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

Rains, Eric M. (2011) An Isomonodromy Interpretation of the Hypergeometric Solution of the Elliptic Painlevé Equation (and Generalizations). Symmetry, Integrability and Geometry, Methods and Applications (SIGMA), 7 . Art. No. 088. ISSN 1815-0659. https://resolver.caltech.edu/CaltechAUTHORS:20110929-113549134

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Abstract

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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.3842/SIGMA.2011.088 DOIArticle
http://www.emis.de/journals/SIGMA/2011/088/PublisherArticle
http://arxiv.org/abs/0807.0258arXivDiscussion Paper
Additional Information:© 2011 The author. The authors retain the copyright for their papers published in SIGMA under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. Received April 25, 2011, in final form September 06, 2011; Published online September 09, 2011. 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 DMS-0401387, with additional work on the project supported by NSF grants numbered DMS-0833464 and DMS-1001645.
Funders:
Funding AgencyGrant Number
NSFDMS-0401387
NSFDMS-1001645
NSFDMS-0833464
Subject Keywords:isomonodromy; hypergeometric; Painlevé; biorthogonal functions.
Classification Code:2010 MSC: 33E17; 34M55; 39A13
Record Number:CaltechAUTHORS:20110929-113549134
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20110929-113549134
Official Citation:An Isomonodromy Interpretation of the Hypergeometric Solution of the Elliptic Painlevé Equation (and Generalizations) Eric M. Rains SIGMA 7 (2011), 088, 24 pages
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:25495
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:30 Sep 2011 14:42
Last Modified:03 Oct 2019 03:06

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