Dzhamay, A; Filipuk, G; Stokes, A; (2020) Recurrence coefficients for discrete orthogonal polynomials with hypergeometric weight and discrete Painlevé equations. Journal of Physics A: Mathematical and Theoretical 10.1088/1751-8121/abbd54. (In press).

Preview

Text Dzhamay+et+al_2020_J._Phys._A__Math._Theor._10.1088_1751-8121_abbd54.pdf - Accepted Version Download (657kB) | Preview

Abstract

Over the last decade it has become clear that discrete Painlevé equations appear in a wide range of important mathematical and physical problems. Thus, the question of recognizing a given non-autonomous recurrence as a discrete Painlevé equation and determining its type according to Sakai's classification scheme, understanding whether it is equivalent to some known (model) example, and especially finding an explicit change of coordinates transforming it to such an example, becomes one of the central ones. Fortunately, Sakai's geometric theory provides an almost algorithmic procedure for answering this question. In this paper we illustrate this procedure by studying an example coming from the theory of discrete orthogonal polynomials. There are many connections between orthogonal polynomials and Painlevé equations, both differential and discrete. In particular, often the coefficients of three-term recurrence relations for discrete orthogonal polynomials can be expressed in terms of solutions of discrete Painlevé equations. In this work we study discrete orthogonal polynomials with general hypergeometric weight and show that their recurrence coefficients satisfy, after some change of variables, the standard discrete Painlevé-V equation. We also provide an explicit change of variables transforming this equation to the standard form.

Download activity - last month

Export as JSONXMLCSV

Download activity - last 12 months

Export as JSONXMLCSV

Downloads by country - last 12 months

Export as XMLCSVJSON

Archive Staff Only

View Item