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Mathematics of Computation

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Roots of two transcendental equations determining the frequency spectra of standing spherical electromagnetic waves

Authors: Robert L. Pexton and Arno D. Steiger
Journal: Math. Comp. 31 (1977), 1000-1002
MSC: Primary 65A05
MathSciNet review: 0443286
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Abstract: Roots of the transcendental equations

$\displaystyle \frac{{{j_l}(\lambda )}}{{{y_l}(\lambda )}} = \frac{{{j_l}(\alpha... ... }} - \frac{1}{{\sqrt {\vert\varepsilon \vert} }}{y_{l - 1}}(\alpha \lambda )}}$


$\displaystyle \frac{{\eta {j_{l - 1}}(\eta ) - l{j_l}(\eta )}}{{\eta {y_{l - 1}... ...t\varepsilon \vert)} }}{{{i_l}(\alpha \eta \sqrt {\vert\varepsilon \vert)} }}}}$

for the spherical Bessel functions of the first and second kind, $ {j_l}(x)$ and $ {y_l}(x)$, and for the modified spherical Bessel functions of the first kind, $ {i_l}(x)$, have been computed. The ranges for the parameters $ \sqrt {\vert\varepsilon \vert} $ and $ \alpha $, the order l and the root index n are:

$\displaystyle \sqrt {\vert\varepsilon \vert} = 1.0,10.0,100.0,500.0;\quad \alpha = 0.1(0.1)0.7;\quad l = 1(1)15;\quad n = 1(1)30.$

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Keywords: Roots of transcendental equations, spherical Bessel functions, modified spherical Bessel functions, electromagnetic cavity resonators
Article copyright: © Copyright 1977 American Mathematical Society

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