Formula:7831

Digital Library of Mathematical Functions ID 22.16.E18

${\displaystyle{\displaystyle\mathcal{E}\left(x,k\right)=-k^{2}\int_{0}^{x}{\operatorname{cd}^{2}}\left(t,k\right)\mathrm{d}t+x+k^{2}\operatorname{sn}\left(x,k\right)\operatorname{cd}\left(x,k\right),}}$

Symbols List

• ${\displaystyle{\displaystyle\mathcal{E}\left(\NVar{x},\NVar{k}\right)}}$: Jacobi’s epsilon 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
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle x}}$: real
• ${\displaystyle{\displaystyle k}}$: modulus
 

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