Recurrence coefficients of generalized Charlier polynomials and the fifth Painlevé equation

DOI10.1090/S0002-9939-2012-11468-6zbMath1269.34095arXiv1106.2959MaRDI QIDQ4908270

Walter Van Assche, Galina Filipuk

Publication date: 5 March 2013

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1106.2959

zbMATH Keywords

orthogonal polynomialsBäcklund transformationsclassical solutionsPainlevé equationsrecurrence coefficients

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Other special orthogonal polynomials and functions (33C47) Painlevé-type functions (33E17)

Related Items (13)

Classical solutions of the degenerate fifth Painlevé equation ⋮ Polynomial sequences associated with the moments of hypergeometric weights ⋮ Pearson equations for discrete orthogonal polynomials: I. Generalized hypergeometric functions and Toda equations ⋮ Laguerre–Freud equations for three families of hypergeometric discrete orthogonal polynomials ⋮ The relationship between semiclassical Laguerre polynomials and the fourth Painlevé equation ⋮ Discrete orthogonal polynomials with hypergeometric weights and Painlevé VI ⋮ On the Recurrence Coefficients for Generalized q-Laguerre Polynomials ⋮ Pearson equations for discrete orthogonal polynomials. III: Christoffel and Geronimus transformations ⋮ Recurrence coefficients of Toda-type orthogonal polynomials I. Asymptotic analysis ⋮ The generalized Krawtchouk polynomials and the fifth Painlevé equation ⋮ On the recurrence coefficients of the generalized littleq-Laguerre polynomials ⋮ Differential and difference equations for recurrence coefficients of orthogonal polynomials with hypergeometric weights and Bäcklund transformations of the sixth Painlevé equation ⋮ Pointwise asymptotics of the ratio of Jacobi-type polynomials

Uses Software

• DLMF

Cites Work

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• Recurrence coefficients of a new generalization of the Meixner polynomials
• Orthogonal polynomials on a bi-lattice
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• Recurrence coefficients of generalized Meixner polynomials and Painlevé equations
• From the continuous PV to discrete Painlev$eacute$ equations
• On a unified approach to transformations and elementary solutions of Painlevé equations
• Analysis of Non-Linear Recurrence Relations for the Recurrence Coefficients of Generalized Charlier Polynomials

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