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

Gegenbauer_sub() Sub Gegenbauer_sub ( Ret As  Double, N As  Long, Lambda As  Double, X As  Double, Optional Info As  Long  ) Gegenbauer polynomial Cn(λ)(x) (Subroutine version) Purpose Computes the Gegenbauer polynomial. The Gegenbauer polynomial Cn(λ)(x) is an orthogonal polynomial defined on the interval [-1, 1] with a weight function w(x) = (1 - x^2)^(λ - 1/2). It is the special case of the Jacobi polynomial with α = β = λ - 1/2. The Gegenbauern polynomial satisfies the following three term recurrence relation. C0(λ)(x) = 1 C1(λ)(x) = 2λx Cn(λ)(x) = (1/n)(2x(n + λ - 1)C(n - 1)(λ)(x) - (n + 2λ - 2)C(n - 2)(λ)(x)) Parameters [out] Ret Gegenbauer polynomial Cn(λ)(x). [in] N Degree of polynomial n. (N >= 0) [in] Lambda Parameter λ. [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