Generalized Ellipsoidal and Sphero-Conal Harmonics
Classical ellipsoidal and sphero-conal harmonics are polynomial solutions of the Laplace equation that can be expressed in terms of Lamé polynomials. Generalized ellipsoidal and sphero-conal harmonics are polynomial solutions of the more general Dunkl equation that can be expressed in terms of Stiel...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2006 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2006
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/146110 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Generalized Ellipsoidal and Sphero-Conal Harmonics / H. Volkmer // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 22 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862646407679180800 |
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| author | Volkmer, H. |
| author_facet | Volkmer, H. |
| citation_txt | Generalized Ellipsoidal and Sphero-Conal Harmonics / H. Volkmer // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 22 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Classical ellipsoidal and sphero-conal harmonics are polynomial solutions of the Laplace equation that can be expressed in terms of Lamé polynomials. Generalized ellipsoidal and sphero-conal harmonics are polynomial solutions of the more general Dunkl equation that can be expressed in terms of Stieltjes polynomials. Niven's formula connecting ellipsoidal and sphero-conal harmonics is generalized. Moreover, generalized ellipsoidal harmonics are applied to solve the Dirichlet problem for Dunkl's equation on ellipsoids.
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| first_indexed | 2025-12-01T11:30:40Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146110 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-01T11:30:40Z |
| publishDate | 2006 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Volkmer, H. 2019-02-07T13:37:31Z 2019-02-07T13:37:31Z 2006 Generalized Ellipsoidal and Sphero-Conal Harmonics / H. Volkmer // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 22 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 33C50; 35C10 https://nasplib.isofts.kiev.ua/handle/123456789/146110 Classical ellipsoidal and sphero-conal harmonics are polynomial solutions of the Laplace equation that can be expressed in terms of Lamé polynomials. Generalized ellipsoidal and sphero-conal harmonics are polynomial solutions of the more general Dunkl equation that can be expressed in terms of Stieltjes polynomials. Niven's formula connecting ellipsoidal and sphero-conal harmonics is generalized. Moreover, generalized ellipsoidal harmonics are applied to solve the Dirichlet problem for Dunkl's equation on ellipsoids. This paper is a contribution to the Vadim Kuznetsov Memorial Issue “Integrable Systems and Related Topics”. The author thanks W. Miller Jr. and two anonymous referees for helpful comments. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Generalized Ellipsoidal and Sphero-Conal Harmonics Article published earlier |
| spellingShingle | Generalized Ellipsoidal and Sphero-Conal Harmonics Volkmer, H. |
| title | Generalized Ellipsoidal and Sphero-Conal Harmonics |
| title_full | Generalized Ellipsoidal and Sphero-Conal Harmonics |
| title_fullStr | Generalized Ellipsoidal and Sphero-Conal Harmonics |
| title_full_unstemmed | Generalized Ellipsoidal and Sphero-Conal Harmonics |
| title_short | Generalized Ellipsoidal and Sphero-Conal Harmonics |
| title_sort | generalized ellipsoidal and sphero-conal harmonics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146110 |
| work_keys_str_mv | AT volkmerh generalizedellipsoidalandspheroconalharmonics |