\[\sin\left(\nu\pi\right){H^{(2)}_{\nu}}\left(ze^{m\pi i}\right)=e^{\nu\pi i}%
\sin\left(m\nu\pi\right){H^{(1)}_{\nu}}\left(z\right)+\sin\left((m+1)\nu\pi%
\right){H^{(2)}_{\nu}}\left(z\right).\]