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

Namespace:  Meta.Numerics.Functions
Assembly:  Meta.Numerics (in Meta.Numerics.dll) Version: 3.1.0.0 (3.1.0.0)
Syntax
public static double HermiteH(
	int n,
	double x
)

Parameters

n
Type: SystemInt32
The order, which must be non-negative.
x
Type: SystemDouble
The argument.

Return Value

Type: Double
The value Hn(x).
Exceptions
ExceptionCondition
ArgumentOutOfRangeExceptionn is negative.
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 Hn(x) = 2nHn(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.

See Also