CAOP

\[ \begin{align} P_n^{(\alpha)}(x|q) &= \frac{(q^{\alpha+1};q)_n}{(q;q)_n} \sum_{k=0}^\infty \frac{(q^{-n};q)_k (q^{1/2\alpha+1/4}e^{i \theta};q)_k (q^{1/2\alpha+1/4}e^{-i \theta};q)_k}{(q^{\alpha+1};q)_k (q;q)_k} q^k\\ &= \frac{(q^{\alpha+1};q)_n}{(q;q)_n} {}_{3}\phi_{2}\!\left(\left. {q^{-n}, q^{1/2\alpha+1/4}e^{i \theta}, q^{1/2\alpha+1/4}e^{-i \theta} \atop q^{\alpha+1}, 0} \; \right| q ; q \right),\quad x=\cos(\theta) \end{align} \]