Discrete orthogonal polynomials with hypergeometric weights and Painlevé VI

DOI10.3842/SIGMA.2018.088zbMath1400.33016arXiv1804.02856MaRDI QIDQ1792491

Walter Van Assche, Galina Filipuk

Publication date: 12 October 2018

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.02856

zbMATH Keywords

discrete orthogonal polynomialsdiscrete Painlevé equationsPainlevé VIhypergeometric weights

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Painlevé-type functions (33E17)

Related Items (12)

Orthogonal polynomials, Toda lattices and Painlevé equations ⋮ Discrete semiclassical orthogonal polynomials of class 2 ⋮ Comparative asymptotics for discrete semiclassical orthogonal polynomials ⋮ Differential equations for the recurrence coefficients of semiclassical orthogonal polynomials and their relation to the Painlevé equations via the geometric approach ⋮ Pearson equations for discrete orthogonal polynomials: I. Generalized hypergeometric functions and Toda equations ⋮ Laguerre–Freud equations for three families of hypergeometric discrete orthogonal polynomials ⋮ Asymptotic behaviours of \(q\)-orthogonal polynomials from a \(q\)-Riemann Hilbert problem ⋮ Recurrence relations for the moments of discrete semiclassical functionals of class s≤2 ⋮ Pearson equations for discrete orthogonal polynomials. III: Christoffel and Geronimus transformations ⋮ Recurrence coefficients of Toda-type orthogonal polynomials I. Asymptotic analysis ⋮ Differential and difference equations for recurrence coefficients of orthogonal polynomials with hypergeometric weights and Bäcklund transformations of the sixth Painlevé equation ⋮ Recurrence coefficients for discrete orthogonal polynomials with hypergeometric weight and discrete Painlevé equations

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