Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 33A55

Retrieve articles in all journals with MSC: 33A55

Additional Information

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

American Mathematical Society