CAOP

\[ \begin{align} H_n(x;a|q) &= a^{-n} \sum_{k=0}^\infty \frac{(q^{-n};q)_k (a e^{i \theta};q)_k (a e^{-i \theta};q)_k}{(q;q)_k} q^k\\ &= a^{-n} {}_{3}\phi_{2}\!\left(\left. {q^{-n}, a e^{i \theta}, a e^{-i\theta} \atop 0, 0} \; \right| q ; q \right),\quad x=\cos(\theta) \end{align} \]