#!/usr/bin/perl
# zeta.pl  c.2011 stan kulikowski ii, stankuli@etherways.com, pensacola, fl 32514


$SERIES_DEPTH = 1000000;
&QUERY_DIRICHLET;


sub QUERY_DIRICHLET
{
  my $POWERS = 1;
  my $PRECISION = 0;

  print "\n Dirichlet's zeta function. \n";

  my $OK = 0;

  until ($OK)
  {
    print " How many powers : ";
    chop($POWERS = <>);
    $POWERS = int $POWERS;

    ($POWERS > 1) ? $OK = 1 : print " value must be greater than 1 \n";
  } # until $OK #

  $OK = 0;
  until ($OK)
  {
    print " To what precision : ";
    chop($PRECISION = <>);

    ($PRECISION < 1 && $PRECISION > 0) ? $OK = 1 : print " value must be between 1 and 0 \n";
  } # until $OK #

  &DIRICHLET ($POWERS,$PRECISION);
  print "\n\n"; 

} # QUERY_DIRICHLET #


sub HARMONIC_SERIES
{
  my ($POWER) = @_;

  my $RESULT = 1;
  my $SERIES = $SERIES_DEPTH;

  while ($SERIES > 1)
  {
    $RESULT += 1/($SERIES-- **$POWER);
  } # while ($SERIES > 1) #
  return $RESULT;
} # HARMONIC_SERIES #


sub DIRICHLET
{
  my ($POWERS,$PRECISION) = @_;
  my $POWER = 2;

  print "\n\n\t Power \t Dirichlet's zeta result  (harmonic series depth = $SERIES_DEPTH)\n\n";

  while ($POWER < $POWERS+1)
  {
    print "\t $POWER \t " . &HARMONIC_SERIES ($POWER) . " \n";
    $POWER += $PRECISION;          # problem here at 5.9?
  } # while ($POWER <= $POWERS) #  
} # DIRICHLET #


# eof zeta.pl

##</code><code>##



 Dirichlet's zeta function. 
 How many powers : 6
 To what precision : 0.1


	 Power 	 Dirichlet's zeta result  (harmonic series depth = 1000000)

	 2 	 1.64493306684877 
	 2.1 	 1.56021630515022 
	 2.2 	 1.49054320392715 
	 2.3 	 1.43241778712389 
	 2.4 	 1.38334285599691 
	 2.5 	 1.34148725658587 
	 2.6 	 1.30547780891302 
	 2.7 	 1.27426464440048 
	 2.8 	 1.24703142229228 
	 2.9 	 1.22313389528938 
	 3 	 1.20205690315031 
	 3.1 	 1.18338365210598 
	 3.2 	 1.16677337098058 
	 3.3 	 1.15194479471816 
	 3.4 	 1.13866377572624 
	 3.5 	 1.12673386731579 
	 3.6 	 1.11598907912243 
	 3.7 	 1.10628824146401 
	 3.8 	 1.09751057645852 
	 3.9 	 1.08955218466995 
	 4 	 1.08232323371086 
	 4.1 	 1.07574569034329 
	 4.2 	 1.06975147723364 
	 4.3 	 1.0642809643257 
	 4.4 	 1.05928172597973 
	 4.5 	 1.05470751076137 
	 4.6 	 1.0505173825665 
	 4.7 	 1.04667500069907 
	 4.8 	 1.04314801333513 
	 4.9 	 1.03990754404931 
	 5 	 1.03692775514334 
	 5.1 	 1.03418547468746 
	 5.2 	 1.03165987667789 
	 5.3 	 1.0293322056832 
	 5.4 	 1.02718553892034 
	 5.5 	 1.02520457995467 
	 5.6 	 1.02337547922702 
	 5.7 	 1.02168567742621 
	 5.8 	 1.02012376838834 
	 5.9 	 1.01867937874473 
	 5.99999999999999 	 1.01734306198444 
	 6.09999999999999 	 1.0161062049622 
	 6.19999999999999 	 1.01496094518522 
	 6.29999999999999 	 1.0139000974628 
	 6.39999999999999 	 1.01291708871218 
	 6.49999999999999 	 1.01200589988852 
	 6.59999999999999 	 1.01116101415427 
	 6.69999999999999 	 1.01037737052638 
	 6.79999999999999 	 1.00965032234471 
	 6.89999999999999 	 1.00897559999333 
	 6.99999999999999 	 1.00834927738192