\[{F_{2}}\left(\alpha;\beta,\beta^{\prime};\gamma,\gamma^{\prime};x,y\right)=(1-%
x)^{-\alpha}{F_{2}}\left(\alpha;\gamma-\beta,\beta^{\prime};\gamma,\gamma^{%
\prime};\frac{x}{x-1},\frac{y}{1-x}\right),\]