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.

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