Formula:7964

Digital Library of Mathematical Functions ID 23.6.E28

${\displaystyle{\displaystyle\zeta\left(z|\mathbb{L}_{\mspace{1.0mu }2}\right)-\zeta\left(z+2K|\mathbb{L}_{\mspace{1.0mu }2}\right)+\zeta\left(2K|\mathbb{L}_{\mspace{1.0mu }2}\right)=\operatorname{ds}\left(z,k\right),}}$

Symbols List

• ${\displaystyle{\displaystyle\operatorname{ds}\left(\NVar{z},\NVar{k}\right)}}$: Jacobian elliptic function
• ${\displaystyle{\displaystyle\zeta\left(\NVar{z}\right)}}$: 23.2.E5
• ${\displaystyle{\displaystyle K\left(\NVar{k}\right)}}$: Legendre’s complete elliptic integral of the first kind
• ${\displaystyle{\displaystyle\mathbb{L}}}$: lattice
• ${\displaystyle{\displaystyle z}}$: complex
• ${\displaystyle{\displaystyle k}}$: modulus
 

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