Recurrence coefficients for discrete orthonormal polynomials and the Painlevé equations

DOI10.1088/1751-8113/46/18/185205zbMath1275.34109arXiv1301.2396OpenAlexW1966691026MaRDI QIDQ4923836

Peter A. Clarkson

Publication date: 27 May 2013

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.2396

zbMATH Keywords

Painlevé equationHankel determinantWronskianHamiltonian structureBessel functionPearson equationdiscrete Charlier polynomialsdiscrete Meixner polynomials

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55)

Related Items (15)

The Padé interpolation method applied to \(q\)-Painlevé equations. II (differential grid version) ⋮ Polynomial sequences associated with the moments of hypergeometric weights ⋮ A hidden analytic structure of the Rabi model ⋮ Comparative asymptotics for discrete semiclassical orthogonal polynomials ⋮ Pearson equations for discrete orthogonal polynomials: I. Generalized hypergeometric functions and Toda equations ⋮ Laguerre–Freud equations for three families of hypergeometric discrete orthogonal polynomials ⋮ Recurrence relations for the moments of discrete semiclassical functionals of class s≤2 ⋮ Orthogonal and Multiple Orthogonal Polynomials, Random Matrices, and Painlevé Equations ⋮ The relationship between semiclassical Laguerre polynomials and the fourth Painlevé equation ⋮ The Padé interpolation method applied to \(q\)-Painlevé equations ⋮ A representation of joint moments of CUE characteristic polynomials in terms of Painlevé functions ⋮ Discrete orthogonal polynomials with hypergeometric weights and Painlevé VI ⋮ The Padé interpolation method applied to additive difference Painlevé equations ⋮ A q-generalization of the Toda equations for the q-Laguerre/Hermite orthogonal polynomials ⋮ Pearson equations for discrete orthogonal polynomials. III: Christoffel and Geronimus transformations

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