Asymptotic expansion of error in interpolatory quadrature

AbstractThe classical bounds on the truncation error of quadrature formulas obtained by Peano's Theorem are revisited, by assuming slightly stronger regularity conditions on the integrand function. The resulting series expansion of the error can be useful when studying the asymptotic complexity of automatic quadrature algorithms. New constants, related to the classical error coefficients are tabulated for the most common symmetric interpolatory rules