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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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On the remainder in quadrature rules
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by P. D. Tuan PDF
Math. Comp. 25 (1971), 819-826 Request permission

Abstract:

An expression is obtained for the remainder in quadrature rules applied to functions whose Hubert transforms exist. The estimation of the remainder is illustrated by means of a particular example.
References
  • Gabor Szegö, Orthogonal polynomials, American Mathematical Society Colloquium Publications, Vol. 23, American Mathematical Society, Providence, R.I., 1959. Revised ed. MR 0106295
  • W. Barrett, Convergence properties of Gaussian quadrature formulae, Comput. J. 3 (1960/61), 272–277. MR 128073, DOI 10.1093/comjnl/3.4.272
  • W. Barrett, On the convergence of Cotes’ quadrature formulae, J. London Math. Soc. 39 (1964), 296–302. MR 185812, DOI 10.1112/jlms/s1-39.1.296
  • I. D. Donaldson & D. Elliott, Quadrature I: A Unified Approach to the Development of Quadrature Rules, Math. Dept. Technical Report #23, University of Tasmania, 1970. J. S. Donaldson & D. Elliott, Quadrature II: The Estimation of Remainders in Certain Quadrature Rules, Math. Dept. Technical Report #24, University of Tasmania, 1970. E. C. Titchmarsh, Introduction to the Theory of Fourier Integrals, Clarendon Press, Oxford, 1937.
  • F. G. Tricomi, Integral equations, Pure and Applied Mathematics, Vol. V, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1957. MR 0094665
  • D. Elliott, Uniform Asymptotic Expansions of the Classical Orthogonal Polynomials and some Associated Functions, Math. Dept. Technical Report #21, University of Tasmania, 1970.
  • L. J. Slater, Confluent hypergeometric functions, Cambridge University Press, New York, 1960. MR 0107026
  • A. Erdélyi, et al., Tables of Integral Transforms, vol. 2, McGraw-Hill, New York, 1954. MR 16, 468.
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Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Math. Comp. 25 (1971), 819-826
  • MSC: Primary 65D30
  • DOI: https://doi.org/10.1090/S0025-5718-1971-0298949-6
  • MathSciNet review: 0298949