CAOP

\[ \begin{align} p_n(x;a,b,c|q) &= a^{-n} e^{-inu} (abe^{2iu}, a c, a d; q)_n \sum_{k=0}^\infty \frac{(q^{-n};q)_k (abcdq^{n-1};q)_k (ae^{i(t+2u};q)_k (ae^{-it};q)_k}{(abe^{2iu};q)_k (ac;q)_k (ad;q)_k (q;q)_k} q^k\\ &= a^{-n} e^{-inu} (abe^{2iu}, a c, a d; q)_n {}_{4}\phi_{3}\!\left(\left. {q^{-n}, abcdq^{n-1}, ae^{i(t+2u)}, a e^{-it} \atop abe^{2iu}, ac, ad} \; \right| q ; q \right),\quad x=\cos(t+u) \end{align} \]