GAMMA(3)						User Contributed Perl Documentation						  GAMMA(3)

NAME

       PDL::GSLSF::GAMMA - PDL interface to GSL Special Functions

DESCRIPTION

       This is an interface to the Special Function package present in the GNU Scientific Library.

SYNOPSIS

Functions
FUNCTIONS

       gsl_sf_lngamma

	 Signature: (double x(); double [o]y(); double [o]s(); double [o]e())

       Log[Gamma(x)], x not a negative integer Uses real Lanczos method. Determines the sign of Gamma[x] as well as Log[|Gamma[x]|] for x < 0. So
       Gamma[x] = sgn * Exp[result_lg].

       gsl_sf_gamma

	 Signature: (double x(); double [o]y(); double [o]e())

       Gamma(x), x not a negative integer

       gsl_sf_gammastar

	 Signature: (double x(); double [o]y(); double [o]e())

       Regulated Gamma Function, x > 0 Gamma^*(x) = Gamma(x)/(Sqrt[2Pi] x^(x-1/2) exp(-x)) = (1 + 1/(12x) + ...),  x->Inf

       gsl_sf_gammainv

	 Signature: (double x(); double [o]y(); double [o]e())

       1/Gamma(x)

       gsl_sf_lngamma_complex

	 Signature: (double zr(); double zi(); double [o]x(); double [o]y(); double [o]xe(); double [o]ye())

       Log[Gamma(z)] for z complex, z not a negative integer. Calculates: lnr = log|Gamma(z)|, arg = arg(Gamma(z))  in (-Pi, Pi]

       gsl_sf_taylorcoeff

	 Signature: (double x(); double [o]y(); double [o]e(); int n)

       x^n / n!

       gsl_sf_fact

	 Signature: (x(); double [o]y(); double [o]e())

       n!

       gsl_sf_doublefact

	 Signature: (x(); double [o]y(); double [o]e())

       n!! = n(n-2)(n-4)

       gsl_sf_lnfact

	 Signature: (x(); double [o]y(); double [o]e())

       ln n!

       gsl_sf_lndoublefact

	 Signature: (x(); double [o]y(); double [o]e())

       ln n!!

       gsl_sf_lnchoose

	 Signature: (n(); m(); double [o]y(); double [o]e())

       log(n choose m)

       gsl_sf_choose

	 Signature: (n(); m(); double [o]y(); double [o]e())

       n choose m

       gsl_sf_lnpoch

	 Signature: (double x(); double [o]y(); double [o]s(); double [o]e(); double a)

       Logarithm of Pochammer (Apell) symbol, with sign information. result = log( |(a)_x| ), sgn    = sgn( (a)_x ) where (a)_x := Gamma[a +
       x]/Gamma[a]

       gsl_sf_poch

	 Signature: (double x(); double [o]y(); double [o]e(); double a)

       Pochammer (Apell) symbol (a)_x := Gamma[a + x]/Gamma[x]

       gsl_sf_pochrel

	 Signature: (double x(); double [o]y(); double [o]e(); double a)

       Relative Pochammer (Apell) symbol ((a,x) - 1)/x where (a,x) = (a)_x := Gamma[a + x]/Gamma[a]

       gsl_sf_gamma_inc_Q

	 Signature: (double x(); double [o]y(); double [o]e(); double a)

       Normalized Incomplete Gamma Function Q(a,x) = 1/Gamma(a) Integral[ t^(a-1) e^(-t), {t,x,Infinity} ]

       gsl_sf_gamma_inc_P

	 Signature: (double x(); double [o]y(); double [o]e(); double a)

       Complementary Normalized Incomplete Gamma Function P(a,x) = 1/Gamma(a) Integral[ t^(a-1) e^(-t), {t,0,x} ]

       gsl_sf_lnbeta

	 Signature: (double a(); double b(); double [o]y(); double [o]e())

       Logarithm of Beta Function Log[B(a,b)]

       gsl_sf_beta

	 Signature: (double a(); double b();double [o]y(); double [o]e())

       Beta Function B(a,b)

AUTHOR

       This file copyright (C) 1999 Christian Pellegrin <chri@infis.univ.trieste.it> All rights reserved. There is no warranty. You are allowed to
       redistribute this software / documentation under certain conditions. For details, see the file COPYING in the PDL distribution. If this
       file is separated from the PDL distribution, the copyright notice should be included in the file.

       The GSL SF modules were written by G. Jungman.

perl v5.8.0							    2003-01-29								  GAMMA(3)