CAOP

\[ \begin{align} K_n^{qtm}(q^{-x};p,N;q) &= \sum_{k=0}^\infty \frac{(q^{-n};q)_k (q^{-x};q)_k}{(q^{-N};q)_k (q;q)_k} \left(pq^{n+1}\right)^k\\ &= {}_{2}\phi_{1}\!\left(\left. {q^{-n}, q^{-x} \atop q^{-N}} \; \right| q ; p q^{n+1} \right) \end{align} \]