A characterization of classical and semiclassical orthogonal polynomials from their dual polynomials

DOI10.1016/j.cam.2004.01.031zbMath1054.33005OpenAlexW1977239245MaRDI QIDQ1883471

Luc Vinet, Alexei Zhedanov

Publication date: 12 October 2004

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2004.01.031

zbMATH Keywords

Classical orthogonal polynomialsSemiclassical orthogonal polynomials

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05)

Related Items (15)

Zeros of quasi-orthogonal Jacobi polynomials ⋮ Toda chain, Stieltjes function, and orthogonal polynomials ⋮ The uniqueness of an orthogonality measure ⋮ Stieltjes interlacing of zeros of little \(q\)-Jacobi and \(q\)-Laguerre polynomials from different sequences ⋮ Freezing limits for Calogero–Moser–Sutherland particle models ⋮ Interlacing properties and bounds for zeros of some quasi-orthogonal Laguerre polynomials ⋮ Orthogonal polynomials for self-dual weights ⋮ The theorems of Stieltjes and Favard ⋮ Interlacing of zeros of Gegenbauer polynomials of non-consecutive degree from different sequences ⋮ Bounds for zeros of Meixner and Kravchuk polynomials ⋮ Bounds for extreme zeros of some classical orthogonal polynomials ⋮ Limit theorems and soft edge of freezing random matrix models via dual orthogonal polynomials ⋮ Freezing limits for beta-Cauchy ensembles ⋮ Ramanujan's trigonometric sums and orthogonal polynomials on the unit circle ⋮ The average search probabilities of discrete-time quantum walks

Cites Work

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• Toda-type differential equations for the recurrence coefficients of orthogonal polynomials and Freud transformation
• Prolégomènes à l'étude des polynômes orthogonaux semi- classiques. (Preliminary remarks for the study of semi-classical orthogonal polynomials)
• On a new characterization of the classical orthogonal polynomials
• Variations around classical orthogonal polynomials. Connected problems
• Finite sequences of orthogonal polynomials connected by a Jacobi matrix
• Duality of orthogonal polynomials on a finite set
• Finitely many mass points on the line under the influence of an exponential potential -- an integrable system
• On Toda lattices and orthogonal polynomials

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