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