Formula:7840

Digital Library of Mathematical Functions ID 22.16.E27

${\displaystyle{\displaystyle\mathcal{E}\left(x_{1}+x_{2},k\right)=\mathcal{E}\left(x_{1},k\right)+\mathcal{E}\left(x_{2},k\right)-k^{2}\operatorname{sn}\left(x_{1},k\right)\operatorname{sn}\left(x_{2},k\right)\operatorname{sn}\left(x_{1}+x_{2},k\right),}}$

Symbols List

• ${\displaystyle{\displaystyle\mathcal{E}\left(\NVar{x},\NVar{k}\right)}}$: Jacobi’s epsilon function
• ${\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}$: Jacobian elliptic function
• ${\displaystyle{\displaystyle x}}$: real
• ${\displaystyle{\displaystyle k}}$: modulus
 

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