GAMMA

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())

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.

Index

NAME
DESCRIPTION
SYNOPSIS
Functions
FUNCTIONS
gsl_sf_lngamma
gsl_sf_gamma
gsl_sf_gammastar
gsl_sf_gammainv
gsl_sf_lngamma_complex
gsl_sf_taylorcoeff
gsl_sf_fact
gsl_sf_doublefact
gsl_sf_lnfact
gsl_sf_lndoublefact
gsl_sf_lnchoose
gsl_sf_choose
gsl_sf_lnpoch
gsl_sf_poch
gsl_sf_pochrel
gsl_sf_gamma_inc_Q
gsl_sf_gamma_inc_P
gsl_sf_lnbeta
gsl_sf_beta
AUTHOR