\[x(1-x)\frac{{\partial}^{2}{F_{1}}}{{\partial x}^{2}}+y(1-x)\frac{\,{\partial}^%
{2}{F_{1}}}{\,\partial x\,\partial y}+\left(\gamma-(\alpha+\beta+1)x\right)%
\frac{\partial{F_{1}}}{\partial x}-\beta y\frac{\partial{F_{1}}}{\partial y}-%
\alpha\beta{F_{1}}=0,\]