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Common zeros of two Bessel functions. II. Approximations and tables

Author: T. C. Benton
Journal: Math. Comp. 41 (1983), 203-217
MSC: Primary 33A40; Secondary 65A05
MathSciNet review: 701635
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Abstract: In [1] it was shown that two Bessel functions $ {J_\nu}(x)$, $ {J_\mu }(x)$ could have two zeros which were common to both functions, and a computer program was made which takes approximate values of $ \nu $, $ \mu $ and $ {j_{\nu,k}} = {j_{\mu ,h}}$ and $ {j_{\nu, k + n}} = {j_{\mu ,h + m}}$ and from them computes the exact values. Here it will be shown how to find the necessary approximate values to initiate the computation. A table of the smaller ratios m : n with the orders of the functions less than one hundred is given.

References [Enhancements On Off] (What's this?)

  • [1] T. C. Benton & H. D. Knoble, "Common zeros of two Bessel functions," Math. Comp., v. 32, 1978, pp. 533-535. MR 0481160 (58:1303)
  • [2] G. N. Watson, Treatise on Bessel Functions, Cambridge Univ. Press, Oxford, 1945.
  • [3] Royal Society Mathematical Tables 7. Bessel Functions III (F. W. T. Olver, ed.), Cambridge Univ. Press, Oxford, 1960.

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Article copyright: © Copyright 1983 American Mathematical Society

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