\[{{}_{r}\psi_{s}}\left({a_{1},a_{2},\dots,a_{r}\atop b_{1},b_{2},\dots,b_{s}};q%
,z\right)={{}_{r}\psi_{s}}\left(a_{1},a_{2},\dots,a_{r};b_{1},b_{2},\dots,b_{s%
};q,z\right)=\sum_{n=-\infty}^{\infty}\frac{\left(a_{1},a_{2},\dots,a_{r};q%
\right)_{n}(-1)^{(s-r)n}q^{(s-r)\genfrac{(}{)}{0.0pt}{}{n}{2}}z^{n}}{\left(b_{%
1},b_{2},\dots,b_{s};q\right)_{n}}=\sum_{n=0}^{\infty}\frac{\left(a_{1},a_{2},%
\dots,a_{r};q\right)_{n}(-1)^{(s-r)n}q^{(s-r)\genfrac{(}{)}{0.0pt}{}{n}{2}}z^{%
n}}{\left(b_{1},b_{2},\dots,b_{s};q\right)_{n}}+\sum_{n=1}^{\infty}\frac{\left%
(q/b_{1},q/b_{2},\dots,q/b_{s};q\right)_{n}}{\left(q/a_{1},q/a_{2},\dots,q/a_{%
r};q\right)_{n}}\left(\frac{b_{1}b_{2}\cdots b_{s}}{a_{1}a_{2}\cdots a_{r}z}%
\right)^{n}.\]