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.\" ========================================================================
.\"
.IX Title "LEGENDRE 3pm"
.TH LEGENDRE 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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.SH "NAME"
PDL::GSLSF::LEGENDRE \- 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_legendre_Pl"
.IX Subsection "gsl_sf_legendre_Pl"
.Vb 1
\&  Signature: (double x(); double [o]y(); double [o]e(); int l)
.Ve
.PP
P_l(x)
.PP
gsl_sf_legendre_Pl 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_legendre_Pl_array"
.IX Subsection "gsl_sf_legendre_Pl_array"
.Vb 1
\&  Signature: (double x(); double [o]y(num); int l=>num)
.Ve
.PP
P_l(x) from 0 to n\-1.
.PP
gsl_sf_legendre_Pl_array 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_legendre_Ql"
.IX Subsection "gsl_sf_legendre_Ql"
.Vb 1
\&  Signature: (double x(); double [o]y(); double [o]e(); int l)
.Ve
.PP
Q_l(x)
.PP
gsl_sf_legendre_Ql 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_legendre_Plm"
.IX Subsection "gsl_sf_legendre_Plm"
.Vb 1
\&  Signature: (double x(); double [o]y(); double [o]e(); int l; int m)
.Ve
.PP
P_lm(x)
.PP
gsl_sf_legendre_Plm 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_legendre_Plm_array"
.IX Subsection "gsl_sf_legendre_Plm_array"
.Vb 1
\&  Signature: (double x(); double [o]y(num); int l=>num; int m)
.Ve
.PP
P_lm(x) for l from 0 to n\-2+m.
.PP
gsl_sf_legendre_Plm_array 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_legendre_sphPlm"
.IX Subsection "gsl_sf_legendre_sphPlm"
.Vb 1
\&  Signature: (double x(); double [o]y(); double [o]e(); int l; int m)
.Ve
.PP
P_lm(x), normalized properly for use in spherical harmonics
.PP
gsl_sf_legendre_sphPlm 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_legendre_sphPlm_array"
.IX Subsection "gsl_sf_legendre_sphPlm_array"
.Vb 1
\&  Signature: (double x(); double [o]y(num); int n=>num; int m)
.Ve
.PP
P_lm(x), normalized properly for use in spherical harmonics for l from 0 to n\-2+m.
.PP
gsl_sf_legendre_sphPlm_array 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_conicalP_half"
.IX Subsection "gsl_sf_conicalP_half"
.Vb 1
\&  Signature: (double x(); double [o]y(); double [o]e(); double lambda)
.Ve
.PP
Irregular Spherical Conical Function P^{1/2}_{\-1/2 + I lambda}(x)
.PP
gsl_sf_conicalP_half 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_conicalP_mhalf"
.IX Subsection "gsl_sf_conicalP_mhalf"
.Vb 1
\&  Signature: (double x(); double [o]y(); double [o]e(); double lambda)
.Ve
.PP
Regular Spherical Conical Function P^{\-1/2}_{\-1/2 + I lambda}(x)
.PP
gsl_sf_conicalP_mhalf 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_conicalP_0"
.IX Subsection "gsl_sf_conicalP_0"
.Vb 1
\&  Signature: (double x(); double [o]y(); double [o]e(); double lambda)
.Ve
.PP
Conical Function P^{0}_{\-1/2 + I lambda}(x)
.PP
gsl_sf_conicalP_0 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_conicalP_1"
.IX Subsection "gsl_sf_conicalP_1"
.Vb 1
\&  Signature: (double x(); double [o]y(); double [o]e(); double lambda)
.Ve
.PP
Conical Function P^{1}_{\-1/2 + I lambda}(x)
.PP
gsl_sf_conicalP_1 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_conicalP_sph_reg"
.IX Subsection "gsl_sf_conicalP_sph_reg"
.Vb 1
\&  Signature: (double x(); double [o]y(); double [o]e(); int l; double lambda)
.Ve
.PP
Regular Spherical Conical Function P^{\-1/2\-l}_{\-1/2 + I lambda}(x)
.PP
gsl_sf_conicalP_sph_reg 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_conicalP_cyl_reg_e"
.IX Subsection "gsl_sf_conicalP_cyl_reg_e"
.Vb 1
\&  Signature: (double x(); double [o]y(); double [o]e(); int m; double lambda)
.Ve
.PP
Regular Cylindrical Conical Function P^{\-m}_{\-1/2 + I lambda}(x)
.PP
gsl_sf_conicalP_cyl_reg_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_legendre_H3d"
.IX Subsection "gsl_sf_legendre_H3d"
.Vb 1
\&  Signature: (double [o]y(); double [o]e(); int l; double lambda; double eta)
.Ve
.PP
lth radial eigenfunction of the Laplacian on the 3\-dimensional hyperbolic space.
.PP
gsl_sf_legendre_H3d 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_legendre_H3d_array"
.IX Subsection "gsl_sf_legendre_H3d_array"
.Vb 1
\&  Signature: (double [o]y(num); int l=>num; double lambda; double eta)
.Ve
.PP
Array of H3d(ell), for l from 0 to n\-1.
.PP
gsl_sf_legendre_H3d_array 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>
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.