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Some error expansions for Gaussian quadrature. (English) Zbl 0824.41032
Summary: 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.

##### MSC:
 41A55 Approximate quadratures 41A80 Remainders in approximation formulas