# Laguerre Functions¶

The generalized Laguerre polynomials are defined in terms of confluent hypergeometric functions as $$L^a_n(x) = ((a+1)_n / n!) {}_1F_1(-n,a+1,x)$$, 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.

gsl_sf_laguerre_1(a, x)
gsl_sf_laguerre_2(a, x)
gsl_sf_laguerre_3(a, x)

These routines evaluate the generalized Laguerre polynomials $$L^a_1(x), L^a_2(x), L^a_3(x)$$ using explicit representations.

gsl_sf_laguerre_n(n, a, x)

This routine evaluates the generalized Laguerre polynomials $$L^a_n(x)$$ for $$a > -1, n >= 0$$.