CAOP

\[ \begin{align} H_n(x|q) &= e^{in\theta} \sum_{k=0}^\infty \frac{(q^{-n};q)_k}{(q;q)_k} (-1)^k q^{-{k \choose 2}} \left(q^ne^{-2i\theta}\right)^k\\ &= e^{in\theta} {}_{2}\phi_{0}\!\left(\left. {q^{-n}, 0 \atop -} \; \right| q ; q^ne^{-2i\theta} \right),\quad x=\cos(\theta) \end{align} \]