OrthogonalPolynomialsHermiteH Method

public static double HermiteH(
	int n,
	double x
)

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

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

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

Parameters

n

Type: SystemInt32
The order, which must be non-negative.

x

Type: SystemDouble
The argument.

Return Value

Hermite polynomials are orthogonal on the interval (-∞,+∞) with the weight e^-x2.

They appear in the solution of the one-dimensional, quantum mechanical, harmonic oscillator.

Statisticans' Hermite polynomials (see HermiteHe(Int32, Double)) are related to physicists' Hermite polynomials via H_n(x) = 2ⁿH_n(x √2). Statisticians' Hermite polynomials do not grow as quickly as physicists', and may therefore be preferable for large values of n and x which could overflow Double.

Reference

Other Resources