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), 10001002
MSC:
Primary 65A05
MathSciNet review:
0443286
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Abstract: Roots of the transcendental equations and for the spherical Bessel functions of the first and second kind, and , and for the modified spherical Bessel functions of the first kind, , have been computed. The ranges for the parameters and , the order l and the root index n are:
 [1]
Robert
L. Pexton and Arno
D. Steiger, Roots of two transcendental equations
involving spherical Bessel functions, Math.
Comp. 31 (1977), no. 139, 752–753. MR 0438662
(55 #11570), http://dx.doi.org/10.1090/S00255718197704386620
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H. L. BOYEN, A. M. MESSIAEN & P. E. VANDENPLAS, "Experimental and theoretical eigenmodes of a spherical cavity partially filled with plasma," J. Appl. Phys., v. 40, 1969, pp. 22962305.
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J.
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Comput. J. 7 (1975), no. 2, 51–57. MR 0386219
(52 #7077)
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Fr. MECHEL, "Improvement in recurrence techniques for the computation of Bessel functions of integral order," Math. Comp., v. 22, 1968, pp. 202205.
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W. J. LENTZ, "Generating Bessel functions in Mie scattering calculations using continued fractions," Applied Optics, v. 15, 1976, pp. 668671.
 [1]
 R. L. PEXTON & A. D. STEIGER, "Roots of two transcendental equations involving spherical Bessel functions," Math. Comp., v. 31, 1977, pp. MR 0438662 (55:11570)
 [2]
 H. L. BOYEN, A. M. MESSIAEN & P. E. VANDENPLAS, "Experimental and theoretical eigenmodes of a spherical cavity partially filled with plasma," J. Appl. Phys., v. 40, 1969, pp. 22962305.
 [3]
 M. ABRAMOWITZ & I. A. STEGUN (Editors), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Nat. Bur. Standards, Appl. Math. Ser., no. 55, Superintendent of Documents, U.S. Government Printing Office, Washington, D.C., 1965. MR 31 #1400. MR 0167642 (29:4914)
 [4]
 J. M. BLATT, "A stable method of inverse interpolation," Austral. Comput. J., v. 7, 1975, pp. 5157. MR 52 #7077. MR 0386219 (52:7077)
 [5]
 Fr. MECHEL, "Improvement in recurrence techniques for the computation of Bessel functions of integral order," Math. Comp., v. 22, 1968, pp. 202205.
 [6]
 W. J. LENTZ, "Generating Bessel functions in Mie scattering calculations using continued fractions," Applied Optics, v. 15, 1976, pp. 668671.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197704432865
PII:
S 00255718(1977)04432865
Keywords:
Roots of transcendental equations,
spherical Bessel functions,
modified spherical Bessel functions,
electromagnetic cavity resonators
Article copyright:
© Copyright 1977
American Mathematical Society
