Translational addition theorems for spheroidal scalar and vector wave functions
Authors:
Bateshwar P. Sinha and Robert H. Macphie
Journal:
Quart. Appl. Math. 38 (1980), 143-158
MSC:
Primary 33A55
DOI:
https://doi.org/10.1090/qam/580875
MathSciNet review:
580875
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Abstract: The translational addition theorems for spheroidal scalar wave functions $R_{mn}^{\left ( i \right )}\left ( {h, \xi } \right ){S_{mn}}\left ( {h, \eta } \right )\exp \left ( {jm\phi } \right ); i = 1, 3, 4$ and spheroidal vector wave functions $M_{mn}^{x, y, z\left ( i \right )}\left ( {h; \xi , \\ \eta , \phi } \right ), N_{mn}^{x, y, z\left ( i \right )}\left ( {h; \xi , \eta , \phi } \right ); i = 1, 3, 4$, with reference to the spheroidal coordinate system at the origin $O$, have been obtained in terms of spheroidal scalar and vector wave functions with reference to the translated spheroidal coordinate system at the origin $O’$, where $O’$ has the spherical coordinates (${r_0},{\theta _0},{\phi _0}$) with respect to $O$. These addition theorems are useful in acoustics and electromagnetics in those cases involving spheroidal radiators and scatterers.
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J. H. Bruning and Y. T. Lo, Multiple scattering of EM waves by spheres, Part I, IEEE Trans. AP-19, 379–390 (1971)
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B. Friedman and J. Russek, Addition theorems for spherical waves, Quart. Appl. Math. 12, 13–23 (1954)
S. Stein, Addition theorems for spherical wave functions, Quart. Appl. Math. 19, 15–24 (1961)
O. R. Cruzan, Translational addition theorems for spherical vector wave functions, Quart. Appl. Math. 20, 33–40 (1962)
J. H. Bruning and Y. T. Lo, Multiple scattering of EM waves by spheres, Part I, IEEE Trans. AP-19, 379–390 (1971)
B. P. Sinha and R. H. MacPhie, Electromagnetic scattering by prolate spheroids for plane waves with arbitrary polarization and angle of incidence, Rad. Sc. 12, 171–184 (1977)
C. Flammer, Spheroidal wave functions, Stanford Univ. Press, Stanford, Calif., 1957, pp. 16–43
J. A. Stratton, Electromagnetic theory, McGraw-Hill, N.Y., 1941, p. 410, eq. (60)
A. R. Edmonds, Angular momentum in quantum mechanics, Princeton Univ. Press, Princeton, N.J., 1957
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Article copyright:
© Copyright 1980
American Mathematical Society