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

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

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.

SYNOPSIS
Functions
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_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_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_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_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_D

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

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

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_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_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_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}]

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