CAOP

\[ \begin{align} P_n(x;a,b;q) &= \frac{1}{(b^{-1}q^{-n};q)_n} \sum_{k=0}^\infty \frac{(q^{-n};q)_k (aqx^{-1};q)_k}{(aq;q)_k (q;q)_k}\left(\frac{x}{b}\right)^k\\ &= \frac{1}{(b^{-1}q^{-n};q)_n} {}_{2}\phi_{1}\!\left(\left. {q^{-n}, aqx^{-1}\atop a q} \; \right| q ; \frac{x}{b} \right) \end{align} \]