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Roots of two transcendental equations involving spherical Bessel functions


Authors: Robert L. Pexton and Arno D. Steiger
Journal: Math. Comp. 31 (1977), 752-753
MSC: Primary 65D20; Secondary 33A40
MathSciNet review: 0438662
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Abstract: Roots of the transcendental equations $ {j_l}(\alpha \lambda ){y_l}(\lambda ) = {j_l}(\lambda ){y_l}(\alpha \lambda )$ and

$\displaystyle {[x{j_l}(x)]'_{x = \alpha \eta }}{[x{y_l}(x)]'_{x = \eta }} = {[x{j_l}(x)]'_{x = \eta }}{[x{y_l}(x)]'_{x = \alpha \eta }}$

for the spherical Bessel functions of the first and second kind, $ {j_l}(z)$ and $ {y_l}(z)$, have been computed. The ranges for the parameter $ \alpha $, the order l and the root index n are: $ \alpha = 0.1(0.1)0.7$, $ l = 1(1)15$, $ n = 1(1)30$.

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

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1977-0438662-0
Keywords: Roots of transcendental equations, spherical Bessel functions, electromagnetic cavity resonators
Article copyright: © Copyright 1977 American Mathematical Society