CAOP

\[ \begin{align} h_n(x;q) &= i^{-n} q^{-{n \choose 2}} \sum_{k=0}^\infty \frac{(q^{-n};q)_k (ix;q)_k}{(q;q)_k} q^{-{k \choose 2}} \left(q^n\right)^k\\ &= i^{-n} q^{-{n \choose 2}} {}_{2}\phi_{0}\!\left(\left. {q^{-n}, ix \atop -} \; \right| q ; -q^n \right) \end{align} \]