\[\left(\frac{z+\zeta}{z-\zeta}\right)^{\frac{1}{2}\nu}Y_{\nu}\left((z^{2}-\zeta%
^{2})^{\frac{1}{2}}\right)=\frac{1}{\pi}\int_{0}^{\pi}e^{\zeta\cos\theta}\sin%
\left(z\sin\theta-\nu\theta\right)\,\mathrm{d}\theta-\frac{1}{\pi}\int_{0}^{%
\infty}\left(e^{\nu t+\zeta\cosh t}+e^{-\nu t-\zeta\cosh t}\cos\left(\nu\pi%
\right)\right)\*e^{-z\sinh t}\,\mathrm{d}t,\]