Abstract

We summarize results of a forthcoming paper on Plancherel–Rotach asymptotic expansions for the q −1 -Hermite, q-Laguerre and Stieltjes–Wigert polynomials. The asymptotics in the bulk exhibit chaotic behavior when a certain variable is irrational. In the rational case the main terms in the asymptotic expansion involve theta functions. To cite this article: M.E.H. Ismail, R. Zhang, C. R. Acad. Sci. Paris, Ser. I 344 (2007).

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