Connection Formulae between Ellipsoidal and Spherical Harmonics with Applications to Fluid Dynamics and Electromagnetic Scattering
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 c...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2015/572458 |
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| author | Michael Doschoris Panayiotis Vafeas |
| author_facet | Michael Doschoris Panayiotis Vafeas |
| author_sort | Michael Doschoris |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-e184176a36e04c0780b81a5bb411f76b |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-e184176a36e04c0780b81a5bb411f76b2025-02-03T06:06:51ZengWileyAdvances in Mathematical Physics1687-91201687-91392015-01-01201510.1155/2015/572458572458Connection Formulae between Ellipsoidal and Spherical Harmonics with Applications to Fluid Dynamics and Electromagnetic ScatteringMichael Doschoris0Panayiotis Vafeas1Department of Chemical Engineering, University of Patras, 26504 Patras, GreeceDepartment of Chemical Engineering, University of Patras, 26504 Patras, GreeceThe 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.http://dx.doi.org/10.1155/2015/572458 |
| spellingShingle | Michael Doschoris Panayiotis Vafeas Connection Formulae between Ellipsoidal and Spherical Harmonics with Applications to Fluid Dynamics and Electromagnetic Scattering Advances in Mathematical Physics |
| title | Connection Formulae between Ellipsoidal and Spherical Harmonics with Applications to Fluid Dynamics and Electromagnetic Scattering |
| title_full | Connection Formulae between Ellipsoidal and Spherical Harmonics with Applications to Fluid Dynamics and Electromagnetic Scattering |
| title_fullStr | Connection Formulae between Ellipsoidal and Spherical Harmonics with Applications to Fluid Dynamics and Electromagnetic Scattering |
| title_full_unstemmed | Connection Formulae between Ellipsoidal and Spherical Harmonics with Applications to Fluid Dynamics and Electromagnetic Scattering |
| title_short | Connection Formulae between Ellipsoidal and Spherical Harmonics with Applications to Fluid Dynamics and Electromagnetic Scattering |
| title_sort | connection formulae between ellipsoidal and spherical harmonics with applications to fluid dynamics and electromagnetic scattering |
| url | http://dx.doi.org/10.1155/2015/572458 |
| work_keys_str_mv | AT michaeldoschoris connectionformulaebetweenellipsoidalandsphericalharmonicswithapplicationstofluiddynamicsandelectromagneticscattering AT panayiotisvafeas connectionformulaebetweenellipsoidalandsphericalharmonicswithapplicationstofluiddynamicsandelectromagneticscattering |