\[{F_{3}}\left(\alpha,\alpha^{\prime};\beta,\beta^{\prime};\gamma;x,y\right)=%
\sum_{m,n=0}^{\infty}\frac{{\left(\alpha\right)_{m}}{\left(\alpha^{\prime}%
\right)_{n}}{\left(\beta\right)_{m}}{\left(\beta^{\prime}\right)_{n}}}{{\left(%
\gamma\right)_{m+n}}m!n!}x^{m}y^{n},\]