Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Rotational-translational addition theorems for spheroidal vector wave functions


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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DOI: https://doi.org/10.1090/qam/998107
Article copyright: © Copyright 1989 American Mathematical Society


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