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Evaluation of an integral arising in numerical integration near a logarithmic singularity


Author: Yudell L. Luke
Journal: Math. Comp. 10 (1956), 14-21
MSC: Primary 65.0X
DOI: https://doi.org/10.1090/S0025-5718-1956-0077219-7
MathSciNet review: 0077219
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  • [2] ``Tables of Lagrangian interpolation coefficients,'' National Bureau of Standards, Columbia University Press, 1948.
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  • [4] W. E. Milne, Numerical Calculus, Princeton University Press, p. 108-116.
  • [5] W. Barrett, ``On the remainders of numerical formulae, with special reference to differentiation formulae,'' London Math. Soc., Jn., v. 27, Part 4, 1952, p. 456-464. See also, ``On the remainder term in numerical integration formulae,'' same author and journal, p. 465-470. MR 0050991 (14:412j)
  • [6] E. L. Kaplan, ``Numerical integration near a singularity,'' J. Math. Phys., v. 26, 1952, p. 1-28. MR 0046747 (13:782f)
  • [7] R. E. Beard, ``Some notes on approximate product integration,'' Inst. of Actuaries, Jn., v. 73, 1948, p. 356-414. MR 0025281 (9:623k)
  • [8] J. W. Sheldon, ``Numerical evaluation of integrals of the form $ \int_\infty ^\beta {f(x)g(x)dx} $,'' International Business Machines Corporation Seminar, New York, 1950, p. 74-78. MR 0048910 (14:91g)
  • [9] Y. L. Luke, ``Mechanical quadrature near a singularity,'' MTAC, v. 6, 1952, p. 215-219. MR 0050993 (14:413a)
  • [10] Y. L. Luke, ``On the computation of oscillatory integrals,'' Cambridge Philos. Soc., Proc., v. 50, 1954, p. 269-277. MR 0062518 (15:992b)

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DOI: https://doi.org/10.1090/S0025-5718-1956-0077219-7
Article copyright: © Copyright 1956 American Mathematical Society

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