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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

On the remainder in quadrature rules


Author: P. D. Tuan
Journal: Math. Comp. 25 (1971), 819-826
MSC: Primary 65D30
MathSciNet review: 0298949
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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 [Enhancements On Off] (What's this?)

  • [1] Gabor Szegö, Orthogonal polynomials, American Mathematical Society Colloquium Publications, Vol. 23. Revised ed, American Mathematical Society, Providence, R.I., 1959. MR 0106295 (21 #5029)
  • [2] W. Barrett, Convergence properties of Gaussian quadrature formulae, Comput. J. 3 (1960/1961), 272–277. MR 0128073 (23 #B1117)
  • [3] W. Barrett, On the convergence of Cotes’ quadrature formulae, J. London Math. Soc. 39 (1964), 296–302. MR 0185812 (32 #3272)
  • [4] 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.
  • [5] J. S. Donaldson & D. Elliott, Quadrature II: The Estimation of Remainders in Certain Quadrature Rules, Math. Dept. Technical Report #24, University of Tasmania, 1970.
  • [6] E. C. Titchmarsh, Introduction to the Theory of Fourier Integrals, Clarendon Press, Oxford, 1937.
  • [7] F. G. Tricomi, Integral equations, Pure and Applied Mathematics. Vol. V, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1957. MR 0094665 (20 #1177)
  • [8] D. Elliott, Uniform Asymptotic Expansions of the Classical Orthogonal Polynomials and some Associated Functions, Math. Dept. Technical Report #21, University of Tasmania, 1970.
  • [9] L. J. Slater, Confluent hypergeometric functions, Cambridge University Press, New York, 1960. MR 0107026 (21 #5753)
  • [10] A. Erdélyi, et al., Tables of Integral Transforms, vol. 2, McGraw-Hill, New York, 1954. MR 16, 468.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1971-0298949-6
PII: S 0025-5718(1971)0298949-6
Keywords: Remainder, quadrature rules, Hilbert transform, Cauchy principal value, contour integral
Article copyright: © Copyright 1971 American Mathematical Society