2837110871 2.46743043973 absolute error = 0.0002539 relative error = 0.001306 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.514 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1591 2.374 h = 0.0001 0.003 y[1] (numeric) = -19.2839818647 2.47252597118 y[1] (closed_form) = -19.2842082151 2.47264233673 absolute error = 0.0002545 relative error = 0.001309 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.519 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] = -1.159 2.377 h = 0.001 0.001 y[1] (numeric) = -19.284238923 2.47565792376 y[1] (closed_form) = -19.2844655019 2.4757742955 absolute error = 0.0002547 relative error = 0.00131 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.521 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.158 2.378 h = 0.001 0.003 y[1] (numeric) = -19.2833194556 2.47681839941 y[1] (closed_form) = -19.2835460365 2.47693482184 absolute error = 0.0002547 relative error = 0.00131 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.523 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.157 2.381 h = 0.0001 0.004 y[1] (numeric) = -19.2826411058 2.48005901685 y[1] (closed_form) = -19.2828678955 2.48017558333 absolute error = 0.000255 relative error = 0.001312 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.526 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 memory used=5582.6MB, alloc=52.3MB, time=68.81 x[1] = -1.1569 2.385 h = 0.003 0.006 y[1] (numeric) = -19.2830199427 2.48423134749 y[1] (closed_form) = -19.2832471384 2.48434791826 absolute error = 0.0002554 relative error = 0.001313 % Correct digits = 5 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] = -1.1539 2.391 h = 0.0001 0.005 y[1] (numeric) = -19.2806252394 2.49083446053 y[1] (closed_form) = -19.2808531556 2.49095191653 absolute error = 0.0002564 relative error = 0.001319 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.536 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1538 2.396 h = 0.0001 0.003 y[1] (numeric) = -19.2811273384 2.49604759252 y[1] (closed_form) = -19.2813558892 2.49616504894 absolute error = 0.000257 relative error = 0.001322 % Correct digits = 5 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] = -1.1537 2.399 h = 0.001 0.001 y[1] (numeric) = -19.2813877511 2.49918033122 y[1] (closed_form) = -19.2816165305 2.49929779376 absolute error = 0.0002572 relative error = 0.001323 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.544 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1527 2.4 h = 0.001 0.003 y[1] (numeric) = -19.2804691849 2.50034215698 y[1] (closed_form) = -19.2806979663 2.50045967022 absolute error = 0.0002572 relative error = 0.001323 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.545 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1517 2.403 h = 0.0001 0.004 y[1] (numeric) = -19.2797939877 2.50358457344 y[1] (closed_form) = -19.2800229778 2.50370223067 absolute error = 0.0002574 relative error = 0.001324 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.548 Order of pole (given) = 0.5 0 NO 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=5628.5MB, alloc=52.3MB, time=69.38 x[1] = -1.1516 2.407 h = 0.003 0.006 y[1] (numeric) = -19.2801773049 2.50775791426 y[1] (closed_form) = -19.2804067012 2.50787557563 absolute error = 0.0002578 relative error = 0.001326 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.552 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 x[1] = -1.1486 2.413 h = 0.0001 0.005 y[1] (numeric) = -19.2777886828 2.5143657504 y[1] (closed_form) = -19.2780188 2.51448429682 absolute error = 0.0002589 relative error = 0.001331 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.559 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1485 2.418 h = 0.0001 0.003 y[1] (numeric) = -19.2782963884 2.51958011611 y[1] (closed_form) = -19.2785271402 2.51969866272 absolute error = 0.0002594 relative error = 0.001334 % Correct digits = 5 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] = -1.1484 2.421 h = 0.001 0.001 y[1] (numeric) = -19.2785601562 2.52271363981 y[1] (closed_form) = -19.2787911366 2.52283219244 absolute error = 0.0002596 relative error = 0.001335 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.566 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1474 2.422 h = 0.001 0.003 y[1] (numeric) = -19.2776424917 2.52387681548 y[1] (closed_form) = -19.2778734741 2.52399541881 absolute error = 0.0002597 relative error = 0.001335 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.568 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=5674.4MB, alloc=52.3MB, time=69.94 x[1] = -1.1464 2.425 h = 0.0001 0.004 y[1] (numeric) = -19.2769704479 2.52712102998 y[1] (closed_form) = -19.2772016393 2.52723977725 absolute error = 0.0002599 relative error = 0.001337 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.571 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1463 2.429 h = 0.003 0.006 y[1] (numeric) = -19.2773582463 2.53129537944 y[1] (closed_form) = -19.2775898437 2.5314141307 absolute error = 0.0002603 relative error = 0.001339 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.575 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] = -1.1433 2.435 h = 0.0001 0.005 y[1] (numeric) = -19.2749757078 2.53790793692 y[1] (closed_form) = -19.2752080266 2.53802757305 absolute error = 0.0002613 relative error = 0.001344 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.581 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1432 2.44 h = 0.0001 0.003 y[1] (numeric) = -19.2754890209 2.54312353443 y[1] (closed_form) = -19.2757219743 2.54324317052 absolute error = 0.0002619 relative error = 0.001347 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.586 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1431 2.443 h = 0.001 0.001 y[1] (numeric) = -19.2757561443 2.54625784197 y[1] (closed_form) = -19.2759893264 2.546377484 absolute error = 0.0002621 relative error = 0.001348 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.589 Order of pole (given) = 0.5 0 NO 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=5720.4MB, alloc=52.3MB, time=70.50 x[1] = -1.1421 2.444 h = 0.0001 0.004 y[1] (numeric) = -19.2748393821 2.54742236735 y[1] (closed_form) = -19.2750725663 2.54754206009 absolute error = 0.0002621 relative error = 0.001348 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.59 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.142 2.448 h = 0.003 0.006 y[1] (numeric) = -19.2752310503 2.5515975304 y[1] (closed_form) = -19.2754646406 2.551717227 absolute error = 0.0002625 relative error = 0.00135 % Correct digits = 5 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] = -1.139 2.454 h = 0.0001 0.005 y[1] (numeric) = -19.2728538065 2.55821407793 y[1] (closed_form) = -19.2730881183 2.55833465924 absolute error = 0.0002635 relative error = 0.001355 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.601 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1389 2.459 h = 0.0001 0.003 y[1] (numeric) = -19.2733719617 2.56343066738 y[1] (closed_form) = -19.2736069084 2.56355124845 absolute error = 0.0002641 relative error = 0.001358 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.605 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] = -1.1388 2.462 h = 0.001 0.001 y[1] (numeric) = -19.2736419833 2.56656560872 y[1] (closed_form) = -19.2738771586 2.56668619567 absolute error = 0.0002643 relative error = 0.001359 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.608 Order of pole (given) = 0.5 0 NO 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=5766.4MB, alloc=52.3MB, time=71.07 x[1] = -1.1378 2.463 h = 0.001 0.003 y[1] (numeric) = -19.2727260144 2.56773128497 y[1] (closed_form) = -19.2729611917 2.56785192262 absolute error = 0.0002643 relative error = 0.001359 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.61 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] = -1.1368 2.466 h = 0.0001 0.004 y[1] (numeric) = -19.2720598625 2.57097880503 y[1] (closed_form) = -19.2722952488 2.57109958649 absolute error = 0.0002646 relative error = 0.001361 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.613 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] = -1.1367 2.47 h = 0.003 0.006 y[1] (numeric) = -19.2724560132 2.57515497386 y[1] (closed_form) = -19.2726918058 2.57527575904 absolute error = 0.0002649 relative error = 0.001363 % Correct digits = 5 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] = -1.1337 2.476 h = 0.0001 0.005 y[1] (numeric) = -19.2700848571 2.58177623941 y[1] (closed_form) = -19.2703213717 2.58189790912 absolute error = 0.000266 relative error = 0.001368 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.623 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1336 2.481 h = 0.0001 0.003 y[1] (numeric) = -19.2706086217 2.58699405707 y[1] (closed_form) = -19.2708457711 2.58711572631 absolute error = 0.0002665 relative error = 0.001371 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.628 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 memory used=5812.2MB, alloc=52.3MB, time=71.64 x[1] = -1.1335 2.484 h = 0.001 0.001 y[1] (numeric) = -19.270882 2.59012978012 y[1] (closed_form) = -19.2711193781 2.59025145516 absolute error = 0.0002667 relative error = 0.001372 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.631 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1325 2.485 h = 0.001 0.003 y[1] (numeric) = -19.2699669345 2.59129680569 y[1] (closed_form) = -19.2702043146 2.59141853144 absolute error = 0.0002668 relative error = 0.001372 % Correct digits = 5 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] = -1.1315 2.488 h = 0.0001 0.004 y[1] (numeric) = -19.2693039388 2.59454612099 y[1] (closed_form) = -19.269541528 2.59466799049 absolute error = 0.000267 relative error = 0.001373 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.635 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1314 2.492 h = 0.003 0.006 y[1] (numeric) = -19.2697045728 2.59872329407 y[1] (closed_form) = -19.2699425683 2.59884516714 absolute error = 0.0002674 relative error = 0.001375 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.639 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1284 2.498 h = 0.0001 0.005 y[1] (numeric) = -19.2673395069 2.60534927587 y[1] (closed_form) = -19.2675782247 2.6054720333 absolute error = 0.0002684 relative error = 0.001381 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.646 Order of pole (given) = 0.5 0 NO 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=5858.2MB, alloc=52.3MB, time=72.20 x[1] = -1.1283 2.503 h = 0.0001 0.003 y[1] (numeric) = -19.2678688817 2.61056831983 y[1] (closed_form) = -19.2681082344 2.61069107655 absolute error = 0.000269 relative error = 0.001383 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.65 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 x[1] = -1.1282 2.506 h = 0.001 0.001 y[1] (numeric) = -19.2681456174 2.61370482344 y[1] (closed_form) = -19.2683851988 2.61382758587 absolute error = 0.0002692 relative error = 0.001384 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.653 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1272 2.507 h = 0.001 0.003 y[1] (numeric) = -19.2672314558 2.61487319813 y[1] (closed_form) = -19.2674710393 2.61499601128 absolute error = 0.0002692 relative error = 0.001385 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.655 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] = -1.1262 2.51 h = 0.0001 0.004 y[1] (numeric) = -19.2665716172 2.6181243077 y[1] (closed_form) = -19.2668114098 2.61824726453 absolute error = 0.0002695 relative error = 0.001386 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.658 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1261 2.514 h = 0.003 0.006 y[1] (numeric) = -19.2669767354 2.62230248349 y[1] (closed_form) = -19.2672169344 2.62242544375 absolute error = 0.0002698 relative error = 0.001388 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.662 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 memory used=5904.3MB, alloc=52.3MB, time=72.77 x[1] = -1.1231 2.52 h = 0.0001 0.005 y[1] (numeric) = -19.2646177618 2.62893317978 y[1] (closed_form) = -19.2648586835 2.62905702421 absolute error = 0.0002709 relative error = 0.001393 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.668 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.123 2.525 h = 0.0001 0.003 y[1] (numeric) = -19.2651527479 2.63415344811 y[1] (closed_form) = -19.2653943045 2.6342772916 absolute error = 0.0002715 relative error = 0.001396 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.673 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1229 2.528 h = 0.001 0.001 y[1] (numeric) = -19.2654328415 2.63729073113 y[1] (closed_form) = -19.2656746268 2.63741458025 absolute error = 0.0002717 relative error = 0.001397 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.676 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1219 2.529 h = 0.001 0.003 y[1] (numeric) = -19.2645195845 2.63846045474 y[1] (closed_form) = -19.2647613719 2.63858435459 absolute error = 0.0002717 relative error = 0.001397 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.677 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1209 2.532 h = 0.0001 0.004 y[1] (numeric) = -19.2638629039 2.6417133576 y[1] (closed_form) = -19.2641049006 2.64183740107 absolute error = 0.0002719 relative error = 0.001399 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.68 Order of pole (given) = 0.5 0 NO 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=5950.1MB, alloc=52.3MB, time=73.33 x[1] = -1.1208 2.536 h = 0.003 0.006 y[1] (numeric) = -19.2642725071 2.64589253457 y[1] (closed_form) = -19.2645149101 2.64601658131 absolute error = 0.0002723 relative error = 0.0014 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.684 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1178 2.542 h = 0.0001 0.005 y[1] (numeric) = -19.2619196282 2.65252794357 y[1] (closed_form) = -19.2621627543 2.65265287431 absolute error = 0.0002733 relative error = 0.001406 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.691 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1177 2.547 h = 0.0001 0.003 y[1] (numeric) = -19.2624602264 2.65774943435 y[1] (closed_form) = -19.2627039876 2.65787436392 absolute error = 0.0002739 relative error = 0.001409 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.695 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1176 2.55 h = 0.001 0.001 y[1] (numeric) = -19.2627436786 2.66088749564 y[1] (closed_form) = -19.2629876685 2.66101243076 absolute error = 0.0002741 relative error = 0.00141 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.698 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1166 2.551 h = 0.0001 0.004 y[1] (numeric) = -19.2618313266 2.66205856797 y[1] (closed_form) = -19.2620753187 2.66218355382 absolute error = 0.0002741 relative error = 0.00141 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.7 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1165 2.555 h = 0.003 0.006 y[1] (numeric) = -19.2622448028 2.66623855207 y[1] (closed_form) = -19.2624892012 2.66636354105 absolute error = 0.0002745 relative error = 0.001412 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.703 Order of pole (given) = 0.5 0 NO 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=5996.0MB, alloc=52.3MB, time=73.89 x[1] = -1.1135 2.561 h = 0.0001 0.005 y[1] (numeric) = -19.2598972279 2.67287794357 y[1] (closed_form) = -19.2601423498 2.67300381639 absolute error = 0.0002756 relative error = 0.001417 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.71 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1134 2.566 h = 0.0001 0.003 y[1] (numeric) = -19.2604426723 2.67810041818 y[1] (closed_form) = -19.2606884292 2.67822628963 absolute error = 0.0002761 relative error = 0.00142 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.715 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] = -1.1133 2.569 h = 0.001 0.001 y[1] (numeric) = -19.2607290251 2.68123910844 y[1] (closed_form) = -19.2609750107 2.68136498537 absolute error = 0.0002763 relative error = 0.001421 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.718 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1123 2.57 h = 0.001 0.003 y[1] (numeric) = -19.2598174688 2.68241133076 y[1] (closed_form) = -19.2600634566 2.68253725842 absolute error = 0.0002763 relative error = 0.001421 % Correct digits = 5 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] = -1.1113 2.573 h = 0.0001 0.004 y[1] (numeric) = -19.2591666886 2.68566753025 y[1] (closed_form) = -19.2594128857 2.68579360142 absolute error = 0.0002766 relative error = 0.001422 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.722 Order of pole (given) = 0.5 0 NO 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=6041.8MB, alloc=52.3MB, time=74.46 x[1] = -1.1112 2.577 h = 0.003 0.006 y[1] (numeric) = -19.2595846511 2.68984851266 y[1] (closed_form) = -19.2598312546 2.68997458682 absolute error = 0.000277 relative error = 0.001424 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.726 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1082 2.583 h = 0.0001 0.005 y[1] (numeric) = -19.2572431751 2.69649261355 y[1] (closed_form) = -19.2574905025 2.69661957137 absolute error = 0.000278 relative error = 0.00143 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.733 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1081 2.588 h = 0.0001 0.003 y[1] (numeric) = -19.2577942334 2.70171630703 y[1] (closed_form) = -19.2580421959 2.70184326325 absolute error = 0.0002786 relative error = 0.001433 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.737 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.108 2.591 h = 0.001 0.001 y[1] (numeric) = -19.2580839458 2.70485577342 y[1] (closed_form) = -19.2583321371 2.70498273503 absolute error = 0.0002788 relative error = 0.001434 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.74 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.107 2.592 h = 0.001 0.003 y[1] (numeric) = -19.2571732957 2.70602934407 y[1] (closed_form) = -19.2574214891 2.70615635642 absolute error = 0.0002788 relative error = 0.001434 % Correct digits = 5 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 memory used=6087.8MB, alloc=52.3MB, time=75.02 x[1] = -1.106 2.595 h = 0.0001 0.004 y[1] (numeric) = -19.2565256763 2.70928733404 y[1] (closed_form) = -19.2567740791 2.70941448983 absolute error = 0.0002791 relative error = 0.001435 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.745 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1059 2.599 h = 0.003 0.006 y[1] (numeric) = -19.2569481259 2.71346931323 y[1] (closed_form) = -19.2571969352 2.71359647187 absolute error = 0.0002794 relative error = 0.001437 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.748 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1029 2.605 h = 0.0001 0.005 y[1] (numeric) = -19.2546127511 2.72011812174 y[1] (closed_form) = -19.2548622846 2.72024616387 absolute error = 0.0002805 relative error = 0.001442 % Correct digits = 5 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] = -1.1028 2.61 h = 0.0001 0.003 y[1] (numeric) = -19.2551694244 2.72534303216 y[1] (closed_form) = -19.2554195932 2.72547107245 absolute error = 0.000281 relative error = 0.001445 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.76 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] = -1.1027 2.613 h = 0.001 0.001 y[1] (numeric) = -19.2554624971 2.72848327353 y[1] (closed_form) = -19.2557128945 2.72861131913 absolute error = 0.0002812 relative error = 0.001446 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.763 Order of pole (given) = 0.5 0 NO 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=6133.7MB, alloc=52.3MB, time=75.59 x[1] = -1.1017 2.614 h = 0.001 0.003 y[1] (numeric) = -19.2545527537 2.72965819232 y[1] (closed_form) = -19.2548031534 2.72978628866 absolute error = 0.0002813 relative error = 0.001446 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.764 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1007 2.617 h = 0.0001 0.004 y[1] (numeric) = -19.253908296 2.73291797179 y[1] (closed_form) = -19.2541589052 2.73304621151 absolute error = 0.0002815 relative error = 0.001448 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.767 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.1006 2.621 h = 0.003 0.006 y[1] (numeric) = -19.2543352336 2.73710094622 y[1] (closed_form) = -19.2545862492 2.73722918865 absolute error = 0.0002819 relative error = 0.001449 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.771 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0976 2.627 h = 0.0001 0.005 y[1] (numeric) = -19.2520059621 2.74375446059 y[1] (closed_form) = -19.2522577025 2.74388358631 absolute error = 0.0002829 relative error = 0.001455 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.778 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0975 2.632 h = 0.0001 0.003 y[1] (numeric) = -19.2525682514 2.74898058602 y[1] (closed_form) = -19.252820627 2.74910970967 absolute error = 0.0002835 relative error = 0.001458 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.782 Order of pole (given) = 0.5 0 NO 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=6179.7MB, alloc=52.3MB, time=76.15 x[1] = -1.0974 2.635 h = 0.001 0.001 y[1] (numeric) = -19.2528646849 2.75212160122 y[1] (closed_form) = -19.2531172892 2.75225073011 absolute error = 0.0002837 relative error = 0.001459 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.785 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0964 2.636 h = 0.001 0.003 y[1] (numeric) = -19.2519558488 2.75329786795 y[1] (closed_form) = -19.2522084554 2.75342704758 absolute error = 0.0002837 relative error = 0.001459 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.787 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0954 2.639 h = 0.0001 0.004 y[1] (numeric) = -19.2513145538 2.75655943593 y[1] (closed_form) = -19.2515673699 2.75668875888 absolute error = 0.000284 relative error = 0.00146 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.79 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0953 2.643 h = 0.003 0.006 y[1] (numeric) = -19.2517459801 2.76074340408 y[1] (closed_form) = -19.2519992027 2.76087272959 absolute error = 0.0002843 relative error = 0.001462 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.794 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0923 2.649 h = 0.0001 0.005 y[1] (numeric) = -19.2494228144 2.76740162253 y[1] (closed_form) = -19.2496767621 2.76753183115 absolute error = 0.0002854 relative error = 0.001467 % Correct digits = 5 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=6225.7MB, alloc=52.3MB, time=76.72 x[1] = -1.0922 2.654 h = 0.0001 0.003 y[1] (numeric) = -19.2499907206 2.77262896105 y[1] (closed_form) = -19.2502453036 2.77275916737 absolute error = 0.0002859 relative error = 0.00147 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.805 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0921 2.657 h = 0.001 0.001 y[1] (numeric) = -19.2502905155 2.77577074894 y[1] (closed_form) = -19.2505453272 2.77590096042 absolute error = 0.0002862 relative error = 0.001471 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.808 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0911 2.658 h = 0.0001 0.004 y[1] (numeric) = -19.2493825873 2.7769483634 y[1] (closed_form) = -19.2496374013 2.77707862562 absolute error = 0.0002862 relative error = 0.001471 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.809 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.091 2.662 h = 0.003 0.006 y[1] (numeric) = -19.2498178899 2.7811331322 y[1] (closed_form) = -19.2500731104 2.78126339684 absolute error = 0.0002865 relative error = 0.001473 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.813 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.088 2.668 h = 0.0001 0.005 y[1] (numeric) = -19.2475000376 2.78779532557 y[1] (closed_form) = -19.2477559835 2.78792647317 absolute error = 0.0002876 relative error = 0.001479 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.82 Order of pole (given) = 0.5 0 NO 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=6271.5MB, alloc=52.3MB, time=77.29 x[1] = -1.0879 2.673 h = 0.0001 0.003 y[1] (numeric) = -19.2480727938 2.79302363982 y[1] (closed_form) = -19.248329375 2.79315478492 absolute error = 0.0002882 relative error = 0.001482 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.824 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0878 2.676 h = 0.001 0.001 y[1] (numeric) = -19.2483754917 2.79616605185 y[1] (closed_form) = -19.2486323018 2.79629720203 absolute error = 0.0002884 relative error = 0.001483 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.827 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0868 2.677 h = 0.001 0.003 y[1] (numeric) = -19.2474683616 2.7973448154 y[1] (closed_form) = -19.2477251739 2.79747601633 absolute error = 0.0002884 relative error = 0.001483 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.828 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0858 2.68 h = 0.0001 0.004 y[1] (numeric) = -19.2468329754 2.80060967109 y[1] (closed_form) = -19.2470899973 2.80074101522 absolute error = 0.0002886 relative error = 0.001484 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.832 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0857 2.684 h = 0.003 0.006 y[1] (numeric) = -19.247272768 2.80479543073 y[1] (closed_form) = -19.2475301966 2.80492677715 absolute error = 0.000289 relative error = 0.001486 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.835 Order of pole (given) = 0.5 0 NO 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=6317.5MB, alloc=52.3MB, time=77.86 x[1] = -1.0827 2.69 h = 0.0001 0.005 y[1] (numeric) = -19.2449610257 2.81146232486 y[1] (closed_form) = -19.24521918 2.81159455405 absolute error = 0.00029 relative error = 0.001491 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.842 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0826 2.695 h = 0.0001 0.003 y[1] (numeric) = -19.2455394006 2.8166918486 y[1] (closed_form) = -19.2457981903 2.81682407506 absolute error = 0.0002906 relative error = 0.001494 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.847 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0825 2.698 h = 0.001 0.001 y[1] (numeric) = -19.245845461 2.81983503118 y[1] (closed_form) = -19.2461044796 2.81996726264 absolute error = 0.0002908 relative error = 0.001495 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.85 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0815 2.699 h = 0.001 0.003 y[1] (numeric) = -19.2449392399 2.82101514208 y[1] (closed_form) = -19.2451982607 2.82114742429 absolute error = 0.0002908 relative error = 0.001495 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.851 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0805 2.702 h = 0.0001 0.004 y[1] (numeric) = -19.244307019 2.82428178348 y[1] (closed_form) = -19.2445662496 2.82441420882 absolute error = 0.0002911 relative error = 0.001497 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.854 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0804 2.706 h = 0.003 0.006 y[1] (numeric) = -19.2447513026 2.82846853243 y[1] (closed_form) = -19.2450109398 2.82860095991 absolute error = 0.0002915 relative error = 0.001498 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.858 Order of pole (given) = 0.5 0 NO 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=6363.5MB, alloc=52.3MB, time=78.42 x[1] = -1.0774 2.712 h = 0.0001 0.005 y[1] (numeric) = -19.2424456725 2.83514012553 y[1] (closed_form) = -19.2427060359 2.83527343561 absolute error = 0.0002925 relative error = 0.001504 % Correct digits = 5 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] = -1.0773 2.717 h = 0.0001 0.003 y[1] (numeric) = -19.2430296671 2.84037085685 y[1] (closed_form) = -19.2432906659 2.84050416397 absolute error = 0.0002931 relative error = 0.001507 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.869 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0772 2.72 h = 0.001 0.001 y[1] (numeric) = -19.2433390906 2.84351480883 y[1] (closed_form) = -19.2436003183 2.84364812086 absolute error = 0.0002933 relative error = 0.001508 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.872 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0762 2.721 h = 0.001 0.003 y[1] (numeric) = -19.242433779 2.84469626688 y[1] (closed_form) = -19.2426950089 2.84482962966 absolute error = 0.0002933 relative error = 0.001508 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.874 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0752 2.724 h = 0.0001 0.004 y[1] (numeric) = -19.2418047244 2.84796469299 y[1] (closed_form) = -19.2420661642 2.84809819886 absolute error = 0.0002936 relative error = 0.001509 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.877 Order of pole (given) = 0.5 0 NO 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=6409.5MB, alloc=52.3MB, time=78.98 x[1] = -1.0751 2.728 h = 0.003 0.006 y[1] (numeric) = -19.2422534997 2.85215242972 y[1] (closed_form) = -19.2425153462 2.85228593758 absolute error = 0.0002939 relative error = 0.001511 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.881 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0721 2.734 h = 0.0001 0.005 y[1] (numeric) = -19.2399539841 2.85882872003 y[1] (closed_form) = -19.2402165571 2.8589631103 absolute error = 0.000295 relative error = 0.001516 % Correct digits = 5 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] = -1.072 2.739 h = 0.0001 0.003 y[1] (numeric) = -19.2405435993 2.864060657 y[1] (closed_form) = -19.2408068078 2.86419504407 absolute error = 0.0002955 relative error = 0.001519 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.892 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0719 2.742 h = 0.001 0.001 y[1] (numeric) = -19.2408563866 2.86720537723 y[1] (closed_form) = -19.241119824 2.86733976914 absolute error = 0.0002957 relative error = 0.00152 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.895 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0709 2.743 h = 0.001 0.003 y[1] (numeric) = -19.239951985 2.86838818222 y[1] (closed_form) = -19.2402154248 2.86852262488 absolute error = 0.0002958 relative error = 0.00152 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.896 Order of pole (given) = 0.5 0 NO 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=6455.4MB, alloc=52.3MB, time=79.55 x[1] = -1.0699 2.746 h = 0.0001 0.004 y[1] (numeric) = -19.2393260977 2.87165839208 y[1] (closed_form) = -19.2395897474 2.87179297776 absolute error = 0.000296 relative error = 0.001522 % Correct digits = 5 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] = -1.0698 2.75 h = 0.003 0.006 y[1] (numeric) = -19.2397793655 2.87584711505 y[1] (closed_form) = -19.2400434219 2.87598170257 absolute error = 0.0002964 relative error = 0.001523 % Correct digits = 5 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] = -1.0668 2.756 h = 0.0001 0.005 y[1] (numeric) = -19.2374859668 2.88252810078 y[1] (closed_form) = -19.23775075 2.88266357054 absolute error = 0.0002974 relative error = 0.001529 % Correct digits = 5 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] = -1.0667 2.761 h = 0.0001 0.003 y[1] (numeric) = -19.2380812035 2.88776124148 y[1] (closed_form) = -19.2383466223 2.88789670781 absolute error = 0.000298 relative error = 0.001532 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.914 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0666 2.764 h = 0.001 0.001 y[1] (numeric) = -19.2383973551 2.89090672882 y[1] (closed_form) = -19.2386630028 2.8910421999 absolute error = 0.0002982 relative error = 0.001533 % Correct digits = 5 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 memory used=6501.4MB, alloc=52.3MB, time=80.12 x[1] = -1.0656 2.765 h = 0.0001 0.004 y[1] (numeric) = -19.2374938642 2.89209088054 y[1] (closed_form) = -19.2377595143 2.89222640239 absolute error = 0.0002982 relative error = 0.001533 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.919 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0655 2.769 h = 0.003 0.006 y[1] (numeric) = -19.2379510114 2.89628039768 y[1] (closed_form) = -19.2382170682 2.89641592123 absolute error = 0.0002986 relative error = 0.001535 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.922 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0625 2.775 h = 0.0001 0.005 y[1] (numeric) = -19.2356629355 2.90296535076 y[1] (closed_form) = -19.2359297195 2.90310175639 absolute error = 0.0002996 relative error = 0.00154 % Correct digits = 5 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] = -1.0624 2.78 h = 0.0001 0.003 y[1] (numeric) = -19.2362630262 2.90819945906 y[1] (closed_form) = -19.2365304458 2.90833586106 absolute error = 0.0003002 relative error = 0.001543 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.934 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0623 2.783 h = 0.001 0.001 y[1] (numeric) = -19.2365820832 2.9113455657 y[1] (closed_form) = -19.2368497318 2.91148197238 absolute error = 0.0003004 relative error = 0.001544 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.937 Order of pole (given) = 0.5 0 NO 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=6547.4MB, alloc=52.3MB, time=80.68 x[1] = -1.0613 2.784 h = 0.001 0.003 y[1] (numeric) = -19.2356793928 2.91253086563 y[1] (closed_form) = -19.2359470437 2.91266732307 absolute error = 0.0003004 relative error = 0.001544 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.938 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0603 2.787 h = 0.0001 0.004 y[1] (numeric) = -19.2350594228 2.91580435426 y[1] (closed_form) = -19.2353272837 2.9159409546 absolute error = 0.0003007 relative error = 0.001546 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.941 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0602 2.791 h = 0.003 0.006 y[1] (numeric) = -19.2355210639 2.91999485476 y[1] (closed_form) = -19.2357893315 2.92013145667 absolute error = 0.000301 relative error = 0.001547 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.945 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0572 2.797 h = 0.0001 0.005 y[1] (numeric) = -19.233239109 2.92668449994 y[1] (closed_form) = -19.2335081043 2.92682198375 absolute error = 0.0003021 relative error = 0.001553 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.952 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0571 2.802 h = 0.0001 0.003 y[1] (numeric) = -19.233844823 2.93191980837 y[1] (closed_form) = -19.234114454 2.93205728832 absolute error = 0.0003027 relative error = 0.001556 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.956 Order of pole (given) = 0.5 0 NO 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=6593.4MB, alloc=52.3MB, time=81.25 x[1] = -1.057 2.805 h = 0.001 0.001 y[1] (numeric) = -19.2341672454 2.93506667997 y[1] (closed_form) = -19.2344371054 2.93520416451 absolute error = 0.0003029 relative error = 0.001557 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.959 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] = -1.056 2.806 h = 0.001 0.003 y[1] (numeric) = -19.2332654668 2.93625332626 y[1] (closed_form) = -19.2335353291 2.93639086157 absolute error = 0.0003029 relative error = 0.001557 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.961 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.055 2.809 h = 0.0001 0.004 y[1] (numeric) = -19.2326486667 2.93952859581 y[1] (closed_form) = -19.2329187391 2.93966627396 absolute error = 0.0003031 relative error = 0.001558 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.964 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0549 2.813 h = 0.003 0.006 y[1] (numeric) = -19.2331148025 2.94372007815 y[1] (closed_form) = -19.2333852817 2.94385775772 absolute error = 0.0003035 relative error = 0.00156 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.968 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0519 2.819 h = 0.0001 0.005 y[1] (numeric) = -19.2308389709 2.95041441365 y[1] (closed_form) = -19.2311101781 2.95055297493 absolute error = 0.0003046 relative error = 0.001565 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.974 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=6639.4MB, alloc=52.3MB, time=81.82 x[1] = -1.0518 2.824 h = 0.0001 0.003 y[1] (numeric) = -19.2314503093 2.95565092029 y[1] (closed_form) = -19.2317221522 2.95578947748 absolute error = 0.0003051 relative error = 0.001568 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.979 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0517 2.827 h = 0.001 0.001 y[1] (numeric) = -19.2317760977 2.95879855569 y[1] (closed_form) = -19.2320481696 2.9589371174 absolute error = 0.0003053 relative error = 0.001569 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.982 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0507 2.828 h = 0.001 0.003 y[1] (numeric) = -19.2308752313 2.95998654813 y[1] (closed_form) = -19.2311473057 2.96012516061 absolute error = 0.0003053 relative error = 0.001569 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.983 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0497 2.831 h = 0.0001 0.004 y[1] (numeric) = -19.2302616022 2.96326359763 y[1] (closed_form) = -19.2305338867 2.96340235288 absolute error = 0.0003056 relative error = 0.001571 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.986 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0496 2.835 h = 0.003 0.006 y[1] (numeric) = -19.2307322334 2.96745606027 y[1] (closed_form) = -19.2310049248 2.96759481679 absolute error = 0.000306 relative error = 0.001572 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.99 Order of pole (given) = 0.5 0 NO 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=6685.3MB, alloc=52.3MB, time=82.38 x[1] = -1.0466 2.841 h = 0.0001 0.005 y[1] (numeric) = -19.2284625274 2.97415508431 y[1] (closed_form) = -19.2287359472 2.97429472237 absolute error = 0.000307 relative error = 0.001578 % Correct digits = 5 Radius of convergence (given) for eq 1 = 2.997 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 x[1] = -1.0465 2.846 h = 0.0001 0.003 y[1] (numeric) = -19.2290794911 2.97939278723 y[1] (closed_form) = -19.2293535466 2.97953242096 absolute error = 0.0003076 relative error = 0.001581 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.001 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] = -1.0464 2.849 h = 0.001 0.001 y[1] (numeric) = -19.2294086461 2.9825411853 y[1] (closed_form) = -19.2296829306 2.98268082347 absolute error = 0.0003078 relative error = 0.001582 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.004 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] = -1.0454 2.85 h = 0.001 0.003 y[1] (numeric) = -19.2285086926 2.98373052369 y[1] (closed_form) = -19.2287829796 2.98387021263 absolute error = 0.0003078 relative error = 0.001582 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.006 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0444 2.853 h = 0.0001 0.004 y[1] (numeric) = -19.2278982353 2.98700935215 y[1] (closed_form) = -19.2281727325 2.9871491838 absolute error = 0.0003081 relative error = 0.001583 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.009 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0443 2.857 h = 0.003 0.006 y[1] (numeric) = -19.2283733629 2.99120279354 y[1] (closed_form) = -19.228648267 2.99134262632 absolute error = 0.0003084 relative error = 0.001585 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.013 Order of pole (given) = 0.5 0 NO 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=6731.1MB, alloc=52.3MB, time=82.94 x[1] = -1.0413 2.863 h = 0.0001 0.005 y[1] (numeric) = -19.2261097847 2.99790650435 y[1] (closed_form) = -19.2263854176 2.99804721848 absolute error = 0.0003095 relative error = 0.00159 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.019 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] = -1.0412 2.868 h = 0.0001 0.003 y[1] (numeric) = -19.2267323746 3.00314540162 y[1] (closed_form) = -19.2270086434 3.00328611119 absolute error = 0.00031 relative error = 0.001593 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.024 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0411 2.871 h = 0.001 0.001 y[1] (numeric) = -19.2270648968 3.00629456121 y[1] (closed_form) = -19.2273413945 3.00643527514 absolute error = 0.0003102 relative error = 0.001594 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.027 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] = -1.0401 2.872 h = 0.001 0.003 y[1] (numeric) = -19.2261658568 3.00748524534 y[1] (closed_form) = -19.226442357 3.00762601004 absolute error = 0.0003103 relative error = 0.001594 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.028 Order of pole (given) = 0.5 0 NO 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 ) = cosh ( sqrt ( 0.1 * x + 0.2 ) ) ; Iterations = 754 Total Elapsed Time = 1 Minutes 23 Seconds Expected Time Remaining = 0 Seconds Optimized Time Remaining = 0 Seconds Expected Total Time = 1 Minutes 23 Seconds > quit memory used=6775.8MB, alloc=52.3MB, time=83.47