\[{H^{(1)}_{\nu}}\left(z\right)=i\csc\left(\nu\pi\right)\left(e^{-\nu\pi i}J_{%
\nu}\left(z\right)-J_{-\nu}\left(z\right)\right)=\csc\left(\nu\pi\right)\left(%
Y_{-\nu}\left(z\right)-e^{-\nu\pi i}Y_{\nu}\left(z\right)\right),\]