Module rgsl::laguerre [−] [src]

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.

Functions

laguerre_1	This function evaluates the generalized Laguerre polynomials L^a_1(x), L^a_2(x), L^a_3(x) using explicit representations.
laguerre_1_e	This function evaluates the generalized Laguerre polynomials L^a_1(x), L^a_2(x), L^a_3(x) using explicit representations.
laguerre_2	This function evaluates the generalized Laguerre polynomials L^a_1(x), L^a_2(x), L^a_3(x) using explicit representations.
laguerre_2_e	This function evaluates the generalized Laguerre polynomials L^a_1(x), L^a_2(x), L^a_3(x) using explicit representations.
laguerre_3	This function evaluates the generalized Laguerre polynomials L^a_1(x), L^a_2(x), L^a_3(x) using explicit representations.
laguerre_3_e	This function evaluates the generalized Laguerre polynomials L^a_1(x), L^a_2(x), L^a_3(x) using explicit representations.
laguerre_n	the generalized Laguerre polynomials L^a_n(x) for a > -1, n >= 0.
laguerre_n_e	the generalized Laguerre polynomials L^a_n(x) for a > -1, n >= 0.