NAME

Math::GammaFunction - The Gamma and its related functions

SYNOPSIS

  use Math::GammaFunction qw/:all/;
  my $gamma     = gamma(5); # 24
  my $fac       = faculty(4); # same
  my $psi       = psi(4); # 1.256...
  my $psi_deriv = psi_derivative($x, $order); # order==0 => psi
  # ...

DESCRIPTION

This module computes the Gamma function, its logarithmic derivative (the Psi or Digamma function) and the derivatives of the Psi function.

It is a thin wrapper around a couple of functions in the math library of the R statistics package.

EXPORT

None by default. You may choose to export the following functions separately or all at once using the :all tag:

    gamma
    log_gamma
    faculty
        psi
    psi_derivative

SUBROUTINES

gamma

Takes a real, positive number as argument. Computes the Gamma function. (n! == Gamma(n+1))

log_gamma

Takes a real, positive number as argument. Computes the logarithm of the Gamma function.

psi

Takes a real as argument. Computes the Psi (or Digamma) function. (d/dx Gamma(x) == Gamma(x)*Psi(x) or d/dx ln(Gamma(x)) == Psi(x))

psi_derivative

Takes two arguments: The argument x of the function (real) and the order of the derivative (integer 0 or positive). Computes the n-th derivative of Psi at position x.

The maximum derivative is, as far as I can gather from the R sources, 100.

This is basically the Polygamma function.

faculty

Takes a positive integer as argument. Computes its faculty. (Thin wrapper around gamma)

SEE ALSO

The actual computation is carried out in C by the excellent R library.

Thus, refer to the R manual for details. What I call gamma here is the gammafn in R's C sources, log_gamma is is gamma in the C sources. http://www.r-project.org/

Here's a list of Wikipedia pages about related functions:

http://en.wikipedia.org/wiki/Gamma_function, http://en.wikipedia.org/wiki/Polygamma_function, http://en.wikipedia.org/wiki/Digamma_function

AUTHOR

Steffen Mueller, <smueller@cpan.org>

COPYRIGHT AND LICENSE

Copyright (C) 2007 by Steffen Mueller

This library is free software; you can redistribute it and/or modify it under the same terms as Perl itself, either Perl version 5.6 or, at your option, any later version of Perl 5 you may have available.

cpanm Math::GammaFunction

perl -MCPAN -e shell
install Math::GammaFunction