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Mathematics of Computation

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A short table of $ \int \sb{x}{}\sp{\infty }\,J\sb{0}\,(t)t\sp{-n}dt$ and $ \int \sb{x}{}\sp{\infty }\,J\sb{1}\,(t)t\sp{-n}dt$


Author: I. M. Longman
Journal: Math. Comp. 13 (1959), 306-311
MSC: Primary 65.00
DOI: https://doi.org/10.1090/S0025-5718-1959-0108892-5
MathSciNet review: 0108892
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  • [1] I. M. Longman, ``Tables for the rapid and accurate numerical evaluation of certain infinite integrals involving Bessel functions,'' MTAC, v. 11, 1957, p. 166. MR 0091538 (19:985a)
  • [2] Arnold N. Lowan & Milton Abramowitz, ``Table of the integrals $ \int_0^x {{J_0}(t)dt} $ and $ \int_0^x {{J_0}(t)dt} $, Tables of Functions and of Zeros of Functions, NBS Applied Mathematics Series, No. 37, U. S. Government Printing Office, Washington, D. C., 1954, p. 21.
  • [3] Arnold N. Lowan, G. Blanch, & Milton Abramowitz, ``Table of $ J{i_0}(x) = \int_x^\infty {{J_0}(t)/tdt} $ and related functions,'' Ibid., p. 33.
  • [4] G. N. Watson, A Treatise on the Theory of Bessel Functions, The University Press, Cambridge, 1948, p. 752. MR 1349110 (96i:33010)
  • [5] V. G. Smith, ``An asymptotic expansion of $ J{i_0}(x) = \int_x^\infty {{J_0}(t)/tdt} $,'' Journal of Mathematics and Physics, v. 22, 1943, p. 58. MR 0008705 (5:49b)

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DOI: https://doi.org/10.1090/S0025-5718-1959-0108892-5
Article copyright: © Copyright 1959 American Mathematical Society

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