Formula:7742

Digital Library of Mathematical Functions ID 22.12.E11

${\displaystyle{\displaystyle 2K\operatorname{ns}\left(2Kt,k\right)=\sum_{n=-\infty}^{\infty}\frac{\pi}{\sin\left(\pi(t-n\tau)\right)}=\sum_{n=-\infty}^{\infty}\left(\sum_{m=-\infty}^{\infty}\frac{(-1)^{m}}{t-m-n\tau}\right),}}$

Symbols List

• ${\displaystyle{\displaystyle\operatorname{ns}\left(\NVar{z},\NVar{k}\right)}}$: Jacobian elliptic function
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle K\left(\NVar{k}\right)}}$: Legendre’s complete elliptic integral of the first kind
• ${\displaystyle{\displaystyle\sin\NVar{z}}}$: sine function
• ${\displaystyle{\displaystyle k}}$: modulus
• ${\displaystyle{\displaystyle\tau}}$: ratio
 

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