NAME

       PDL::GSLSF::LEGENDRE - PDL interface to GSL Special Functions

DESCRIPTION

       This is an interface to the Special Function package present in the GNU Scientific
       Library.

SYNOPSIS

FUNCTIONS

   gsl_sf_legendre_Pl
         Signature: (double x(); double [o]y(); double [o]e(); int l)

       P_l(x)

       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.

   gsl_sf_legendre_Pl_array
         Signature: (double x(); double [o]y(num); int l=>num)

       P_l(x) from 0 to n-1.

       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.

   gsl_sf_legendre_Ql
         Signature: (double x(); double [o]y(); double [o]e(); int l)

       Q_l(x)

       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.

   gsl_sf_legendre_Plm
         Signature: (double x(); double [o]y(); double [o]e(); int l; int m)

       P_lm(x)

       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.

   gsl_sf_legendre_array
         Signature: (double x(); double [o]y(n); double [t]work(wn); char norm;  int lmax; int csphase)

       Calculate all normalized associated Legendre polynomials.

       $Plm = gsl_sf_legendre_array($x,'P',4,-1);

       The calculation is done for degree 0 <= l <= lmax and order 0 <= m <= l on the range
       abs(x)<=1.

       The parameter norm should be:

       'P' for unnormalized associated Legendre polynomials P_l^m(x),
       'S' for Schmidt semi-normalized associated Legendre polynomials S_l^m(x),
       'Y' for spherical harmonic associated Legendre polynomials Y_l^m(x), or
       'N' for fully normalized associated Legendre polynomials N_l^m(x).

       lmax is the maximum degree l.  csphase should be (-1) to INCLUDE the Condon-Shortley phase
       factor (-1)^m, or (+1) to EXCLUDE it.

       See gsl_sf_legendre_array_index to get the value of "l" and "m" in the returned vector.

       gsl_sf_legendre_array processes bad values.  It will set the bad-value flag of all output
       piddles if the flag is set for any of the input piddles.

   gsl_sf_legendre_array_index
         Signature: (int [o]l(n); int [o]m(n); int lmax)

       Calculate the relation between gsl_sf_legendre_arrays index and l and m values.

       Note that this function is called differently than the corresponding GSL function, to make
       it more useful for PDL: here you just input the maximum l (lmax) that was used in
       "gsl_sf_legendre_array" and it calculates all l and m values.

       gsl_sf_legendre_array_index 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.

   gsl_sf_legendre_sphPlm
         Signature: (double x(); double [o]y(); double [o]e(); int l; int m)

       P_lm(x), normalized properly for use in spherical harmonics

       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.

   gsl_sf_conicalP_half
         Signature: (double x(); double [o]y(); double [o]e(); double lambda)

       Irregular Spherical Conical Function P^{1/2}_{-1/2 + I lambda}(x)

       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.

   gsl_sf_conicalP_mhalf
         Signature: (double x(); double [o]y(); double [o]e(); double lambda)

       Regular Spherical Conical Function P^{-1/2}_{-1/2 + I lambda}(x)

       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.

   gsl_sf_conicalP_0
         Signature: (double x(); double [o]y(); double [o]e(); double lambda)

       Conical Function P^{0}_{-1/2 + I lambda}(x)

       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.

   gsl_sf_conicalP_1
         Signature: (double x(); double [o]y(); double [o]e(); double lambda)

       Conical Function P^{1}_{-1/2 + I lambda}(x)

       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.

   gsl_sf_conicalP_sph_reg
         Signature: (double x(); double [o]y(); double [o]e(); int l; double lambda)

       Regular Spherical Conical Function P^{-1/2-l}_{-1/2 + I lambda}(x)

       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.

   gsl_sf_conicalP_cyl_reg_e
         Signature: (double x(); double [o]y(); double [o]e(); int m; double lambda)

       Regular Cylindrical Conical Function P^{-m}_{-1/2 + I lambda}(x)

       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.

   gsl_sf_legendre_H3d
         Signature: (double [o]y(); double [o]e(); int l; double lambda; double eta)

       lth radial eigenfunction of the Laplacian on the 3-dimensional hyperbolic space.

       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.

   gsl_sf_legendre_H3d_array
         Signature: (double [o]y(num); int l=>num; double lambda; double eta)

       Array of H3d(ell), for l from 0 to n-1.

       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.

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 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.