Degenerate roots of three transcendental equations involving spherical Bessel functions
Authors: Robert L. Pexton and Arno D. Steiger
Journal: Math. Comp. 33 (1979), 1041-1048
MSC: Primary 65H10; Secondary 65D20
MathSciNet review: 528056
Abstract: Roots of the three transcendental equations
Roots of the third equation for , , , together with their minima and associated values of the parameter , are given in the microfiche supplement accompanying this issue. Roots of the first and the second equation and minima of roots of the second equation are published in v. 31 and v. 32 of this journal.
The roots of the first two equations determine the eigenfrequencies of the transverse electric and the transverse magnetic normal modes of an ideal cavity resonator bounded by two concentric spheres ( and ). The roots of the third equation determine the frequencies of the irrotational magnetic eigenfields.
-  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, https://doi.org/10.1090/S0025-5718-1977-0438662-0
-  Robert L. Pexton and Arno D. Steiger, Roots of two transcendental equations as functions of a continuous real parameter, Math. Comp. 32 (1978), no. 142, 511–518. MR 0488704, https://doi.org/10.1090/S0025-5718-1978-0488704-2
-  Milton Abramowitz and Irene A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables, National Bureau of Standards Applied Mathematics Series, vol. 55, For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C., 1964. MR 0167642
- ROBERT L. PEXTON & ARNO D. STEIGER, "Roots of two transcendental equations involving spherical Bessel functions," Math. Comp., v. 31, 1977, pp. 752-753. MR 0438662 (55:11570)
- ROBERT L. PEXTON & ARNO D. STEIGER, "Roots of two transcendental equations as functions of a continuous real parameter," Math. Comp., v. 32, 1978, pp. 511-518. MR 0488704 (58:8222a)
- M. ABRAMOWITZ & I. A. STEGUN (Editors), Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, 3rd ed., 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)
Keywords: Roots of transcendental equations, spherical Bessel functions, degenerate roots, electromagnetic cavity resonators
Article copyright: © Copyright 1979 American Mathematical Society