Abstract
We derive Plancherel-Rotach asymptotic expansions for the q−1-Hermite, q-Laguerre, and Stieltjes-Wigert polynomials using a discrete analogue of Laplace's method. 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.
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