CAOP

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