CAOP

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