alaguerre alegendre chebs chebt chebtd chebu gegenbauer gegenbauerd gegenbauerd1 hermite jacobi jacobid jacobid1 jacobid2 laguerre legendre legendred sharmonic sharmonic_sub sharmonici sharmonicr

jacobi() double jacobi ( unsigned int  n, double  alpha, double  beta, double  x  ) Jacobi polynomial Pn(α, β)(x) Purpose This function 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)) Returns Jacobi polynomial Pn(α, β)(x). Parameters [in] n Degree of polynomial n. (n >= 0) [in] alpha Parameter α. [in] beta Parameter β. [in] x Argument x. Error handling Range error (ERANGE) may be reported. Reference boost/math/special_functions