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Tables for the rapid and accurate numerical evaluation of certain infinite integrals involving Bessel functions


Author: I. M. Longman
Journal: Math. Comp. 11 (1957), 166-180
MSC: Primary 65.3X
DOI: https://doi.org/10.1090/S0025-5718-1957-0091538-0
MathSciNet review: 0091538
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  • [1] I. M. Longman, Note on a method for computing infinite integrals of oscillatory functions, Proc. Cambridge Philos. Soc. 52 (1956), 764–768. MR 0082193
  • [2] T. J. I'A. Bromwich, An Introduction to the Theory of Infinite Series, The Macmillan Co., New York, 1942.
  • [3] NBS Applied Mathematics Series, No. 37, Tables of Functions and of Zeros of Functions, U. S. Gov. Printing Office, Washington, D. C., 1954.
  • [4] Harvard University, Computation Laboratory, Annals, v. 3: Tables of the Bessel Functions of the First Kind of Orders Zero and One, Harvard University Press, Cambridge, Mass., 1947.
  • [5] British Association For The Advancement of Science, Committee on Mathematical Tables, Bessel Functions, v. 6, ``Zeros of $ {J_0}(x)$ and $ {J_1}(x)$,'' Cambridge: at the University Press, 1950.
  • [6] G. N. Watson, A treatise on the theory of Bessel functions, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1995. Reprint of the second (1944) edition. MR 1349110
  • [7] P. Davis and P. Rabinowitz, Abscissas and weights for Gaussian quadratures of high order, J. Res. Nat. Bur. Standards 56 (1956), 35–37. MR 0076463, https://doi.org/10.6028/jres.056.005

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DOI: https://doi.org/10.1090/S0025-5718-1957-0091538-0
Article copyright: © Copyright 1957 American Mathematical Society