Convergence properties of a quadrature formula of ClenshawCurtis type for the Gegenbauer weight function
A quadrature formula of ClenshawCurtis type for functions of the form \((1-x^2)^{\lambda - \frac{1}{2}}f(x)\) over the interval [\(-\)1,1] exhibits a curious phenomenon when applied to certain analytic functions. As the number of points in the quadrature rule increases the error may sometimes decay to zero in two distinct stages rather than in one depending on the value of \(\lambda \). In this paper we shall derive explicit and asymptotic error formulae which describe this phenomenon.
gegenbauer weight function clenshawcurtis quadrature convergence rate lobatto-chebyshev quadrature 65d32