An improved error bound on Gauss quadrature

In this paper, the refined estimates on aliasing errors on integration of Chebyshev polynomials by Gauss quadrature are present, which, together with the asymptotic formulae on the coefficients of Chebyshev expansions, deduces an improved convergence rate for Gauss quadrature. The convergence orders are attainable for some functions of finite regularities.