Special.HermiteHeSeries Method

Definition

Namespace: Numerics.NET
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 9.0.2

Overload List

HermiteHeSeries(Vector<Double>, Double) Evaluates a series of Chebyshev-Hermite polynomials.
HermiteHeSeries(Vector<Double>, Double, Int32) Evaluates a series of Chebyshev-Hermite polynomials up to the specified degree.

HermiteHeSeries(Vector<Double>, Double)

Evaluates a series of Chebyshev-Hermite polynomials.
C# 
public static double HermiteHeSeries(
	Vector<double> coefficients,
	double x
)

Parameters

coefficients  Vector<Double>
A vector containing the coefficients.
x  Double
The value for which to evaluate the series.

Return Value

Double
The sum of the Chebyshev-Hermite polynomials at x multiplied by the corresponding element of coefficients.

Remarks

Also called the "probabilist's" Hermite polynomials, the Chebyshev-Hermite polynomials are scaled Hermite polynomials with leading coefficient 1.

Exceptions

ArgumentNullException

coefficients is null.

HermiteHeSeries(Vector<Double>, Double, Int32)

Evaluates a series of Chebyshev-Hermite polynomials up to the specified degree.
C# 
public static double HermiteHeSeries(
	Vector<double> coefficients,
	double x,
	int maxDegree
)

Parameters

coefficients  Vector<Double>
A vector containing the coefficients.
x  Double
The value for which to evaluate the series.
maxDegree  Int32
The degree of the highest order polynomial to include in the series.

Return Value

Double
The sum of the Chebyshev-Hermite polynomials up to degree maxDegree evaluated at x and multiplied by the corresponding element of coefficients.

Remarks

If maxDegree is less than zero, then zero is returned.

Exceptions

ArgumentNullException

coefficients is null.

See Also