\[\gamma\left(a,x+y\right)-\gamma\left(a,x\right)=\Gamma\left(a,x\right)-\Gamma%
\left(a,x+y\right)=e^{-x}x^{a-1}\sum_{n=0}^{\infty}\frac{{\left(1-a\right)_{n}%
}}{(-x)^{n}}(1-e^{-y}e_{n}(y)),\]