Class GaussLaguerreCosinePolynomial

Namespace

NanoQL.Numerics

Assembly

NanoQL.dll

The Gauss-Laguerre cosine polynomial: orthogonal under the weight w(x; u) = e^(−x)·(1 + cos(ux))/m₀ on [0, ∞), m₀ = 1 + 1/(1 + u²) normalising it, for the Gaussian quadrature of ∫₀^∞ f(x) dx.

public sealed class GaussLaguerreCosinePolynomial : GaussLaguerreTrigonometricBase

Inheritance

object

GaussianOrthogonalPolynomial

MomentBasedGaussianPolynomial

GaussLaguerreTrigonometricBase

GaussLaguerreCosinePolynomial

Inherited Members

MomentBasedGaussianPolynomial.Mu_0()

MomentBasedGaussianPolynomial.Alpha(int)

MomentBasedGaussianPolynomial.Beta(int)

GaussianOrthogonalPolynomial.LogW(double)

GaussianOrthogonalPolynomial.Value(int, double)

GaussianOrthogonalPolynomial.WeightedValue(int, double)

object.GetType()

object.ToString()

object.Equals(object)

object.Equals(object, object)

object.ReferenceEquals(object, object)

object.GetHashCode()

Constructors

GaussLaguerreCosinePolynomial(double)

Initializes a new instance of the GaussLaguerreCosinePolynomial class.

public GaussLaguerreCosinePolynomial(double u)

Parameters

u double

The frequency u.

Methods

M0()

The zeroth moment of the trigonometric weight, the recurrence's start.

protected override double M0()

Returns

double

The moment.

M1()

The first moment of the trigonometric weight, the recurrence's second start.

protected override double M1()

Returns

double

The moment.

Moment(int)

The i-th moment of the distribution, its zeroth 1.

public override double Moment(int i)

Parameters

i int

The moment's order, non-negative.

Returns

double

The moment.

W(double)

The weight function w(x).

public override double W(double x)

Parameters

x double

The point.

Returns

double

w(x).