\[U\left(a,x+y\right)=e^{-\frac{1}{2}xy-\frac{1}{4}y^{2}}\sum_{m=0}^{\infty}%
\genfrac{(}{)}{0.0pt}{}{-a-\tfrac{1}{2}}{m}y^{m}U\left(a+m,x\right),\]