Laguerre Functions

The Laguerre polynomials are defined in terms of confluent hypergeometric functions as @math{L^a_n(x) = ((a+1)_n / n!) 1F1(-n,a+1,x)}. These functions 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 @math{L^a_1(x)}, @math{L^a_2(x)}, @math{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)

Thse routines evaluate the generalized Laguerre polynomials @math{L^a_n(x)} for @math{a > -1}, @math{n >= 0}.