An Isomonodromy Interpretation of the Hypergeometric Solution of the Elliptic Painlevé Equation (and Generalizations)

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dc.contributor.authorRains, E.M.
dc.date.accessioned2019-02-14T16:57:33Z
dc.date.available2019-02-14T16:57:33Z
dc.date.issued2011
dc.description.abstractWe 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.uk_UA
dc.description.sponsorshipThis 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.uk_UA
dc.identifier.citationAn 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.uk_UA
dc.identifier.issn1815-0659
dc.identifier.other2010 Mathematics Subject Classification: 33E17; 34M55; 39A13
dc.identifier.urihttps://nasplib.isofts.kiev.ua/handle/123456789/147389
dc.language.isoenuk_UA
dc.publisherІнститут математики НАН Україниuk_UA
dc.relation.ispartofSymmetry, Integrability and Geometry: Methods and Applications
dc.statuspublished earlieruk_UA
dc.titleAn Isomonodromy Interpretation of the Hypergeometric Solution of the Elliptic Painlevé Equation (and Generalizations)uk_UA
dc.typeArticleuk_UA

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Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7, випуск за цей рік