Ladder operators for \(q\)-orthogonal polynomials

DOI10.1016/j.jmaa.2008.03.031zbMath1154.33010arXiv0711.2454OpenAlexW2143446835MaRDI QIDQ930969

Mourad E. H. Ismail, Yang Chen

Publication date: 24 June 2008

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0711.2454

zbMATH Keywords

difference equationsmoment problemsorthogonal polynomials and their \(q\)-analogues

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Additive difference equations (39A10) Moment problems (44A60) Difference equations, scaling ((q)-differences) (39A13) Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.) (33D52)

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Cites Work

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• Estimates of the Hermite and the Freud polynomials
• Estimates of asymmetric Freud polynomials on the real line
• Bounds for certain Freud-type orthogonal polynomials
• The q-analogue of the Laguerre polynomials
• Difference equations and quantized discriminants for \(q\)-orthogonal polynomials
• The moment problem associated with the Stieltjes-Wigert polynomials
• Difference equations and discriminants for discrete orthogonal polynomials
• Ladder operators and differential equations for orthogonal polynomials
• Jacobi polynomials from compatibility conditions