Rotational-translational addition theorems for spheroidal vector wave functions

Dalmas, Jeannine; Deleuil, Roger; MacPhie, R. H.

doi:10.1090/qam/998107

Authors: Jeannine Dalmas, Roger Deleuil and R. H. MacPhie
Journal: Quart. Appl. Math. 47 (1989), 351-364
MSC: Primary 78A45; Secondary 33A55
DOI: https://doi.org/10.1090/qam/998107
MathSciNet review: 998107
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Abstract: Rotational-translational addition theorems for spherical and spheroidal vector wave functions are established. These theorems concern the vector wave functions ${M^a}$ and ${N^a}$ (with $a = r, x, y, z$) which can be obtained and used to treat various electromagnetic problems such as multiple scattering of a plane wave from prolate spheroids (with arbitrary spacings and orientations of their axes of symmetry) or radiation from thin-wire antennas. For sake of completeness, rotational-translational addition theorems for the vector wave function L are also established. This work is a natural extension of previous studies concerning simpler transformations of coordinate systems, such as rotation or translation. The two cases $r \ge d$ and $r \le d$ are distinguished, where $d$ is the distance between the centers of the spheroids.

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