CAOP

$$\begin{align} R_n(\lambda(x);b,c,d,N;q) &= \sum_{k=0}^\infty \frac{(q^{-n};q)_k (bq^{n-N};q)_k (q^{-x};q)_k (c d q^{x+1};q)_k}{(q^{-N};q)_k (bdq;q)_k (cq;q)_k (q;q)_k} q^k\\ &= {}_{4}\phi_{3}\!\left(\left. {q^{-n}, bq^{n-N}, q^{-x}, cdq^{x+1} \atop q^{-N}, bdq, cq} \; \right| q ; q \right) \end{align}$$