\[2iKk\operatorname{cn}\left(2Kt,k\right)=\sum_{n=-\infty}^{\infty}\frac{(-1)^{n%
}\pi}{\sin\left(\pi(t-(n+\frac{1}{2})\tau)\right)}=\sum_{n=-\infty}^{\infty}%
\left(\sum_{m=-\infty}^{\infty}\frac{(-1)^{m+n}}{t-m-(n+\frac{1}{2})\tau}%
\right),\]