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 Publication | Random Matrices: Theory and Application |
ISSN | 2010-3263 |
Abstract | It 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. |
Keyword | Bäcklund transformations Discrete orthogonal polynomials Hypergeometric weights Painlevé VI |
DOI | 10.1142/S2010326321500295 |
URL | View the original |
Language | 英语 |
Fulltext Access | |
Citation statistics | |
Document Type | Journal article |
Collection | DEPARTMENT OF MATHEMATICS |
Corresponding Author | Hu，Jie |
Affiliation | 1.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 Affilication | Faculty of Science and Technology |
Corresponding Author Affilication | Faculty 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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