OrthogonalPolynomialsHermiteH Method

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

Definition

Namespace: Meta.Numerics.Functions
Assembly: Meta.Numerics (in Meta.Numerics.dll) Version: 4.2.0+6d77d64445f7d5d91b12e331399c4362ecb25333
C#
public static double HermiteH(
	int n,
	double x
)

Parameters

n  Int32
The order, which must be non-negative.
x  Double
The argument.

Return Value

Double
The value Hn(x).

Remarks

The 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 Hn(x) = 2nHn(x √2). Statisticians' Hermite polynomials do not grow as quickly as physicists', and may therefore be preferable for large values of n and x, for which the return value of this method can overflow.

Exceptions

See Also