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

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

PDL interface to GSL Special Functions

## NAME

PDL::GSLSF::ELLINT - 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\_ellint\_Kcomp

```
  Signature: (double k(); double [o]y(); double [o]e())
```

Legendre form of complete elliptic integrals K(k) = Integral\[1/Sqrt\[1 - k^2 Sin\[t\]^2\], {t, 0, Pi/2}\].

gsl\_sf\_ellint\_Kcomp 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\_ellint\_Ecomp

```
  Signature: (double k(); double [o]y(); double [o]e())
```

Legendre form of complete elliptic integrals E(k) = Integral\[  Sqrt\[1 - k^2 Sin\[t\]^2\], {t, 0, Pi/2}\]

gsl\_sf\_ellint\_Ecomp 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\_ellint\_F

```
  Signature: (double phi(); double k(); double [o]y(); double [o]e())
```

Legendre form of incomplete elliptic integrals F(phi,k)   = Integral\[1/Sqrt\[1 - k^2 Sin\[t\]^2\], {t, 0, phi}\]

gsl\_sf\_ellint\_F 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\_ellint\_E

```
  Signature: (double phi(); double k(); double [o]y(); double [o]e())
```

Legendre form of incomplete elliptic integrals E(phi,k)   = Integral\[  Sqrt\[1 - k^2 Sin\[t\]^2\], {t, 0, phi}\]

gsl\_sf\_ellint\_E 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\_ellint\_P

```
  Signature: (double phi(); double k(); double n();
              double [o]y(); double [o]e())
```

Legendre form of incomplete elliptic integrals P(phi,k,n) = Integral\[(1 + n Sin\[t\]^2)^(-1)/Sqrt\[1 - k^2 Sin\[t\]^2\], {t, 0, phi}\]

gsl\_sf\_ellint\_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.

### gsl\_sf\_ellint\_D

```
  Signature: (double phi(); double k();
              double [o]y(); double [o]e())
```

Legendre form of incomplete elliptic integrals D(phi,k)

gsl\_sf\_ellint\_D 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\_ellint\_RC

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

Carlsons symmetric basis of functions RC(x,y)   = 1/2 Integral\[(t+x)^(-1/2) (t+y)^(-1)\], {t,0,Inf}

gsl\_sf\_ellint\_RC 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\_ellint\_RD

```
  Signature: (double x(); double yy(); double z(); double [o]y(); double [o]e())
```

Carlsons symmetric basis of functions RD(x,y,z) = 3/2 Integral\[(t+x)^(-1/2) (t+y)^(-1/2) (t+z)^(-3/2), {t,0,Inf}\]

gsl\_sf\_ellint\_RD 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\_ellint\_RF

```
  Signature: (double x(); double yy(); double z(); double [o]y(); double [o]e())
```

Carlsons symmetric basis of functions RF(x,y,z) = 1/2 Integral\[(t+x)^(-1/2) (t+y)^(-1/2) (t+z)^(-1/2), {t,0,Inf}\]

gsl\_sf\_ellint\_RF 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\_ellint\_RJ

```
  Signature: (double x(); double yy(); double z(); double p(); double [o]y(); double [o]e())
```

Carlsons symmetric basis of functions RJ(x,y,z,p) = 3/2 Integral\[(t+x)^(-1/2) (t+y)^(-1/2) (t+z)^(-1/2) (t+p)^(-1), {t,0,Inf}\]

gsl\_sf\_ellint\_RJ 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\>, 2002 Christian Soeller. 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.