# alpha (3) - Linux Manuals

## alpha: orthogonal polynomial for Gaussian quadratures

## 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.