Wiman–Valiron Theory for a Polynomial Series Based on the Askey–Wilson Operator

We establish a Wiman–Valiron theory of polynomial series based on the Askey–Wilson operator $${\mathcal {D}}_q$$ , where $$q\in (0,1)$$ . For an entire function f log-order smaller than 2, this includes (i) estimate which shows that behaves locally like consisting terms near maximal term its expansion, and (ii) {D}}_q^n f$$ compared to f. then apply in studying growth solutions difference equations involving operator.