Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On the computation of zeroes of $ J_n(z)-iJ_{n+1}(z)=0$

Author: D. A. MacDonald
Journal: Quart. Appl. Math. 55 (1997), 623-633
MSC: Primary 33C10; Secondary 65H10
DOI: https://doi.org/10.1090/qam/1486539
MathSciNet review: MR1486539
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Abstract | References | Similar Articles | Additional Information

Abstract: The roots of the equation

$\displaystyle J_n^2(z) + J_{n + 1}^2(z) = 0$

, in which $ n$ is a positive integer or zero, are of interest to the specialist in wave reflection from multi-sloped beaches [1]. This note shows how to obtain accurate roots of the equation when $ n$ is not large.

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

  • [1] S. Tadepalli and C. E. Synolakis, Roots of $ {J_\gamma }\left( z \right) \pm i{J_{\gamma + 1}}\left( z \right) = 0$ and the evaluation of integrals with cylindrical function kernals, Quart. Appl. Math. LII, 103-111 (1994) MR 1262322
  • [2] G. N. Watson, Theory of Bessel Functions, Cambridge University Press, 1944 MR 0010746
  • [3] D. A. MacDonald, The roots of $ {J_0}\left( z \right) - i{J_1}\left( z \right)$, Quart. Appl. Math. XLVII, 375-378 (1989) MR 998110
  • [4] M. Renardy, Problems and Solutions, Ed. M. Klamkin, Siam Review, vol. 31, 1989, pp. 126-127

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DOI: https://doi.org/10.1090/qam/1486539
Article copyright: © Copyright 1997 American Mathematical Society

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