\[{{}_{q+1}F_{q}}\left({a_{1},\dots,a_{q+1}\atop b_{1},\dots,b_{q}};z\right)=%
\sum_{j=1}^{q+1}\left({\textstyle\ifrac{\prod\limits_{\begin{subarray}{c}k=1\\
k\neq j\end{subarray}}^{q+1}\frac{\Gamma\left(a_{k}-a_{j}\right)}{\Gamma\left(%
a_{k}\right)}}{\prod\limits_{k=1}^{q}\frac{\Gamma\left(b_{k}-a_{j}\right)}{%
\Gamma\left(b_{k}\right)}}}\right)\widetilde{w}_{j}(z),\]