\[k^{2}{\operatorname{sn}}^{2}\left(z,k\right)=\frac{{E^{\prime}}}{{K^{\prime}}}%
-\left(\frac{\pi}{2{K^{\prime}}}\right)^{2}\sum_{n=-\infty}^{\infty}\left({%
\operatorname{sech}}^{2}\left(\frac{\pi}{2{K^{\prime}}}(z-2nK)\right)\right),\]