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

Michael Doschoris and Panayiotis Vafeas

Advances in Mathematical Physics, 2015, vol. 2015, 1-12

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.

Date: 2015
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/AMP/2015/572458.pdf (application/pdf)
http://downloads.hindawi.com/journals/AMP/2015/572458.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlamp:572458

DOI: 10.1155/2015/572458

Access Statistics for this article

More articles in Advances in Mathematical Physics from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().