Abstract
We determine (Theorem 3) the smallest closed region, containing the interva of integration, such that the analyticity of the integrand in this closed region implies the convergence of the Newton-Cotes quadratures. By considering, in particular, certain ellipses as regions of analyticity, we obtain (Theorem 4) an improvement of Davis' result on the convergence of Newton-Cotes quadratures for analytic functions.
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P. Davis,On a problem in the theory of mechanical qudratures, Pacific J. Math., 5 (1955), 669–674.
L. W. Johnson and R. D. Riess,A note on a theorem of Davis, Math. Z., 110 (1969), 211–212.
J. F. Steffensen,Interpolation, Chelsea Publishing Co., New York, (Second Edition), 1950.
J. L. Walsh,Interpolation and Approximation by Rational Functions in the Complex Domain, Amer. Math. Soc. Colloquium Publications, Vol. XX, Providence, Rhode Island, (Fifth Edition), 1969.
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Chawla, M.M. Convergence of Newton-Cotes quadratures for analytic functions. BIT 11, 159–167 (1971). https://doi.org/10.1007/BF01934363
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DOI: https://doi.org/10.1007/BF01934363