\[V\left(a,z\right)=\sqrt{\frac{2}{\pi}}\frac{e^{\frac{1}{4}z^{2}}z^{a-\frac{1}{%
2}}}{2\pi i\Gamma\left(\frac{1}{2}-a\right)}\*\int_{-i\infty}^{i\infty}\Gamma%
\left(t\right)\Gamma\left(\tfrac{1}{2}-a-2t\right)2^{t}z^{2t}\cos\left(\pi t%
\right)\,\mathrm{d}t,\]