OrthogonalPolynomialsChebyshevU Method

public static double ChebyshevU(
	int n,
	double x
)

Public Shared Function ChebyshevU ( 
	n As Integer,
	x As Double
) As Double

public:
static double ChebyshevU(
	int n, 
	double x
)

static member ChebyshevU : 
        n : int * 
        x : float -> float 

Parameters

n  Int32

The order, which must be non-negative.

x  Double

The argument, which must lie in the closed interval between -1 and +1.

Return Value

Chebyshev polynomials of the second kind are orthogonal on the interval [-1,1] with the weight (1-x²)^1/2.

Values returned are fully accurate (14-16 decimal digits) over the full range of argument for orders up to thousands. For orders up to a million, ~11 decimal digits remain accurate.

Reference

Other Resources