\[\int_{0}^{\infty}t^{\lambda-1}U\left(a,b,t\right)\,\mathrm{d}t=\frac{\Gamma%
\left(\lambda\right)\Gamma\left(a-\lambda\right)\Gamma\left(\lambda-b+1\right)%
}{\Gamma\left(a\right)\Gamma\left(a-b+1\right)},\]