Scaled asymptotics for some q-functions

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 Aq(z) (a.k.a. q-Airy function), Jacksonʼs q-Bessel function , q−1-Hermite polynomials hn(x|q), Stieltjes–Wigert polynomials Sn(x;q), q-Laguerre polynomials and confluent basic hypergeometric series.