\[\mathbf{H}_{\nu}\left(z\right)=\frac{4}{\pi^{1/2}\Gamma\left(\nu+\tfrac{1}{2}%
\right)}\*\sum_{k=0}^{\infty}\frac{(2k+\nu+1)\Gamma\left(k+\nu+1\right)}{k!(2k%
+1)(2k+2\nu+1)}J_{2k+\nu+1}\left(z\right),\]