(q\)-Discrete Painlevé equations for recurrence coefficients of modified \(q\)-Freud orthogonal polynomials

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 specia...

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Bibliographic Details
Published in:arXiv.org 2008-08
Main Authors: Boelen, Lies, Smet, Christophe, Walter Van Assche
Format: Article
Language:English
Subjects:
Coefficients
Polynomials
Online Access:Get full text
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Summary: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 \(\alpha-q-P_V\).
ISSN:2331-8422