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

Jacobi_sub() Sub Jacobi_sub ( Ret As  Double, N As  Long, Alpha As  Double, Beta As  Double, X As  Double, Optional Info As  Long  ) Jacobi polynomial Pn(α, β)(x) (Subroutine version) Purpose Computes the Jacobi polynomial. The Jacobian polynomial Pn(α, β)(x) is an orthogonal polynomial defined on the interval [-1, 1] with a weight function w(x) = (1 - x)^α (1 + x)^β. The Jacobi polynomial satisfies the following three term recurrence relation. P0(α, β)(x) = 1 P1(α, β)(x) = (1/2)((α + β + 2)x + (α - β)) Pn(α, β)(x) = (1/(2n(n + α + β)(2n + α + β - 2)))((2n + α + β - 1)((2n + α + β - 2)(2n + α + β)x + (α^2 - β^2))P(n - 1)(α, β)(x) - 2(n + α - 1)(n + β - 1)(2n + α + β)P(n - 2)(α, β)(x)) Parameters [out] Ret Jacobi polynomial Pn(α, β)(x). [in] N Degree of polynomial n. (N >= 0) [in] Alpha Parameter α. [in] Beta Parameter β. [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