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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
DOI: https://doi.org/10.1090/S0025-5718-1966-0192634-5
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, New York, 1962. MR 25 #735. MR 0137279 (25:735)
  • [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. L. Harter, New Tables of the Incomplete Gamma-Function Ratio and of Percentage Points of the Chi-Square and Beta Distributions, U. S. Government Printing Office, Washington, D. C., 1964. MR 30 #1562. MR 0171331 (30:1562)

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

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