# RedHat 9 (Linux i386) - man page for pdl::gslsf::gamma (redhat section 3)

```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