\[H\left(a,u\right)=\frac{a}{\pi}\int_{-\infty}^{\infty}\frac{e^{-t^{2}}\,%
\mathrm{d}t}{(u-t)^{2}+a^{2}}=\frac{1}{a\sqrt{\pi}}\mathsf{U}\left(\frac{u}{a}%
,\frac{1}{4a^{2}}\right).\]