Special.HermiteHeSequence Method

Definition

Namespace: Numerics.NET
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 9.0.4

Overload List

HermiteHeSequence(Double, Span<Double>) Evaluates a sequence of Chebyshev-Hermite polynomials of increasing degree and returns the result in the specified span.
HermiteHeSequence(Int32, Double, Vector<Double>) Evaluates a sequence of Chebyshev-Hermite polynomials of increasing degree and returns the result in the specified vector.
HermiteHeSequence(Int32, Double, Span<Double>) Evaluates a sequence of Chebyshev-Hermite polynomials of increasing degree starting at the specified degree and returns the result in the specified span.
HermiteHeSequence(Int32, Int32, Double, Vector<Double>) Evaluates a sequence of Chebyshev-Hermite polynomials of increasing degree starting at the specified degree and returns the result in the specified vector.

HermiteHeSequence(Double, Span<Double>)

Evaluates a sequence of Chebyshev-Hermite polynomials of increasing degree and returns the result in the specified span.
C# 
public static void HermiteHeSequence(
	double x,
	Span<double> result
)

Parameters

x  Double
A real number.
result  Span<Double>
The span that is to hold the result.

Remarks

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

HermiteHeSequence(Int32, Double, Vector<Double>)

Evaluates a sequence of Chebyshev-Hermite polynomials of increasing degree and returns the result in the specified vector.
C# 
public static Vector<double> HermiteHeSequence(
	int length,
	double x,
	Vector<double>? result = null
)

Parameters

length  Int32
The length of the sequence.
x  Double
A real number.
result  Vector<Double>  (Optional)
Optional. The vector that is to hold the result. May be null.

Return Value

Vector<Double>
The vector result, which contains length values of the Chebyshev-Hermite polynomial of increasing orders starting from zero evaluated at x.

Remarks

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

Exceptions

ArgumentOutOfRangeException

length is less than zero.

DimensionMismatchException

The length of result is not long enough to store the results.

HermiteHeSequence(Int32, Double, Span<Double>)

Evaluates a sequence of Chebyshev-Hermite polynomials of increasing degree starting at the specified degree and returns the result in the specified span.
C# 
public static void HermiteHeSequence(
	int startDegree,
	double x,
	Span<double> result
)

Parameters

startDegree  Int32
An integer that specifies the first degree in the sequence.
x  Double
A real number.
result  Span<Double>
The span that is to hold the result.

Remarks

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

Exceptions

ArgumentOutOfRangeException

startDegree is less than zero.

HermiteHeSequence(Int32, Int32, Double, Vector<Double>)

Evaluates a sequence of Chebyshev-Hermite polynomials of increasing degree starting at the specified degree and returns the result in the specified vector.
C# 
public static Vector<double> HermiteHeSequence(
	int startDegree,
	int length,
	double x,
	Vector<double>? result = null
)

Parameters

startDegree  Int32
An integer that specifies the first degree in the sequence.
length  Int32
The length of the sequence.
x  Double
A real number.
result  Vector<Double>  (Optional)
Optional. The vector that is to hold the result. May be null.

Return Value

Vector<Double>
The vector result, which contains length values of the Chebyshev-Hermite polynomial of increasing orders starting from startDegree evaluated at x.

Remarks

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

Exceptions

ArgumentOutOfRangeException

startDegree is less than zero.

-or-

length is less than zero.

DimensionMismatchException

The length of result is not long enough to store the results.

See Also