Some error expansions for Gaussian quadrature

Complex-variable methods are used to obtain some expansions in the error in Gaussian quadrature formulae over the interval – 1, 1]. Much of the work is based on an approach due to Stenger, and both circular and elliptical contours are used. Stenger's theorem on monotonicity of convergence of Gaussian quadrature formulae is generalized, and a number of error bounds are obtained.