Module orthogonal 

Classical orthogonal polynomials by their three-term recurrences. Each evaluates P_n(x) in O(n) with no allocation.

Functions

chebyshev_t

Chebyshev polynomial of the first kind T_n(x). T_{n+1} = 2x T_n − T_{n-1}.

chebyshev_u

Chebyshev polynomial of the second kind U_n(x). U_0 = 1, U_1 = 2x, U_{n+1} = 2x U_n − U_{n-1}.

hermite

Physicists’ Hermite polynomial H_n(x). H_0 = 1, H_1 = 2x, H_{n+1} = 2x H_n − 2n H_{n-1}.

laguerre

Laguerre polynomial L_n(x). L_0 = 1, L_1 = 1 − x, (n+1)L_{n+1} = (2n+1−x)L_n − n L_{n-1}.

legendre

Legendre polynomial P_n(x). (n+1)P_{n+1} = (2n+1)x P_n − n P_{n-1}.