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