Global asymptotics of Stieltjes-Wigert polynomials

Asymptotic formulas are derived for the Stieltjes-Wigert polynomials S _n(z; q) in the complex plane as the degree n grows to infinity. One formula holds in any disc centered at the origin, and the other holds outside any smaller disc centered at the origin; the two regions together cover the whole plane. In each region, the q-Airy function A_q(z) is used as the approximant. For real x > 1/4, a limiting relation is also established between the q-Airy function A_q(x) and the ordinary Airy function Ai(x) as q → 1. © 2013 World Scientific Publishing Company.