Scaled Asymptotics For Some $q$-Series

Abstract

In this work we investigate the asymptotics for Euler's $q$-Exponential $E_q(z)$, $q$-Gamma function ${\Gamma }_q(z)$, Ramanujan's function $A_q(z)$, Jackson's $q$-Bessel function $J_{\nu }^{(2)}$(z;q) of second kind, Stieltjes-Wigert orthogonal polynomials $S_n(x;q)$ and $q$-Laguerre polynomials $L_n^{(\alpha )}(x;q)$ as $q$ approaching 1.

18pages