Class GaussJacobiPolynomial

Namespace

NanoQL.Numerics

Assembly

NanoQL.dll

The Gauss-Jacobi polynomial, with weight w(x; α, β) = (1 − x)^α·(1 + x)^β on [−1, 1], α, β > −1. Unsealed: QuantLib's Legendre, Chebyshev and Gegenbauer polynomials derive from it.

public class GaussJacobiPolynomial : GaussianOrthogonalPolynomial

Inheritance

object

GaussianOrthogonalPolynomial

GaussJacobiPolynomial

Derived

GaussChebyshev2ndPolynomial

GaussChebyshevPolynomial

GaussGegenbauerPolynomial

GaussLegendrePolynomial

Inherited Members

GaussianOrthogonalPolynomial.LogW(double)

GaussianOrthogonalPolynomial.Value(int, double)

GaussianOrthogonalPolynomial.WeightedValue(int, double)

object.GetType()

object.MemberwiseClone()

object.ToString()

object.Equals(object)

object.Equals(object, object)

object.ReferenceEquals(object, object)

object.GetHashCode()

Constructors

GaussJacobiPolynomial(double, double)

Initializes a new instance of the GaussJacobiPolynomial class.

public GaussJacobiPolynomial(double alpha, double beta)

Parameters

alpha double

The power of 1 − x, above −1.

beta double

The power of 1 + x, above −1.

Exceptions

ArgumentException

A power isn't above −1, or their sum isn't above −2.

Methods

Alpha(int)

The recurrence's α_i.

public override double Alpha(int i)

Parameters

i int

The index, non-negative.

Returns

double

α_i.

Exceptions

ArgumentOutOfRangeException

i is negative.

NanoQLException

α_i's denominator is zero and its numerator isn't.

Beta(int)

The recurrence's β_i.

public override double Beta(int i)

Parameters

i int

The index, non-negative.

Returns

double

β_i.

Exceptions

ArgumentOutOfRangeException

i is negative.

NanoQLException

β_i's denominator is zero and its numerator isn't.

Mu_0()

μ₀, the integral of the weight function.

public override double Mu_0()

Returns

double

μ₀.

W(double)

The weight function w(x).

public override double W(double x)

Parameters

x double

The point.

Returns

double

w(x).