Alaguerre Alaguerre_sub Alegendre Alegendre_sub Chebs Chebt Chebt_sub Chebtd Chebtd_sub Chebu Chebu_sub Gegenbauer Gegenbauer_sub Gegenbauerd Gegenbauerd1 Gegenbauerd1_sub Gegenbauerd_sub Hermite Hermite_sub Jacobi Jacobi_sub Jacobid Jacobid1 Jacobid1_sub Jacobid2 Jacobid2_sub Jacobid_sub Laguerre Laguerre_sub Legendre Legendre_sub Legendred Legendred_sub Sharmonic Sharmonici Sharmonici_sub Sharmonicr Sharmonicr_sub

Chebu() Function Chebu ( N As  Long, X As  Double, Optional Info As  Long  ) Chebyshev polynomial of second kind Un(x) Purpose Computes the Chebyshev polynomial of the second kind Un(x). Un-1(x) = sin(nt)/sin(t), where x = cos(t) This polynomial follows the recurrence formula: Un+1(x) = 2xUn(x) - Un-1(x), where U0(x) = 1, U1(x) = 2x (n > 0) Returns Double Chebyshev polynomial of second kind Un(x). Parameters [in] N Argument n. (N > 0) [in] X Argument x. [out] Info (Optional) = 0: Successful exit. = -1: The argument N had an illegal value. (N <= 0) = 1: Floating point range error. Reference boost/math/special_functions