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Evaluation of $ I\sb{n}(b)=2\pi \sp{-1}\int \sb{0}{}\sp \infty \,({\rm sin}x/x)\sp{n}{\rm cos}(bx)\, dx$ and of similar integrals


Author: Rory Thompson
Journal: Math. Comp. 20 (1966), 330-332
MSC: Primary 65.05; Secondary 65.55
Corrigendum: Math. Comp. 23 (1969), 219.
Corrigendum: Math. Comp. 23 (1969), 219.
Corrigendum: Math. Comp. 21 (1967), 130.
MathSciNet review: 0192634
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References [Enhancements On Off] (What's this?)

  • [1] R. G. Medhurst & J. H. Roberts, "Evaluation of the integral $ {I_n}\left( b \right) = 2/\pi \int_0^\infty {{{((\sin x)/x)}^n}\cos (bx)dx} $," Math. Comp., v. 19, 1965, pp. 113-117.
  • [2] R. W. Hamming, Numerical methods for scientists and engineers, International Series in Pure and Applied Mathematics, McGraw-Hill Book Co., Inc., New York-San Francisco, Calif.-Toronto-London, 1962. MR 0137279
  • [3] K. Harumi, S. Katsura & J. W. Wrench, Jr., "Values of $ 2/\pi \int_0^\infty {{{((\sin t)/t)}^n}dt}$," Math. Comp., v. 14, 1960, p. 379. MR 22 #12737.
  • [4] H. Leon Harter, New tables of the incomplete gamma-function ratio and of percentage points of the chi-square and Beta distributions, Aerospace Research Laboratories, Office of Aerospace Research, United States Air Force, For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C., 1964. MR 0171331

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DOI: https://doi.org/10.1090/S0025-5718-1966-0192634-5
Article copyright: © Copyright 1966 American Mathematical Society