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_lngamma does not process bad values.  It will set the bad-value flag of all output piddles if the flag is set for any of the input
       piddles.

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

       Gamma(x), x not a negative integer

       gsl_sf_gamma does not process bad values.  It will set the bad-value flag of all output piddles if the flag is set for any of the input
       piddles.

   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_gammastar does not process bad values.  It will set the bad-value flag of all output piddles if the flag is set for any of the input
       piddles.

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

       1/Gamma(x)

       gsl_sf_gammainv does not process bad values.  It will set the bad-value flag of all output piddles if the flag is set for any of the input
       piddles.

   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_lngamma_complex does not process bad values.  It will set the bad-value flag of all output piddles if the flag is set for any of the
       input piddles.

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

       x^n / n!

       gsl_sf_taylorcoeff does not process bad values.	It will set the bad-value flag of all output piddles if the flag is set for any of the
       input piddles.

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

       n!

       gsl_sf_fact does not process bad values.  It will set the bad-value flag of all output piddles if the flag is set for any of the input
       piddles.

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

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

       gsl_sf_doublefact does not process bad values.  It will set the bad-value flag of all output piddles if the flag is set for any of the
       input piddles.

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

       ln n!

       gsl_sf_lnfact does not process bad values.  It will set the bad-value flag of all output piddles if the flag is set for any of the input
       piddles.

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

       ln n!!

       gsl_sf_lndoublefact does not process bad values.  It will set the bad-value flag of all output piddles if the flag is set for any of the
       input piddles.

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

       log(n choose m)

       gsl_sf_lnchoose does not process bad values.  It will set the bad-value flag of all output piddles if the flag is set for any of the input
       piddles.

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

       n choose m

       gsl_sf_choose does not process bad values.  It will set the bad-value flag of all output piddles if the flag is set for any of the input
       piddles.

   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_lnpoch does not process bad values.  It will set the bad-value flag of all output piddles if the flag is set for any of the input
       piddles.

   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_poch does not process bad values.  It will set the bad-value flag of all output piddles if the flag is set for any of the input
       piddles.

   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_pochrel does not process bad values.  It will set the bad-value flag of all output piddles if the flag is set for any of the input
       piddles.

   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_Q does not process bad values.	It will set the bad-value flag of all output piddles if the flag is set for any of the
       input piddles.

   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_gamma_inc_P does not process bad values.	It will set the bad-value flag of all output piddles if the flag is set for any of the
       input piddles.

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

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

       gsl_sf_lnbeta does not process bad values.  It will set the bad-value flag of all output piddles if the flag is set for any of the input
       piddles.

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

       Beta Function B(a,b)

       gsl_sf_beta does not process bad values.  It will set the bad-value flag of all output piddles if the flag is set for any of the input
       piddles.

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 v5.12.1							    2010-07-05								  GAMMA(3)