Moscow Mathematical Journal

Volume 14, Issue 1, January–March 2014 pp. 1–27.

Orthogonal Polynomials on the Unit Circle, q-Gamma weights, and Discrete Painlevé Equations

Authors: Philippe Biane
Author institution: CNRS, IGM, Université Paris-Est, Champs-sur-Marne, FRANCE
Summary:

We consider orthogonal polynomials on the unit circle with respect to a weight which is a quotient of q-gamma functions. We show that the Verblunsky coefficients of these polynomials satisfy discrete Painlevé equations, in a Lax form, which correspond to an A₃⁽¹⁾ surface in Sakai’s classification.

2010 Mathematics Subject Classification. 33E17, 34L25, 39A45, 42C05.

Keywords: Orthogonal polynomials, Painlevé equations, scattering theory.

Back to Issue TOC Full-Text PDF