\[U\left(\tfrac{1}{2}a+\tfrac{3}{4},\tfrac{3}{2},\tfrac{1}{2}z^{2}\right)=2^{%
\frac{1}{2}a+\frac{3}{4}}\frac{e^{\frac{1}{4}z^{2}}}{z}U\left(a,z\right).\]