\[{F_{3}}\left(\alpha,\alpha^{\prime};\beta,\beta^{\prime};\gamma;x,y\right)=%
\frac{\Gamma\left(\gamma\right)}{\Gamma\left(\beta\right)\Gamma\left(\beta^{%
\prime}\right)\Gamma\left(\gamma-\beta-\beta^{\prime}\right)}\iint_{\Delta}%
\frac{u^{\beta-1}v^{\beta^{\prime}-1}(1-u-v)^{\gamma-\beta-\beta^{\prime}-1}}{%
(1-ux)^{\alpha}(1-vy)^{\alpha^{\prime}}}\,\mathrm{d}u\,\mathrm{d}v,\]