\[2iKk^{\prime}\operatorname{nd}\left(2Kt,k\right)=\lim_{N\to\infty}\sum_{n=-N}^%
{N}(-1)^{n}\frac{\pi}{\tan\left(\pi(t+\frac{1}{2}-(n+\frac{1}{2})\tau)\right)}%
=\lim_{N\to\infty}\sum_{n=-N}^{N}(-1)^{n}\lim_{M\to\infty}\left(\sum_{m=-M}^{M%
}\frac{1}{t+\frac{1}{2}-m-(n+\frac{1}{2})\tau}\right),\]