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
![[img]](https://authors.library.caltech.edu/style/images/fileicons/application_pdf.png)
|
PDF
- Published Version
Creative Commons Attribution Non-commercial Share Alike. 384Kb |
Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20110929-113549134
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: |
| ||||||||||||
| 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: |
| ||||||||||||
| 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 |
Repository Staff Only: item control page
