NAME

QuantLib::GaussianOrthogonalPolynomial - orthogonal polynomial for Gaussian quadratures

SYNOPSIS


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

Inherited by GaussHermitePolynomial, GaussHyperbolicPolynomial, GaussJacobiPolynomial, and GaussLaguerrePolynomial.

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-lpha_k) P_k(x) - nerated automatically by Doxygen for QuantLib from the source code.