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