Formula:7846

Digital Library of Mathematical Functions ID 22.16.E33

${\displaystyle{\displaystyle\mathrm{Z}\left(x+K|k\right)=\mathrm{Z}\left(x|k\right)-k^{2}\operatorname{sn}\left(x,k\right)\operatorname{cd}\left(x,k\right),}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{Z}\left(\NVar{x}|\NVar{k}\right)}}$: Jacobi’s zeta function
• ${\displaystyle{\displaystyle\operatorname{cd}\left(\NVar{z},\NVar{k}\right)}}$: Jacobian elliptic function
• ${\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}$: Jacobian elliptic function
• ${\displaystyle{\displaystyle K\left(\NVar{k}\right)}}$: Legendre’s complete elliptic integral of the first kind
• ${\displaystyle{\displaystyle x}}$: real
• ${\displaystyle{\displaystyle k}}$: modulus
 

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