Discrete Orthogonal Polynomials with Hypergeometric Weights and Painlevé VI

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2018
• Main Authors: Filipuk, G., Van Assche, W.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2018
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/209762
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Discrete Orthogonal Polynomials with Hypergeometric Weights and Painlevé VI / G. Filipuk, W. Van Assche // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 24 назв. — англ.

We investigate the recurrence coefficients of discrete orthogonal polynomials on the non-negative integers with hypergeometric weights and show that they satisfy a system of non-linear difference equations and a non-linear second-order differential equation in one of the parameters of the weights. T...