\[{H^{(2)}_{\nu}}\left(z\right)=\frac{e^{\frac{1}{2}\nu\pi i}}{2\pi^{2}}\int_{c-%
i\infty}^{c+i\infty}\Gamma\left(t\right)\Gamma\left(t-\nu\right)(\tfrac{1}{2}%
iz)^{\nu-2t}\,\mathrm{d}t,\]