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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, <[email protected]>

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.