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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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An upper bound for the first zero of Bessel functions
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by Ll. G. Chambers PDF
Math. Comp. 38 (1982), 589-591 Request permission

Abstract:

It is shown, using the Rayleigh-Ritz method of the calculus of variations, that an upper bound for the first zero ${j_v}$, of ${z^{ - v}}{J_v}(z)$, $v > - 1$, is given by \[ {(v + 1)^{1/2}}\{ {(v + 2)^{1/2}} + 1\} ,\] and that for large v, $v,{j_v} = v + O({v^{1/2}})$.
References
  • J. Irving and N. Mullineux, Mathematics in physics and engineering, Pure and Applied Physics, Vol. 6, Academic Press, New York-London, 1959. MR 0103145
  • J. Irving & N. Mullineux, Loc. cit., p. 39.
  • G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, England; The Macmillan Company, New York, 1944. MR 0010746
  • G. N. Watson, Loc. cit., p. 486.
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Math. Comp. 38 (1982), 589-591
  • MSC: Primary 33A65
  • DOI: https://doi.org/10.1090/S0025-5718-1982-0645673-0
  • MathSciNet review: 645673