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