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.\" ========================================================================
.\"
.IX Title "ELLINT 3pm"
.TH ELLINT 3pm "2012-05-30" "perl v5.14.2" "User Contributed Perl Documentation"
.\" For nroff, turn off justification.  Always turn off hyphenation; it makes
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.nh
.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 \s-1GNU\s0 Scientific Library.
.SH "SYNOPSIS"
.IX Header "SYNOPSIS"
.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 piddles if the flag is set for any of the input piddles.
.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 piddles if the flag is set for any of the input piddles.
.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 piddles if the flag is set for any of the input piddles.
.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 piddles if the flag is set for any of the input piddles.
.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 piddles if the flag is set for any of the input piddles.
.SS "gsl_sf_ellint_D"
.IX Subsection "gsl_sf_ellint_D"
.Vb 2
\&  Signature: (double phi(); double k(); double n();
\&              double [o]y(); double [o]e())
.Ve
.PP
Legendre form of incomplete elliptic integrals D(phi,k,n)
.PP
gsl_sf_ellint_D does not process bad values.
It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.
.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 \s-1RC\s0(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 piddles if the flag is set for any of the input piddles.
.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 \s-1RD\s0(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 piddles if the flag is set for any of the input piddles.
.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 \s-1RF\s0(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 piddles if the flag is set for any of the input piddles.
.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 \s-1RJ\s0(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 piddles if the flag is set for any of the input piddles.
.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
\&\s-1COPYING\s0 in the \s-1PDL\s0 distribution. If this file is separated from the
\&\s-1PDL\s0 distribution, the copyright notice should be included in the file.
.PP
The \s-1GSL\s0 \s-1SF\s0 modules were written by G. Jungman.