7.22 Laguerre Functions
The generalized Laguerre polynomials are defined in terms of confluent
hypergeometric functions as
L^a_n(x) = ((a+1)_n / n!) 1F1(-n,a+1,x), and are sometimes referred to as the
associated Laguerre polynomials. They are related to the plain
Laguerre polynomials L_n(x) by L^0_n(x) = L_n(x) and
L^k_n(x) = (-1)^k (d^k/dx^k) L_(n+k)(x). For
more information see Abramowitz & Stegun, Chapter 22.
The functions described in this section are
declared in the header file gsl_sf_laguerre.h.
— Function: double
gsl_sf_laguerre_1 (
double a, double x)
— Function: double
gsl_sf_laguerre_2 (
double a, double x)
— Function: double
gsl_sf_laguerre_3 (
double a, double x)
— Function: int
gsl_sf_laguerre_1_e (
double a, double x, gsl_sf_result * result)
— Function: int
gsl_sf_laguerre_2_e (
double a, double x, gsl_sf_result * result)
— Function: int
gsl_sf_laguerre_3_e (
double a, double x, gsl_sf_result * result)
These routines evaluate the generalized Laguerre polynomials
L^a_1(x), L^a_2(x), L^a_3(x) using explicit
representations.
— Function: double
gsl_sf_laguerre_n (
const int n, const double a, const double x)
— Function: int
gsl_sf_laguerre_n_e (
int n, double a, double x, gsl_sf_result * result)
These routines evaluate the generalized Laguerre polynomials
L^a_n(x) for a > -1,
n >= 0.