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An Isomonodromy Interpretation of the Hypergeometric Solution of the Elliptic Painlevé Equation (and Generalizations)
Репозиторій DSpace/Manakin
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- Фізико-технічні та математичні науки
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- Відділення математики
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7
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- Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7, випуск за цей рік
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An Isomonodromy Interpretation of the Hypergeometric Solution of the Elliptic Painlevé Equation (and Generalizations)
Інший ID:
2010 Mathematics Subject Classification: 33E17; 34M55; 39A13
Посилання:
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.
Підтримка:
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.
Дата:
2011
Переглядів:
585
Завантажень:
245
Анотація:
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.
