\[G_{3}(\alpha,\alpha^{\prime};x,y)=\sum_{m,n=0}^{\infty}\frac{\Gamma\left(%
\alpha+2n-m\right)\Gamma\left(\alpha^{\prime}+2m-n\right)}{\Gamma\left(\alpha%
\right)\Gamma\left(\alpha^{\prime}\right)}\frac{x^{m}y^{n}}{m!n!},\]