Scaled Asymptotics For Q-Orthogonal Polynomials

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). © 2006 Académie des sciences