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.IX Title "ELLINT 3pm"
.TH ELLINT 3pm 2024-04-25 "perl v5.38.2" "User Contributed Perl Documentation"
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.SH NAME
PDL::GSLSF::ELLINT \- PDL interface to GSL Special Functions
.SH DESCRIPTION
.IX Header "DESCRIPTION"
This is an interface to the Special Function package present in the GNU Scientific Library.
.SH FUNCTIONS
.IX Header "FUNCTIONS"
.SS gsl_sf_ellint_Kcomp
.IX Subsection "gsl_sf_ellint_Kcomp"
.Vb 1
\&  Signature: (double k(); double [o]y(); double [o]e())
.Ve
.PP
Legendre form of complete elliptic integrals K(k) = Integral[1/Sqrt[1 \- k^2 Sin[t]^2], {t, 0, Pi/2}].
.PP
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.
.SS gsl_sf_ellint_Ecomp
.IX Subsection "gsl_sf_ellint_Ecomp"
.Vb 1
\&  Signature: (double k(); double [o]y(); double [o]e())
.Ve
.PP
Legendre form of complete elliptic integrals E(k) = Integral[  Sqrt[1 \- k^2 Sin[t]^2], {t, 0, Pi/2}]
.PP
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.
.SS gsl_sf_ellint_F
.IX Subsection "gsl_sf_ellint_F"
.Vb 1
\&  Signature: (double phi(); double k(); double [o]y(); double [o]e())
.Ve
.PP
Legendre form of incomplete elliptic integrals F(phi,k)   = Integral[1/Sqrt[1 \- k^2 Sin[t]^2], {t, 0, phi}]
.PP
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.
.SS gsl_sf_ellint_E
.IX Subsection "gsl_sf_ellint_E"
.Vb 1
\&  Signature: (double phi(); double k(); double [o]y(); double [o]e())
.Ve
.PP
Legendre form of incomplete elliptic integrals E(phi,k)   = Integral[  Sqrt[1 \- k^2 Sin[t]^2], {t, 0, phi}]
.PP
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.
.SS gsl_sf_ellint_P
.IX Subsection "gsl_sf_ellint_P"
.Vb 2
\&  Signature: (double phi(); double k(); double n();
\&              double [o]y(); double [o]e())
.Ve
.PP
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}]
.PP
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.
.SS gsl_sf_ellint_D
.IX Subsection "gsl_sf_ellint_D"
.Vb 2
\&  Signature: (double phi(); double k();
\&              double [o]y(); double [o]e())
.Ve
.PP
Legendre form of incomplete elliptic integrals D(phi,k)
.PP
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.
.SS gsl_sf_ellint_RC
.IX Subsection "gsl_sf_ellint_RC"
.Vb 1
\&  Signature: (double x(); double yy(); double [o]y(); double [o]e())
.Ve
.PP
Carlsons symmetric basis of functions RC(x,y)   = 1/2 Integral[(t+x)^(\-1/2) (t+y)^(\-1)], {t,0,Inf}
.PP
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.
.SS gsl_sf_ellint_RD
.IX Subsection "gsl_sf_ellint_RD"
.Vb 1
\&  Signature: (double x(); double yy(); double z(); double [o]y(); double [o]e())
.Ve
.PP
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}]
.PP
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.
.SS gsl_sf_ellint_RF
.IX Subsection "gsl_sf_ellint_RF"
.Vb 1
\&  Signature: (double x(); double yy(); double z(); double [o]y(); double [o]e())
.Ve
.PP
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}]
.PP
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.
.SS gsl_sf_ellint_RJ
.IX Subsection "gsl_sf_ellint_RJ"
.Vb 1
\&  Signature: (double x(); double yy(); double z(); double p(); double [o]y(); double [o]e())
.Ve
.PP
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}]
.PP
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.
.SH AUTHOR
.IX Header "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.
.PP
The GSL SF modules were written by G. Jungman.