\[{F_{4}}\left(\alpha,\beta;\gamma,\gamma^{\prime};x(1-y),y(1-x)\right)=\sum_{k=%
0}^{\infty}\frac{{\left(\alpha\right)_{k}}{\left(\beta\right)_{k}}{\left(%
\alpha+\beta-\gamma-\gamma^{\prime}+1\right)_{k}}}{{\left(\gamma\right)_{k}}{%
\left(\gamma^{\prime}\right)_{k}}k!}x^{k}y^{k}{{}_{2}F_{1}}\left({\alpha+k,%
\beta+k\atop\gamma+k};x\right){{}_{2}F_{1}}\left({\alpha+k,\beta+k\atop\gamma^%
{\prime}+k};y\right);\]