CAOP

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