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