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Integration formulae involving derivatives


Author: T. N. L. Patterson
Journal: Math. Comp. 23 (1969), 411-412
MSC: Primary 65.55
DOI: https://doi.org/10.1090/S0025-5718-1969-0242371-6
Corrigendum: Math. Comp. 24 (1970), 243.
MathSciNet review: 0242371
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Abstract: A method, developed by Hammer and Wicke, for deriving high precision integration formulae involving derivatives is modified. It is shown how such formulae may be simply derived in terms of well-known polynomials.


References [Enhancements On Off] (What's this?)

  • [1] A. H. Stroud & D. D. Stancu, ``Quadrature formulas with multiple Gaussian modes,'' J. Soc. Indust. Appl. Math., Ser. B, Numer. Anal., v. 2, 1965, pp. 129-143. MR 31 #4177. MR 0179940 (31:4177)
  • [2] P. C. Hammer & H. H. Wicke, ``Quadrature formulas involving derivatives of the integrand,'' Math. Comp., v. 14, 1960, pp. 3-7. MR 22 #1073. MR 0110191 (22:1073)
  • [3] G. W. Struble, ``Tables for use in quadrature formulas involving derivatives of the integrand,'' Math. Comp., v. 14, 1960, pp. 8-12. MR 22 #1074. MR 0110192 (22:1074)
  • [4] V. I. Krylov, Approximate Calculation of Integrals, Fizmatgiz, Moscow, 1959; English transl., Macmillan, New York, 1962. MR 22 #2002; MR 26 #2008. MR 0144464 (26:2008)
  • [5] A. H. Stroud & D. Secrest, Gaussian Quadrature Formulas, Prentice-Hall, Englewood Cliffs, N. J., 1966, 374 pp. MR 34 #2185. MR 0202312 (34:2185)

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DOI: https://doi.org/10.1090/S0025-5718-1969-0242371-6
Article copyright: © Copyright 1969 American Mathematical Society

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