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: 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, 103โ112. 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, 375โ378. 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. 126โ127
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, 103โ111 (1994)
G. N. Watson, Theory of Bessel Functions, Cambridge University Press, 1944
D. A. MacDonald, The roots of ${J_0}\left ( z \right ) - i{J_1}\left ( z \right )$, Quart. Appl. Math. XLVII, 375โ378 (1989)
M. Renardy, Problems and Solutions, Ed. M. Klamkin, Siam Review, vol. 31, 1989, pp. 126โ127
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Article copyright:
© Copyright 1997
American Mathematical Society
