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Advances in Mathematical Physics
Volume 2015, Article ID 572458, 12 pages
http://dx.doi.org/10.1155/2015/572458
Research Article

Connection Formulae between Ellipsoidal and Spherical Harmonics with Applications to Fluid Dynamics and Electromagnetic Scattering

1Department of Chemical Engineering, University of Patras, 26504 Patras, Greece
2Institute of Chemical Engineering Sciences, Stadiou Street, P.O. Box 1414, Platani, 26504 Patras, Greece

Received 26 July 2014; Accepted 30 October 2014

Academic Editor: George Dassios

Copyright © 2015 Michael Doschoris and Panayiotis Vafeas. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The environment of the ellipsoidal system, significantly more complex than the spherical one, provides the necessary settings for tackling boundary value problems in anisotropic space. However, the theory of Lamé functions and ellipsoidal harmonics affiliated with the ellipsoidal system is rather complicated. A turning point would reside in the existence of expressions interlacing these two different systems. Still, there is no simple way, if at all, to bridge the gap. The present paper addresses this issue. We provide explicit formulas of specific ellipsoidal harmonics expressed in terms of their counterparts in the classical spherical system. These expressions are then put into practice in the framework of physical applications.