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More on the calculation of the integral $ I_n(b) = (2/\pi) \int_0^\infty \left(\frac{\sin x}{x}\right)^n \cos bx\,dx$


Author: Henry E. Fettis
Journal: Math. Comp. 21 (1967), 727-730
DOI: https://doi.org/10.1090/S0025-5718-67-99904-8
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  • [1] R. G. Medhurst & J. H. Roberts, "Evaluation of the integral $ {I_n}(b) = (2/\pi )\int_0^\infty {{{((\sin x)/x)}^n}\cos (bx)dx} $ ," Math. Comp., v. 19, 1965, pp. 113-117. MR 30 #2665. MR 0172446 (30:2665)
  • [2] R. Thompson, "Evaluation of $ {I_n}(b) = (2/\pi )\int_0^\infty {{{((\sin x)/x)}^n}\cos (bx)dx} $," Math. Comp., v. 20, 1966, pp. 330-331. MR 33 #859. MR 0192634 (33:859)
  • [3] W. Magnus & F. Oberhettinger, Formeln und Sätze für die speziellen Funktionen der mathematischen Physik, 2nd ed., Springer-Verlag, Berlin, 1948, p. 217; English transl., Chelsea, New York, 1949. MR 10, 38; MR 10, 532. MR 0025629 (10:38a)
  • [4] R. Butler, "On the evaluation $ \int_0^\infty {({{\sin }^m}t)/{t^m}dt} $ by the trapezoidal rule," Amer. Math. Monthly, v. 67, 1960, pp. 566-569. MR 22 #4841. MR 0114011 (22:4841)


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DOI: https://doi.org/10.1090/S0025-5718-67-99904-8
Article copyright: © Copyright 1967 American Mathematical Society

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