This article is cited in 3 papers

Orthogonal polynomials on the unit circle, $q$-Gamma weights, and discrete Painlevé equations

Philippe Biane

CNRS, IGM, Université Paris-Est, Champs-sur-Marne, France

Abstract: 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 $A_3^{(1)}$ surface in Sakai's classification.

Key words and phrases: orthogonal polynomials Painlevé equations scattering theory.

MSC: 33E17, 34L25, 39A45, 42C05

Received: July 6, 2010; in revised form June 18, 2013

Language: English

DOI: 10.17323/1609-4514-2014-14-1-1-27

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