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QuantLib_GaussianOrthogonalPolynomial
Langue: en
Version: 380916 (fedora - 01/12/10)
Section: 3 (Bibliothèques de fonctions)
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.
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