An Isomonodromy Interpretation of the Hypergeometric Solution of the Elliptic Painlevé Equation (and Generalizations)
We construct a family of second-order linear difference equations parametrized by the hypergeometric solution of the elliptic Painlevé equation (or higher-order analogues), and admitting a large family of monodromy-preserving deformations. The solutions are certain semiclassical biorthogonal functio...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2011 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2011
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/147389 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | An Isomonodromy Interpretation of the Hypergeometric Solution of the Elliptic Painlevé Equation (and Generalizations) / E.M. Rains // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 26 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862707823983460352 |
|---|---|
| author | Rains, E.M. |
| author_facet | Rains, E.M. |
| citation_txt | An Isomonodromy Interpretation of the Hypergeometric Solution of the Elliptic Painlevé Equation (and Generalizations) / E.M. Rains // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 26 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We construct a family of second-order linear difference equations parametrized by the hypergeometric solution of the elliptic Painlevé equation (or higher-order analogues), and admitting a large family of monodromy-preserving deformations. The solutions are certain semiclassical biorthogonal functions (and their Cauchy transforms), biorthogonal with respect to higher-order analogues of Spiridonov's elliptic beta integral.
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| first_indexed | 2025-12-07T17:07:53Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147389 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:07:53Z |
| publishDate | 2011 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Rains, E.M. 2019-02-14T16:57:33Z 2019-02-14T16:57:33Z 2011 An Isomonodromy Interpretation of the Hypergeometric Solution of the Elliptic Painlevé Equation (and Generalizations) / E.M. Rains // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 26 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 33E17; 34M55; 39A13 https://nasplib.isofts.kiev.ua/handle/123456789/147389 We construct a family of second-order linear difference equations parametrized by the hypergeometric solution of the elliptic Painlevé equation (or higher-order analogues), and admitting a large family of monodromy-preserving deformations. The solutions are certain semiclassical biorthogonal functions (and their Cauchy transforms), biorthogonal with respect to higher-order analogues of Spiridonov's elliptic beta integral. This paper is a contribution to the Special Issue “Relationship of Orthogonal Polynomials and Special Functions with Quantum Groups and Integrable Systems”. The full collection is available at http://www.emis.de/journals/SIGMA/OPSF.html.
 The author would like to thank N. Witte for some helpful discussions of the orthogonal polynomial approach to isomonodromy (and the University of Melbourne for hosting the author’s sabbatical when the discussions took place), and D. Arinkin and A. Borodin for discussions leading to [3] (and thus clarifying what needed (and, perhaps more importantly, what did not need) to be established here). The author was supported in part by NSF grant numbered DMS0401387, with additional work on the project supported by NSF grants numbered DMS-0833464 and DMS-1001645. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications An Isomonodromy Interpretation of the Hypergeometric Solution of the Elliptic Painlevé Equation (and Generalizations) Article published earlier |
| spellingShingle | An Isomonodromy Interpretation of the Hypergeometric Solution of the Elliptic Painlevé Equation (and Generalizations) Rains, E.M. |
| title | An Isomonodromy Interpretation of the Hypergeometric Solution of the Elliptic Painlevé Equation (and Generalizations) |
| title_full | An Isomonodromy Interpretation of the Hypergeometric Solution of the Elliptic Painlevé Equation (and Generalizations) |
| title_fullStr | An Isomonodromy Interpretation of the Hypergeometric Solution of the Elliptic Painlevé Equation (and Generalizations) |
| title_full_unstemmed | An Isomonodromy Interpretation of the Hypergeometric Solution of the Elliptic Painlevé Equation (and Generalizations) |
| title_short | An Isomonodromy Interpretation of the Hypergeometric Solution of the Elliptic Painlevé Equation (and Generalizations) |
| title_sort | isomonodromy interpretation of the hypergeometric solution of the elliptic painlevé equation (and generalizations) |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147389 |
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