## File: Laguerre-Functions.html

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 `123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112` `````` GNU Scientific Library – Reference Manual: Laguerre Functions

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.

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