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Moscow Mathematical Journal, 2014, Volume 14, Number 1, Pages 1–27
DOI: https://doi.org/10.17323/1609-4514-2014-14-1-1-27
(Mi mmj512)
 

This article is cited in 3 scientific papers (total 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
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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.
Received: July 6, 2010; in revised form June 18, 2013
Bibliographic databases:
Document Type: Article
Language: English
Citation: Philippe Biane, “Orthogonal polynomials on the unit circle, $q$-Gamma weights, and discrete Painlevé equations”, Mosc. Math. J., 14:1 (2014), 1–27
Citation in format AMSBIB
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\by Philippe~Biane
\paper Orthogonal polynomials on the unit circle, $q$-Gamma weights, and discrete Painlev\'e equations
\jour Mosc. Math.~J.
\yr 2014
\vol 14
\issue 1
\pages 1--27
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\crossref{https://doi.org/10.17323/1609-4514-2014-14-1-1-27}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3221944}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000342789200001}
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  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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