The recurrence coe#cients of generalized Charlier polynomials satisfy a system of nonlinear recurrence relations. We simplify the recurrence relations, show that they are related to certain discrete Painleve equations, and analyze the asymptotic behaviour.

Abstract not found

Abstract not found

We present an asymmetric q-Painlevé equation. We will derive this using q-orthogonal polynomials with respect to generalized Freud weights: their recurrence coefficients will obey this q-Painlevé equation (up to a simple transformation). We will show a stable method of computing a special solution which gives the recurrence coefficients. We establish a connection with α-q-PV. 1

Orthonormal polynomials on the real line are defined by the orthogonality conditions pn(x)pm(x) dµ(x) =δm,n, m,n ≥ 0, (1.1)

Discrete Painlevé equations for recurrence coefficients of orthogonal polynomials

Discrete Painlevé equations for recurrence coefficients of orthogonal polynomials

polynomials on the unit circle, q-Gamma