\[\Phi^{(1)}\left(a;b,b^{\prime};c;q;x,y\right)=\sum_{m,n\geq 0}\frac{\left(a;q%
\right)_{m+n}\left(b;q\right)_{m}\left(b^{\prime};q\right)_{n}x^{m}y^{n}}{%
\left(q;q\right)_{m}\left(q;q\right)_{n}\left(c;q\right)_{m+n}},\]