The numerical evaluation of the error term in a quadrature formula of Clenshaw-Curtis type for the Gegenbauer weight function

Abstract

A method is derived for the numerical evaluation of the error term arising in a quadrature formula of Clenshaw-Curtis type for functions of the form \((1-x^{2})^{\lambda - \frac{1}{2}}f(x)\) over the interval [−1,1]. The method is illustrated by an example.