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

       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.

perl v5.34.0                                       2022-02-08                                      LEGENDRE(3pm)

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

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 ndarrays if
       the flag is set for any of the input ndarrays.

   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
       ndarrays if the flag is set for any of the input ndarrays.

   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 ndarrays if
       the flag is set for any of the input ndarrays.

   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 ndarrays
       if the flag is set for any of the input ndarrays.

   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 ndarrays if the
       flag is set for any of the input ndarrays.

   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
       ndarrays if the flag is set for any of the input ndarrays.

   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
       ndarrays if the flag is set for any of the input ndarrays.

   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  ndarrays
       if the flag is set for any of the input ndarrays.

   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 ndarrays
       if the flag is set for any of the input ndarrays.

   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 ndarrays if
       the flag is set for any of the input ndarrays.

   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 ndarrays  if
       the flag is set for any of the input ndarrays.

   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
       ndarrays if the flag is set for any of the input ndarrays.

   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
       ndarrays if the flag is set for any of the input ndarrays.

   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 ndarrays
       if the flag is set for any of the input ndarrays.

   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
       ndarrays if the flag is set for any of the input ndarrays.

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