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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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2006
Main Author: Volkmer, H.
Format: Article
Language:English
Published: Інститут математики НАН України 2006
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/146110
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this: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
id nasplib_isofts_kiev_ua-123456789-146110
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
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Generalized Ellipsoidal and Sphero-Conal Harmonics
spellingShingle Generalized Ellipsoidal and Sphero-Conal Harmonics
Volkmer, H.
title_short 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_sort generalized ellipsoidal and sphero-conal harmonics
author Volkmer, H.
author_facet Volkmer, H.
publishDate 2006
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
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.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/146110
citation_txt Generalized Ellipsoidal and Sphero-Conal Harmonics / H. Volkmer // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 22 назв. — англ.
work_keys_str_mv AT volkmerh generalizedellipsoidalandspheroconalharmonics
first_indexed 2025-12-01T11:30:40Z
last_indexed 2025-12-01T11:30:40Z
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