## Linux and UNIX Man Pages

Test Your Knowledge in Computers #912
Difficulty: Medium
A null pointer in C always contains the value "".
True or False?

# pdl::gslsf::hyperg(3) [redhat man page]

```HYPERG(3)						User Contributed Perl Documentation						 HYPERG(3)

NAME
PDL::GSLSF::HYPERG - 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_hyperg_0F1

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

/* Hypergeometric function related to Bessel functions 0F1[c,x] = Gamma[c]    x^(1/2(1-c)) I_{c-1}(2 Sqrt[x]) Gamma[c] (-x)^(1/2(1-c))
J_{c-1}(2 Sqrt[-x])

gsl_sf_hyperg_1F1

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

Confluent hypergeometric function  for integer parameters. 1F1[a,b,x] = M(a,b,x)

gsl_sf_hyperg_U

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

Confluent hypergeometric function  for integer parameters. U(a,b,x)

gsl_sf_hyperg_2F1

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

Confluent hypergeometric function  for integer parameters. 2F1[a,b,c,x]

gsl_sf_hyperg_2F1_conj

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

Gauss hypergeometric function 2F1[aR + I aI, aR - I aI, c, x]

gsl_sf_hyperg_2F1_renorm

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

Renormalized Gauss hypergeometric function 2F1[a,b,c,x] / Gamma[c]

gsl_sf_hyperg_2F1_conj_renorm

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

Renormalized Gauss hypergeometric function 2F1[aR + I aI, aR - I aI, c, x] / Gamma[c]

gsl_sf_hyperg_2F0

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

Mysterious hypergeometric function. The series representation is a divergent hypergeometric series. However, for x < 0 we have 2F0(a,b,x) =
(-1/x)^a U(a,1+a-b,-1/x)

AUTHOR
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 v5.8.0							    2003-01-29								 HYPERG(3)```

## Check Out this Related Man Page

```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