Orthogonal polynomials on a bi-lattice

DOI10.1007/s00365-011-9145-8zbMath1262.34103arXiv1101.1817OpenAlexW2109979374MaRDI QIDQ714942

Walter Van Assche, Christophe Smet

Publication date: 12 October 2012

Published in: Constructive Approximation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1101.1817

zbMATH Keywords

Meixner polynomialsdiscrete orthogonal polynomialsdiscrete Painlevé equationsCharlier polynomialsrecurrence coefficientsnon-linear recurrence relations

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) Discrete version of topics in analysis (39A12) Other special orthogonal polynomials and functions (33C47) Numerical aspects of recurrence relations (65Q30)

Related Items (16)

Classical solutions of the degenerate fifth Painlevé equation ⋮ Laguerre-Freud equations for Generalized Hahn polynomials of type I ⋮ Power series expansion of a Hankel determinant ⋮ 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 ⋮ Asymptotic analysis of a family of Sobolev orthogonal polynomials related to the generalized Charlier polynomials ⋮ Orthogonal and Multiple Orthogonal Polynomials, Random Matrices, and Painlevé Equations ⋮ On differential systems related to generalized Meixner and deformed Laguerre orthogonal polynomials ⋮ Recurrence coefficients of generalized Charlier polynomials and the fifth Painlevé equation ⋮ Discrete orthogonal polynomials with hypergeometric weights and Painlevé VI ⋮ 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 Laurent biorthogonal polynomials and Painlevé-type equations

Uses Software

• DLMF

Cites Work

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• Painlevé V and a Pollaczek-Jacobi type orthogonal polynomials
• Nonlinear equations for the recurrence coefficients of discrete orthogonal polynomials
• Painlevé III and a singular linear statistics in Hermitian random matrix ensembles. I.
• Recurrence coefficients of generalized Meixner polynomials and Painlevé equations
• Painlevé IV and degenerate Gaussian unitary ensembles
• Hypergeometric Orthogonal Polynomials and Their q-Analogues
• Painlevé VI and the Unitary Jacobi Ensembles
• Painlevé V and the distribution function of a discontinuous linear statistic in the Laguerre unitary ensembles
• Ladder operators and differential equations for orthogonal polynomials
• Extremal Polynomials on Discrete Sets
• Orthogonal polynomials with discontinuous weights
• Analysis of Non-Linear Recurrence Relations for the Recurrence Coefficients of Generalized Charlier Polynomials
• Painlevé V and time-dependent Jacobi polynomials

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