HermiteH Method (n, x)

Computes the value of a (physicists') Hermite polynomial.

Declaration Syntax

Visual Basic

Visual C++

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 (Int32): The order, which must be non-negative.

x (Double): The argument.

Return Value

The value H_n(x).

Remarks

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

They appear in the solution of the one-dimensional, quantum mehanical, harmonic oscilator.

Statisticans' Hermite polynomials (see HermiteHe(Int32, Double)) are related to physicists' Hermite polynomials via H_n(x) = 2ⁿH_n(x √2). Staticians' 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.