Plancherel–Rotach asymptotics for some q-orthogonal polynomials with complex scalings

In this work we study the Plancherel–Rotach type asymptotics for Stieltjes–Wigert, q-Laguerre and Ismail–Masson orthogonal polynomials with complex scalings. The main terms of the asymptotics for Stieltjes–Wigert and q-Laguerre polynomials (Ismail–Masson polynomials) contain Ramanujan function Aq(z) for scaling parameters above the vertical line R(s)=2 (); the main terms of the asymptotics involve theta function for scaling parameters in the vertical strip 0