CAOP

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