Math::GammaFunction - The Gamma and its related functions
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 # ...
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.
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
Takes a real, positive number as argument. Computes the Gamma function. (n! == Gamma(n+1))
Takes a real, positive number as argument. Computes the logarithm of the Gamma function.
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))
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.
Takes a positive integer as argument. Computes its faculty. (Thin wrapper around gamma)
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
Steffen Mueller, <smueller@cpan.org>
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.
