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.