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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
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: The roots of the equation \[ J_n^2(z) + J_{n + 1}^2(z) = 0\], 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.
- Srinivas Tadepalli and Costas Emmanuel Synolakis, Roots of $J_\gamma (z)\pm iJ_{\gamma +1}(z)=0$ and the evaluation of integrals with cylindrical function kernels, Quart. Appl. Math. 52 (1994), no. 1, 103–112. MR 1262322, DOI https://doi.org/10.1090/qam/1262322
- G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, England; The Macmillan Company, New York, 1944. MR 0010746
- D. A. Macdonald, The roots of $J_0(z)-iJ_1(z)=0$, Quart. Appl. Math. 47 (1989), no. 2, 375–378. MR 998110, DOI https://doi.org/10.1090/S0033-569X-1989-0998110-X M. Renardy, Problems and Solutions, Ed. M. Klamkin, Siam Review, vol. 31, 1989, pp. 126–127
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Article copyright:
© Copyright 1997
American Mathematical Society