Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Rotational-translational addition theorems for scalar spheroidal wave functions


Authors: R. H. MacPhie, J. Dalmas and R. Deleuil
Journal: Quart. Appl. Math. 44 (1987), 737-749
MSC: Primary 33A55
DOI: https://doi.org/10.1090/qam/872824
MathSciNet review: 872824
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Abstract: Rotational-translational addition theorems for the scalar spheroidal wave function $ \psi _{mn}^{\left( i \right)}\left( {h;\eta ,\xi ,\phi } \right)$, with $ i = 1,3,4$, are deduced. This permits one to represent the $ m{n^{th}}$ scalar spheroidal wave function, associated with one spheroidal coordinate system $ \left( {{h_q};{\eta _q},{\xi _q},{\phi _q}} \right)$ centered at its local origin $ {O_q}$, by an addition series of spheroidal wave functions associated with a second rotated and translated system $ \left( {{h_r};{\eta _r},{\xi _r},{\phi _r}} \right)$, centered at $ {O_r}$. Such theorems are necessary in the rigorous analysis of radiation and scattering by spheroids with arbitrary spacings and orientations.


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DOI: https://doi.org/10.1090/qam/872824
Article copyright: © Copyright 1987 American Mathematical Society


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