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Differential and difference equations for recurrence coefficients of orthogonal polynomials with hypergeometric weights and Bäcklund transformations of the sixth Painlevé equation
Hu,Jie1; Filipuk,Galina2; Chen,Yang1
2020
Source PublicationRandom Matrices: Theory and Application
ISSN2010-3263
AbstractIt is known from [G. Filipuk and W. Van Assche, Discrete orthogonal polynomials with hypergeometric weights and Painlevé VI, Symmetry Integr. Geom. Methods Appl. 14 (2018), Article ID: 088, 19 pp.] that the recurrence coefficients of discrete orthogonal polynomials on the nonnegative integers with hypergeometric weights satisfy a system of nonlinear difference equations. There is also a connection to the solutions of the σform of the sixth Painlevé equation (one of the parameters of the weights being the independent variable in the differential equation) [G. Filipuk and W. Van Assche, Discrete orthogonal polynomials with hypergeometric weights and Painlevé VI, Symmetry Integr. Geom. Methods Appl. 14 (2018), Article ID: 088, 19 pp.]. In this paper, we derive a second-order nonlinear difference equation from the system and present explicit formulas showing how this difference equation arises from the Bäcklund transformations of the sixth Painlevé equation. We also present an alternative way to derive the connection between the recurrence coefficients and the solutions of the sixth Painlevé equation.
KeywordBäcklund transformations Discrete orthogonal polynomials Hypergeometric weights Painlevé VI
DOI10.1142/S2010326321500295
URLView the original
Language英语
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Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Corresponding AuthorHu,Jie
Affiliation1.Faculty of Science and Technology,Department of Mathematics,University of Macau,Taipa,Avenida da Universidade,Macao
2.Faculty of Mathematics Informatics and Mechanics,University of Warsaw,Warsaw,Banacha 2,02-097,Poland
First Author AffilicationFaculty of Science and Technology
Corresponding Author AffilicationFaculty of Science and Technology
Recommended Citation
GB/T 7714
Hu,Jie,Filipuk,Galina,Chen,Yang. Differential and difference equations for recurrence coefficients of orthogonal polynomials with hypergeometric weights and Bäcklund transformations of the sixth Painlevé equation[J]. Random Matrices: Theory and Application,2020.
APA Hu,Jie,Filipuk,Galina,&Chen,Yang.(2020).Differential and difference equations for recurrence coefficients of orthogonal polynomials with hypergeometric weights and Bäcklund transformations of the sixth Painlevé equation.Random Matrices: Theory and Application.
MLA Hu,Jie,et al."Differential and difference equations for recurrence coefficients of orthogonal polynomials with hypergeometric weights and Bäcklund transformations of the sixth Painlevé equation".Random Matrices: Theory and Application (2020).
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