\[\int_{0}^{\infty}e^{-zt}t^{b-1}U\left(a,c,t\right)\,\mathrm{d}t=\Gamma\left(b%
\right)\Gamma\left(b-c+1\right)\*z^{-b}{{}_{2}{\mathbf{F}}_{1}}\left(a,b;a+b-c%
+1;1-\frac{1}{z}\right),\]