Scaled asymptotics for some q-functions

Abstract

In this work we investigate Plancherel–Rotach type asymptotics for some q-series as q → 1 in a more general setting by introducing admissible sequences. These q-series generalize Ramanujan function A q ( z ) (a.k.a. q-Airy function), Jacksonʼs q-Bessel function J ν ( 2 ) ( z ; q ) , q − 1 -Hermite polynomials h n ( x | q ) , Stieltjes–Wigert polynomials S n ( x ; q ) , q-Laguerre polynomials L n ( α ) ( x ; q ) and confluent basic hypergeometric series.