\[x(1-x)\frac{{\partial}^{2}{F_{4}}}{{\partial x}^{2}}-2xy\frac{\,{\partial}^{2}%
{F_{4}}}{\,\partial x\,\partial y}-y^{2}\frac{{\partial}^{2}{F_{4}}}{{\partial
y%
}^{2}}+\left(\gamma-(\alpha+\beta+1)x\right)\frac{\partial{F_{4}}}{\partial x}%
-(\alpha+\beta+1)y\frac{\partial{F_{4}}}{\partial y}-\alpha\beta{F_{4}}=0,\]