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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 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,Macao2.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 CitationGB/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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