q-Discrete Painlevé equations for recurrence coefficients of modifiedq-Freud orthogonal polynomials

DOI10.1080/10236190802392435zbMath1189.39009arXiv0808.0982OpenAlexW2149898356MaRDI QIDQ5187737

Walter Van Assche, Christophe Smet, Lies Boelen

Publication date: 1 March 2010

Published in: Journal of Difference Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0808.0982

zbMATH Keywords

orthogonal polynomialsrecurrence relationsdiscrete Painlevé equationsingularity confinement

Mathematics Subject Classification ID

Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Difference equations, scaling ((q)-differences) (39A13) Other special orthogonal polynomials and functions (33C47)

Related Items (7)

Asymptotic behaviours of \(q\)-orthogonal polynomials from a \(q\)-Riemann Hilbert problem ⋮ Asymptotics of discrete q-Freud II orthogonal polynomials from the q-Riemann Hilbert problem ⋮ Nonlinear equations for the recurrence coefficients of discrete orthogonal polynomials ⋮ Non linear difference equations arising from a deformation of the \(q\)-Laguerre weight ⋮ Unique positive solutions to q-discrete equations associated with orthogonal polynomials ⋮ On the Recurrence Coefficients for Generalized q-Laguerre Polynomials ⋮ On Laurent biorthogonal polynomials and Painlevé-type equations

Cites Work

• Unnamed Item
• Nonnegative solutions of a nonlinear recurrence
• Discrete Painlevé equations and their appearance in quantum gravity
• On a \(q\)-deformation of the discrete Painlevé I equation and \(q\)- orthogonal polynomials
• A differential equation for orthogonal polynomials
• On q-Exponential Functions for |q| = 1
• Discrete versions of the Painlevé equations
• Do integrable mappings have the Painlevé property?

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