\[\left(\frac{z+\zeta}{z-\zeta}\right)^{\frac{1}{2}\nu}{H^{(2)}_{\nu}}\left((z^{%
2}-\zeta^{2})^{\frac{1}{2}}\right)=-\frac{1}{\pi i}e^{\frac{1}{2}\nu\pi i}\int%
_{-\infty}^{\infty}e^{-iz\cosh t-i\zeta\sinh t-\nu t}\,\mathrm{d}t,\]