OrthogonalPolynomialsHermiteHe Method

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

Definition

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

Parameters

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

Return Value

Double
The value Hen(x).

Remarks

The (statisticians') Hermite polynomials are orthogonal on the interval (-∞,+∞) with a weight function equal to the standard normal probability distribution.

Their ortho-normality relation makes them a useful basis for expressing perturbations around a normal distribution.

Physicists' Hermite polynomials (HermiteH(Int32, Double)) are related to statisticians' Hermite polynomials via Hn(x) = 2nHn(x √2).

Exceptions

See Also