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