\[\frac{{\mathrm{d}}^{2}}{{\mathrm{d}z}^{2}}\operatorname{nd}\left(z,k\right)=(1%
+{k^{\prime}}^{2})\operatorname{nd}\left(z,k\right)-2{k^{\prime}}^{2}{%
\operatorname{nd}}^{3}\left(z,k\right),\]