Tau-function constructions of the recurrence coefficients of orthogonal polynomials

DOI10.1006/aama.1997.0574zbMath0930.42012OpenAlexW2026887570MaRDI QIDQ1271887

Yang Chen, Mourad E. H. Ismail, Walter Van Assche

Publication date: 24 January 1999

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/aama.1997.0574

zbMATH Keywords

asymptoticsorthogonal polynomialsFreud weightsexponential weightsErdős weightasymptotic behaviour of recurrence coefficients

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

Semiclassical orthogonal polynomial systems on nonuniform lattices, deformations of the Askey table, and analogues of isomonodromy ⋮ Hankel determinant and orthogonal polynomials for a perturbed Gaussian weight: From finite n to large n asymptotics ⋮ The relationship between semiclassical Laguerre polynomials and the fourth Painlevé equation ⋮ Equations of motion for zeros of orthogonal polynomials related to the Toda lattices ⋮ Asymptotics of determinants of Hankel matrices via non-linear difference equations

Cites Work

• A survey of general orthogonal polynomials for weights on finite and infinite intervals
• An update on orthogonal polynomials and weighted approximation on the real line
• Asymptotics for orthogonal polynomials
• Analytic theory of singular difference equations
• Statistical Theory of the Energy Levels of Complex Systems. I
• On the Largest Zeroes of Orthogonal Polynomials for Certain Weights
• Asymptotics of the largest zeros of some orthogonal polynomials
• Some eigenvalue distribution functions of the Laguerre ensemble
• Hermitean Matrix Ensembles and Orthogonal Polynomials
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