  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 $\mathrm{Ai}(x)$
as $q \to 1$.
