A Gauss quadrature rule for hypersingular integrals

Abstract

We construct a set of polynomials phi(n)(x, t) which are orthogonal with respect to v(x, t) = w(x)/(x - t)(P), t is an element of (a, b), where w(x) is a weight function and p is an integer. As an application these polynomials can be used to extract Gaussian quadrature rules for hypersingular integrals. (c) 2006 Elsevier Inc. All rights reserved.