Special.LaguerreLSequence Method

Definition

Namespace: Numerics.NET
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 9.0.3

Overload List

LaguerreLSequence(Double, Span<Double>) Evaluates a sequence of Laguerre polynomials of increasing degree and returns the result in the specified span.
LaguerreLSequence(Double, Double, Span<Double>) Evaluates a sequence of generalized Laguerre polynomials of increasing degree and returns the result in the specified vector.
LaguerreLSequence(Int32, Double, Vector<Double>) Evaluates a sequence of Laguerre polynomials of increasing degree and returns the result in the specified vector.
LaguerreLSequence(Int32, Double, Span<Double>) Evaluates a sequence of Laguerre polynomials of increasing degree starting at the specified degree and returns the result in the specified span.
LaguerreLSequence(Int32, Double, Double, Vector<Double>) Evaluates a sequence of generalized Laguerre polynomials of increasing degree and returns the result in the specified vector.
LaguerreLSequence(Int32, Double, Double, Span<Double>) Evaluates a sequence of generalized Laguerre polynomials of increasing degree starting at the specified degree and returns the result in the specified vector.
LaguerreLSequence(Int32, Int32, Double, Vector<Double>) Evaluates a sequence of Laguerre polynomials of increasing degree starting at the specified degree and returns the result in the specified vector.
LaguerreLSequence(Int32, Int32, Double, Double, Vector<Double>) Evaluates a sequence of generalized Laguerre polynomials of increasing degree starting at the specified degree and returns the result in the specified vector.

LaguerreLSequence(Double, Span<Double>)

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

Parameters

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

LaguerreLSequence(Double, Double, Span<Double>)

Evaluates a sequence of generalized Laguerre polynomials of increasing degree and returns the result in the specified vector.
C#
public static void LaguerreLSequence(
	double alpha,
	double x,
	Span<double> result
)

Parameters

alpha  Double
The parameter of the generalized Laguerre polynomials.
x  Double
A real number.
result  Span<Double>
The span that is to hold the result.

LaguerreLSequence(Int32, Double, Vector<Double>)

Evaluates a sequence of Laguerre polynomials of increasing degree and returns the result in the specified vector.
C#
public static Vector<double> LaguerreLSequence(
	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 Laguerre polynomial of increasing orders starting from zero evaluated at x.

Exceptions

ArgumentOutOfRangeException

length is less than zero.

LaguerreLSequence(Int32, Double, Span<Double>)

Evaluates a sequence of Laguerre polynomials of increasing degree starting at the specified degree and returns the result in the specified span.
C#
public static void LaguerreLSequence(
	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.

Exceptions

ArgumentOutOfRangeException

startDegree is less than zero.

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

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

Parameters

length  Int32
The length of the sequence.
alpha  Double
The parameter of the generalized Laguerre polynomials.
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 generalized Laguerre polynomial with parameter alpha and of increasing orders starting from zero evaluated at x.

Exceptions

ArgumentOutOfRangeException

length is less than zero.

LaguerreLSequence(Int32, Double, Double, Span<Double>)

Evaluates a sequence of generalized Laguerre polynomials of increasing degree starting at the specified degree and returns the result in the specified vector.
C#
public static void LaguerreLSequence(
	int startDegree,
	double alpha,
	double x,
	Span<double> result
)

Parameters

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

Exceptions

ArgumentOutOfRangeException

startDegree is less than zero.

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

Evaluates a sequence of Laguerre polynomials of increasing degree starting at the specified degree and returns the result in the specified vector.
C#
public static Vector<double> LaguerreLSequence(
	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 Laguerre polynomial of increasing orders starting from startDegree evaluated at x.

Exceptions

ArgumentOutOfRangeException

startDegree is less than zero.

-or-

length is less than zero.

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

Evaluates a sequence of generalized Laguerre polynomials of increasing degree starting at the specified degree and returns the result in the specified vector.
C#
public static Vector<double> LaguerreLSequence(
	int startDegree,
	int length,
	double alpha,
	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.
alpha  Double
The parameter of the generalized Laguerre polynomials.
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 generalized Laguerre polynomial with parameter alpha and of increasing orders starting from startDegree evaluated at x.

Exceptions

ArgumentOutOfRangeException

startDegree is less than zero.

-or-

length is less than zero.

See Also