\[\int_{0}^{\infty}e^{-\frac{3}{4}t^{2}}t^{-a-\frac{3}{2}}U\left(a,t\right)\,%
\mathrm{d}t=2^{\frac{1}{4}+\frac{1}{2}a}\Gamma\left(-a-\tfrac{1}{2}\right)\cos%
\left((\tfrac{1}{4}a+\tfrac{1}{8})\pi\right),\]