QuantLib_GaussianOrthogonalPolynomial man page

GaussianOrthogonalPolynomial — orthogonal polynomial for Gaussian quadratures  


#include <ql/math/integrals/gaussianorthogonalpolynomial.hpp>

Inherited by GaussHermitePolynomial, GaussHyperbolicPolynomial, GaussJacobiPolynomial, GaussLaguerrePolynomial, and GaussNonCentralChiSquaredPolynomial.

Public Member Functions

virtual Real mu_0 () const =0
virtual Real alpha (Size i) const =0
virtual Real beta (Size i) const =0
virtual Real w (Real x) const =0
Real value (Size i, Real x) const
Real weightedValue (Size i, Real x) const

Detailed Description

orthogonal polynomial for Gaussian quadratures

References: Gauss quadratures and orthogonal polynomials

G.H. Gloub and J.H. Welsch: Calculation of Gauss quadrature rule. Math. Comput. 23 (1986), 221-230

The polynomials are defined by the three-term recurrence relation [ P_{k+1}(x)=(x-alpha_k) P_k(x) - beta_k P_{k-1}(x) ] and [ mu_0 = int{w(x)dx} ]


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Referenced By

The man page weightedValue(3) is an alias of QuantLib_GaussianOrthogonalPolynomial(3).

Wed Feb 7 2018 Version 1.10.1 QuantLib