Scaled asymptotics for some q-functions

AbstractIn 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 Jν(2)(z;q), q−1-Hermite polynomials hn(x|q), Stieltjes–Wigert polynomials Sn(x;q), q-Laguerre polynomials Ln(α)(x;q) and confluent basic hypergeometric series