\[{\operatorname{sn}}^{2}\left(z,k\right)=\frac{1}{k^{2}}\left(1-\frac{E}{K}%
\right)-\frac{2\pi^{2}}{k^{2}K^{2}}\sum_{n=1}^{\infty}\frac{nq^{n}}{1-q^{2n}}%
\cos\left(2n\zeta\right).\]