\[\operatorname{nd}\left(z,k\right)=\frac{\pi}{2Kk^{\prime}}+\frac{2\pi}{Kk^{%
\prime}}\sum_{n=1}^{\infty}\frac{(-1)^{n}q^{n}\cos\left(2n\zeta\right)}{1+q^{2%
n}}.\]