LEGENDRE(3) User Contributed Perl Documentation LEGENDRE(3)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 FunctionsFUNCTIONS
gsl_sf_legendre_Pl
Signature: (double x(); double [o]y(); double [o]e(); int l)
P_l(x)
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_Ql
Signature: (double x(); double [o]y(); double [o]e(); int l)
Q_l(x)
gsl_sf_legendre_Plm
Signature: (double x(); double [o]y(); double [o]e(); int l; int m)
P_lm(x)
gsl_sf_legendre_Plm_array
Signature: (double x(); double [o]y(num); int l=>num; int m)
P_lm(x) for l from 0 to n-2+m.
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_array
Signature: (double x(); double [o]y(num); int n=>num; int m)
P_lm(x), normalized properly for use in spherical harmonics for l from 0 to n-2+m.
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_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_0
Signature: (double x(); double [o]y(); double [o]e(); double lambda)
Conical Function P^{0}_{-1/2 + I lambda}(x)
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_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_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_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_array
Signature: (double [o]y(num); int l=>num; double lambda; double eta)
Array of H3d(ell), for l from 0 to n-1.
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.
perl v5.8.0 2003-01-29 LEGENDRE(3)
Check Out this Related Man Page
GAMMA(3) User Contributed Perl Documentation GAMMA(3)NAME
PDL::GSLSF::GAMMA - PDL interface to GSL Special Functions
DESCRIPTION
This is an interface to the Special Function package present in the GNU Scientific Library.
SYNOPSIS FunctionsFUNCTIONS
gsl_sf_lngamma
Signature: (double x(); double [o]y(); double [o]s(); double [o]e())
Log[Gamma(x)], x not a negative integer Uses real Lanczos method. Determines the sign of Gamma[x] as well as Log[|Gamma[x]|] for x < 0. So
Gamma[x] = sgn * Exp[result_lg].
gsl_sf_gamma
Signature: (double x(); double [o]y(); double [o]e())
Gamma(x), x not a negative integer
gsl_sf_gammastar
Signature: (double x(); double [o]y(); double [o]e())
Regulated Gamma Function, x > 0 Gamma^*(x) = Gamma(x)/(Sqrt[2Pi] x^(x-1/2) exp(-x)) = (1 + 1/(12x) + ...), x->Inf
gsl_sf_gammainv
Signature: (double x(); double [o]y(); double [o]e())
1/Gamma(x)
gsl_sf_lngamma_complex
Signature: (double zr(); double zi(); double [o]x(); double [o]y(); double [o]xe(); double [o]ye())
Log[Gamma(z)] for z complex, z not a negative integer. Calculates: lnr = log|Gamma(z)|, arg = arg(Gamma(z)) in (-Pi, Pi]
gsl_sf_taylorcoeff
Signature: (double x(); double [o]y(); double [o]e(); int n)
x^n / n!
gsl_sf_fact
Signature: (x(); double [o]y(); double [o]e())
n!
gsl_sf_doublefact
Signature: (x(); double [o]y(); double [o]e())
n!! = n(n-2)(n-4)
gsl_sf_lnfact
Signature: (x(); double [o]y(); double [o]e())
ln n!
gsl_sf_lndoublefact
Signature: (x(); double [o]y(); double [o]e())
ln n!!
gsl_sf_lnchoose
Signature: (n(); m(); double [o]y(); double [o]e())
log(n choose m)
gsl_sf_choose
Signature: (n(); m(); double [o]y(); double [o]e())
n choose m
gsl_sf_lnpoch
Signature: (double x(); double [o]y(); double [o]s(); double [o]e(); double a)
Logarithm of Pochammer (Apell) symbol, with sign information. result = log( |(a)_x| ), sgn = sgn( (a)_x ) where (a)_x := Gamma[a +
x]/Gamma[a]
gsl_sf_poch
Signature: (double x(); double [o]y(); double [o]e(); double a)
Pochammer (Apell) symbol (a)_x := Gamma[a + x]/Gamma[x]
gsl_sf_pochrel
Signature: (double x(); double [o]y(); double [o]e(); double a)
Relative Pochammer (Apell) symbol ((a,x) - 1)/x where (a,x) = (a)_x := Gamma[a + x]/Gamma[a]
gsl_sf_gamma_inc_Q
Signature: (double x(); double [o]y(); double [o]e(); double a)
Normalized Incomplete Gamma Function Q(a,x) = 1/Gamma(a) Integral[ t^(a-1) e^(-t), {t,x,Infinity} ]
gsl_sf_gamma_inc_P
Signature: (double x(); double [o]y(); double [o]e(); double a)
Complementary Normalized Incomplete Gamma Function P(a,x) = 1/Gamma(a) Integral[ t^(a-1) e^(-t), {t,0,x} ]
gsl_sf_lnbeta
Signature: (double a(); double b(); double [o]y(); double [o]e())
Logarithm of Beta Function Log[B(a,b)]
gsl_sf_beta
Signature: (double a(); double b();double [o]y(); double [o]e())
Beta Function B(a,b)
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.
perl v5.8.0 2003-01-29 GAMMA(3)