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Mathematics of Computation

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

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

  • 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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Article copyright: © Copyright 1982 American Mathematical Society