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An upper bound for the first zero of Bessel functions


Author: Ll. G. Chambers
Journal: Math. Comp. 38 (1982), 589-591
MSC: Primary 33A65
DOI: https://doi.org/10.1090/S0025-5718-1982-0645673-0
MathSciNet review: 645673
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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

$\displaystyle {(v + 1)^{1/2}}\{ {(v + 2)^{1/2}} + 1\} ,$

and that for large v, $ v,{j_v} = v + O({v^{1/2}})$.

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

  • [1] J. Irving & N. Mullineux, Mathematics in Physics and Engineering, Academic Press, New York, 1959, p. 388. MR 0103145 (21:1928)
  • [2] J. Irving & N. Mullineux, Loc. cit., p. 39.
  • [3] G. N. Watson, A Treatise on the Theory of Bessel Functions, The University Press, Cambridge, 1944, p. 98. MR 0010746 (6:64a)
  • [4] G. N. Watson, Loc. cit., p. 486.

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1982-0645673-0
Article copyright: © Copyright 1982 American Mathematical Society

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