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.\"
.IX Title "GAMMA 3pm"
.TH GAMMA 3pm "2023-06-17" "perl v5.36.0" "User Contributed Perl Documentation"
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.\" way too many mistakes in technical documents.
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.nh
.SH "NAME"
PDL::GSLSF::GAMMA \- PDL interface to GSL Special Functions
.SH "DESCRIPTION"
.IX Header "DESCRIPTION"
This is an interface to the Special Function package present in the \s-1GNU\s0 Scientific Library.
.SH "FUNCTIONS"
.IX Header "FUNCTIONS"
.SS "gsl_sf_lngamma"
.IX Subsection "gsl_sf_lngamma"
.Vb 1
\&  Signature: (double x(); double [o]y(); double [o]s(); double [o]e())
.Ve
.PP
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].
.PP
gsl_sf_lngamma does not process bad values.
It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
.SS "gsl_sf_gamma"
.IX Subsection "gsl_sf_gamma"
.Vb 1
\&  Signature: (double x(); double [o]y(); double [o]e())
.Ve
.PP
Gamma(x), x not a negative integer
.PP
gsl_sf_gamma does not process bad values.
It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
.SS "gsl_sf_gammastar"
.IX Subsection "gsl_sf_gammastar"
.Vb 1
\&  Signature: (double x(); double [o]y(); double [o]e())
.Ve
.PP
Regulated Gamma Function, x > 0 Gamma^*(x) = Gamma(x)/(Sqrt[2Pi] x^(x\-1/2) exp(\-x)) = (1 + 1/(12x) + ...),  x\->Inf
.PP
gsl_sf_gammastar does not process bad values.
It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
.SS "gsl_sf_gammainv"
.IX Subsection "gsl_sf_gammainv"
.Vb 1
\&  Signature: (double x(); double [o]y(); double [o]e())
.Ve
.PP
1/Gamma(x)
.PP
gsl_sf_gammainv does not process bad values.
It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
.SS "gsl_sf_lngamma_complex"
.IX Subsection "gsl_sf_lngamma_complex"
.Vb 1
\&  Signature: (double zr(); double zi(); double [o]x(); double [o]y(); double [o]xe(); double [o]ye())
.Ve
.PP
Log[Gamma(z)] for z complex, z not a negative integer. Calculates: lnr = log|Gamma(z)|, arg = arg(Gamma(z))  in (\-Pi, Pi]
.PP
gsl_sf_lngamma_complex does not process bad values.
It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
.SS "gsl_sf_taylorcoeff"
.IX Subsection "gsl_sf_taylorcoeff"
.Vb 1
\&  Signature: (double x(); double [o]y(); double [o]e(); int n)
.Ve
.PP
x^n / n!
.PP
gsl_sf_taylorcoeff does not process bad values.
It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
.SS "gsl_sf_fact"
.IX Subsection "gsl_sf_fact"
.Vb 1
\&  Signature: (x(); double [o]y(); double [o]e())
.Ve
.PP
n!
.PP
gsl_sf_fact does not process bad values.
It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
.SS "gsl_sf_doublefact"
.IX Subsection "gsl_sf_doublefact"
.Vb 1
\&  Signature: (x(); double [o]y(); double [o]e())
.Ve
.PP
n!! = n(n\-2)(n\-4)
.PP
gsl_sf_doublefact does not process bad values.
It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
.SS "gsl_sf_lnfact"
.IX Subsection "gsl_sf_lnfact"
.Vb 1
\&  Signature: (x(); double [o]y(); double [o]e())
.Ve
.PP
ln n!
.PP
gsl_sf_lnfact does not process bad values.
It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
.SS "gsl_sf_lndoublefact"
.IX Subsection "gsl_sf_lndoublefact"
.Vb 1
\&  Signature: (x(); double [o]y(); double [o]e())
.Ve
.PP
ln n!!
.PP
gsl_sf_lndoublefact does not process bad values.
It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
.SS "gsl_sf_lnchoose"
.IX Subsection "gsl_sf_lnchoose"
.Vb 1
\&  Signature: (n(); m(); double [o]y(); double [o]e())
.Ve
.PP
log(n choose m)
.PP
gsl_sf_lnchoose does not process bad values.
It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
.SS "gsl_sf_choose"
.IX Subsection "gsl_sf_choose"
.Vb 1
\&  Signature: (n(); m(); double [o]y(); double [o]e())
.Ve
.PP
n choose m
.PP
gsl_sf_choose does not process bad values.
It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
.SS "gsl_sf_lnpoch"
.IX Subsection "gsl_sf_lnpoch"
.Vb 1
\&  Signature: (double x(); double [o]y(); double [o]s(); double [o]e(); double a)
.Ve
.PP
Logarithm of Pochammer (Apell) symbol, with sign information. result = log( |(a)_x| ), sgn    = sgn( (a)_x ) where (a)_x := Gamma[a + x]/Gamma[a]
.PP
gsl_sf_lnpoch does not process bad values.
It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
.SS "gsl_sf_poch"
.IX Subsection "gsl_sf_poch"
.Vb 1
\&  Signature: (double x(); double [o]y(); double [o]e(); double a)
.Ve
.PP
Pochammer (Apell) symbol (a)_x := Gamma[a + x]/Gamma[x]
.PP
gsl_sf_poch does not process bad values.
It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
.SS "gsl_sf_pochrel"
.IX Subsection "gsl_sf_pochrel"
.Vb 1
\&  Signature: (double x(); double [o]y(); double [o]e(); double a)
.Ve
.PP
Relative Pochammer (Apell) symbol ((a,x) \- 1)/x where (a,x) = (a)_x := Gamma[a + x]/Gamma[a]
.PP
gsl_sf_pochrel does not process bad values.
It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
.SS "gsl_sf_gamma_inc_Q"
.IX Subsection "gsl_sf_gamma_inc_Q"
.Vb 1
\&  Signature: (double x(); double [o]y(); double [o]e(); double a)
.Ve
.PP
Normalized Incomplete Gamma Function Q(a,x) = 1/Gamma(a) Integral[ t^(a\-1) e^(\-t), {t,x,Infinity} ]
.PP
gsl_sf_gamma_inc_Q does not process bad values.
It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
.SS "gsl_sf_gamma_inc_P"
.IX Subsection "gsl_sf_gamma_inc_P"
.Vb 1
\&  Signature: (double x(); double [o]y(); double [o]e(); double a)
.Ve
.PP
Complementary Normalized Incomplete Gamma Function P(a,x) = 1/Gamma(a) Integral[ t^(a\-1) e^(\-t), {t,0,x} ]
.PP
gsl_sf_gamma_inc_P does not process bad values.
It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
.SS "gsl_sf_lnbeta"
.IX Subsection "gsl_sf_lnbeta"
.Vb 1
\&  Signature: (double a(); double b(); double [o]y(); double [o]e())
.Ve
.PP
Logarithm of Beta Function Log[B(a,b)]
.PP
gsl_sf_lnbeta does not process bad values.
It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
.SS "gsl_sf_beta"
.IX Subsection "gsl_sf_beta"
.Vb 1
\&  Signature: (double a(); double b();double [o]y(); double [o]e())
.Ve
.PP
Beta Function B(a,b)
.PP
gsl_sf_beta does not process bad values.
It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
.SH "AUTHOR"
.IX Header "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
\&\s-1COPYING\s0 in the \s-1PDL\s0 distribution. If this file is separated from the
\&\s-1PDL\s0 distribution, the copyright notice should be included in the file.
.PP
The \s-1GSL SF\s0 modules were written by G. Jungman.