\[\int_{0}^{\infty}x^{a-1}e^{-sx}\gamma\left(b,x\right)\,\mathrm{d}x=\frac{%
\Gamma\left(a+b\right)}{b(1+s)^{a+b}}\*F\left(1,a+b;1+b;1/(1+s)\right),\]