On the convergence rate of Clenshaw-Curtis quadrature for integrals with algebraic endpoint singularities

In this paper, we are concerned with Clenshaw-Curtis quadrature for integrals with algebraic endpoint singularities. An asymptotic error expansion and convergence rate are derived by combining a delicate analysis of the Chebyshev coefficients of functions with algebraic endpoint singularities and the aliasing formula of Chebyshev polynomials. Numerical examples are provided to confirm our analysis.