---
name: "PDL::GSLSF::HYPERG"
section: "3pm"
platform: "linux"
package: "pdl"
version: "1:2.081-2"
release: "Debian 12 (Bookworm)"
platforms: ["linux"]
url: "https://new.carta.tech/PDL::GSLSF::HYPERG"
---

# PDL::GSLSF::HYPERG(3pm)

PDL interface to GSL Special Functions

## 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.

## 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\_0F1 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.

### 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\_1F1 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.

### 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\_U 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.

### 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 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.

### 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\_conj 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.

### 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\_renorm 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.

### 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\_2F1\_conj\_renorm 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.

### 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)

gsl\_sf\_hyperg\_2F0 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.

## 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.