Theta Functions, Elliptic Hypergeometric Series, and Kawanaka's Macdonald Polynomial Conjecture
We give a new theta-function identity, a special case of which is utilised to prove Kawanaka's Macdonald polynomial conjecture. The theta-function identity further yields a transformation formula for multivariable elliptic hypergeometric series which appears to be new even in the one-variable,...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2009 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2009
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/149148 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Theta Functions, Elliptic Hypergeometric Series, and Kawanaka's Macdonald Polynomial Conjecture / R. Langer, M.J. Schlosser, S.O. Warnaar // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 24 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862734091523194880 |
|---|---|
| author | Langer, R. Schlosser, M.J. Warnaar, S.O. |
| author_facet | Langer, R. Schlosser, M.J. Warnaar, S.O. |
| citation_txt | Theta Functions, Elliptic Hypergeometric Series, and Kawanaka's Macdonald Polynomial Conjecture / R. Langer, M.J. Schlosser, S.O. Warnaar // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 24 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We give a new theta-function identity, a special case of which is utilised to prove Kawanaka's Macdonald polynomial conjecture. The theta-function identity further yields a transformation formula for multivariable elliptic hypergeometric series which appears to be new even in the one-variable, basic case.
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| first_indexed | 2025-12-07T19:41:15Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149148 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T19:41:15Z |
| publishDate | 2009 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Langer, R. Schlosser, M.J. Warnaar, S.O. 2019-02-19T17:41:06Z 2019-02-19T17:41:06Z 2009 Theta Functions, Elliptic Hypergeometric Series, and Kawanaka's Macdonald Polynomial Conjecture / R. Langer, M.J. Schlosser, S.O. Warnaar // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 24 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 05E05; 33D52; 33D67 https://nasplib.isofts.kiev.ua/handle/123456789/149148 We give a new theta-function identity, a special case of which is utilised to prove Kawanaka's Macdonald polynomial conjecture. The theta-function identity further yields a transformation formula for multivariable elliptic hypergeometric series which appears to be new even in the one-variable, basic case. This paper is a contribution to the Proceedings of the Workshop “Elliptic Integrable Systems, Isomonodromy Problems, and Hypergeometric Functions” (July 21–25, 2008, MPIM, Bonn, Germany). We thank the anonymous referees for helpful comments. The work reported in this paper is supported by the Australian Research Council and by FWF Austrian Science Fund grants P17563-N13 and S9607. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Theta Functions, Elliptic Hypergeometric Series, and Kawanaka's Macdonald Polynomial Conjecture Article published earlier |
| spellingShingle | Theta Functions, Elliptic Hypergeometric Series, and Kawanaka's Macdonald Polynomial Conjecture Langer, R. Schlosser, M.J. Warnaar, S.O. |
| title | Theta Functions, Elliptic Hypergeometric Series, and Kawanaka's Macdonald Polynomial Conjecture |
| title_full | Theta Functions, Elliptic Hypergeometric Series, and Kawanaka's Macdonald Polynomial Conjecture |
| title_fullStr | Theta Functions, Elliptic Hypergeometric Series, and Kawanaka's Macdonald Polynomial Conjecture |
| title_full_unstemmed | Theta Functions, Elliptic Hypergeometric Series, and Kawanaka's Macdonald Polynomial Conjecture |
| title_short | Theta Functions, Elliptic Hypergeometric Series, and Kawanaka's Macdonald Polynomial Conjecture |
| title_sort | theta functions, elliptic hypergeometric series, and kawanaka's macdonald polynomial conjecture |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149148 |
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