\[\mathbf{H}_{\nu}\left(z\right)=(\tfrac{1}{2}z)^{\nu+1}\sum_{n=0}^{\infty}\frac%
{(-1)^{n}(\tfrac{1}{2}z)^{2n}}{\Gamma\left(n+\tfrac{3}{2}\right)\Gamma\left(n+%
\nu+\tfrac{3}{2}\right)},\]