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:

'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).

'P' (or any other) for unnormalized associated Legendre polynomials P_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.