Abstract
Explicit bounds for the quadrature error of thenth Gauss-Legendre quadrature rule applied to themth Chebyshev polynomial are derived. They are precise up to the orderO(m 4 n −6). As an application, error constants for classes of functions which are analytic in the interior of an ellipse are estimated. The location of the maxima of the corresponding kernel function is investigated.
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Dedicated to Luigi Gatteschi on the occasion of his 70th birthday
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Petras, K. Gaussian integration of Chebyshev polynomials and analytic functions. Numer Algor 10, 187–202 (1995). https://doi.org/10.1007/BF02198303
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DOI: https://doi.org/10.1007/BF02198303