Plancherel-Rotach asymptotics for some \(q\)-orthogonal polynomials with complex scalings
type: Item
instance of: scholarly article
title: Plancherel-Rotach asymptotics for some \(q\)-orthogonal polynomials with complex scalings
zbMATH Open document ID: 1142.30015
author: Ruiming Zhang
published in: Advances in Mathematics
publication date: 2008-06-09T00:00:00Z
review text: After recalling some properties of \(q\)-series and generalized irrational measures the author presents the Plancherel-Rotach asymptotic formulas for Stieltjes-Wigert, \(q\)-Laguerre and Ismail-Masson orthogonal polynomials under complex scaling depending on two real parameters. They are orthogonal polynomials associated with indeterminant moment problem. According to the different cases where the two parameters of scaling are positive, rational or irrational the author shows that the main term of asymptotics may contain Ramanujan function \(A_q(z)\) or teta function. The obtained results gain some insight to the related random matrix model and number theory.
reviewed by: Jacek Gilewicz
Mathematics Subject Classification ID: 30E15
Mathematics Subject Classification ID: 33D45
zbMATH DE Number: 5285708
zbMATH Keywords: asymptotics under complex scaling
MaRDI profile type: Publication
full work available at URL: j.aim.2008.03.002
OpenAlex ID: W2026283634
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DOI: 10.1016/J.AIM.2008.03.002
description: scientific article; zbMATH DE number 5285708