WAlaguerre WAlegendre WChebt WChebtd WChebu WGegenbauer WGegenbauerd WGegenbauerd1 WHermite WJacobi WJacobid WJacobid1 WJacobid2 WLaguerre WLegendre WLegendred WSharmonic WSharmonici WSharmonicr

WGegenbauer() Function WGegenbauer ( N As  Long, Lambda As  Double, X As  Double  ) Gegenbauer polynomial Cn(λ)(x) Purpose This function 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)) Returns Gegenbauer polynomial Cn(λ)(x). Parameters [in] N Degree of polynomial n. (N >= 0) [in] Lambda Parameter λ. [in] X Argument x. Reference boost/math/special_functions