OrthogonalPolynomialsGegenbauerC Method

public static double GegenbauerC(
	int n,
	double alpha,
	double x
)

Public Shared Function GegenbauerC ( 
	n As Integer,
	alpha As Double,
	x As Double
) As Double

public:
static double GegenbauerC(
	int n, 
	double alpha, 
	double x
)

static member GegenbauerC : 
        n : int * 
        alpha : float * 
        x : float -> float 

Parameters

n  Int32

The order, which must be non-negative.

alpha  Double

The weight parameter, which must be non-negative.

x  Double

The argument, which must lie in the closed interval [-1,+1].

Return Value

The Gegenbauer polynomials, also called the ultraspherical polynomials, are orthogonal on the interval [-1,+1] with the weight (1 - x^2)^(alpha - 1/2).

The Legendre (LegendreP(Int32, Double)) and Chebyshev (ChebyshevT(Int32, Double) polynomials are thus special cases of the Gegenbauer polynomials.

Reference

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