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