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

   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.