\[(U\left(a,z\right))^{2}+(\overline{U}\left(a,z\right))^{2}=\frac{2^{\frac{3}{2%
}}}{\pi}\Gamma\left(\tfrac{1}{2}-a\right)\int_{0}^{\infty}\frac{e^{2at+\frac{1%
}{2}z^{2}\tanh t}}{\sqrt{\sinh\left(2t\right)}}\,\mathrm{d}t,\]