Discrete Painlevé equations for recurrence coefficients of Laguerre–Hahn orthogonal polynomials of class one

Abstract

In this paper we study recurrences for Laguerre–Hahn orthogonal polynomials of class one. It is shown for some families of such Laguerre–Hahn polynomials that the coefficients of the three term recurrence relation satisfy some forms of discrete Painlevé equations, namely dP_I and dP_IV.