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Error bounds for Gaussian quadrature of analytic functions. (English) Zbl 0545.41040
The authors consider Gaussian quadrature rules for finite positive measures defined on compact real intervals. They are applied to analytic functions in certain domains that contain the interval in their interior. They develop error bounds from circular or elliptic contour integral representations. In particular, for a class of measures that contains the Jacobi measure, they determine where the kernel of the circular contour integral representation attains its maximum modulus. The authors also present some empirical results and numerical examples.
Reviewer: M.A.Jimenez

41A55 Approximate quadratures
41A21 Padé approximation
41A10 Approximation by polynomials
41A50 Best approximation, Chebyshev systems
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