\[\int z^{-\nu}\mathbf{H}_{\nu+1}\left(z\right)\,\mathrm{d}z=-z^{-\nu}\mathbf{H}%
_{\nu}\left(z\right)+\frac{2^{-\nu}z}{\sqrt{\pi}\Gamma\left(\nu+\tfrac{3}{2}%
\right)},\]