  In this paper, we investigate the rate of convergence of Clenshaw-Curtis
quadrature and its acceleration for functions with endpoint singularities in
X^s, where X^s denotes the space of functions whose Chebyshev coefficients
decay asymptotically as a_k = O(k^{-s-1}) for some positive s. For such
unctions, we show that the convergence rate of (n + 1)-point Clenshaw-Curtis
quadrature is O(n^{-s-2}). Furthermore, an asymptotic error expansion for
Clenshaw-Curtis quadrature is presented which enables us to employ some
extrapolation techniques to accelerate its convergence. Numerical examples are
provided to confirm our analysis.
