Formula:7829

Digital Library of Mathematical Functions ID 22.16.E16

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

Symbols List

• ${\displaystyle{\displaystyle\mathcal{E}\left(\NVar{x},\NVar{k}\right)}}$: Jacobi’s epsilon function
• ${\displaystyle{\displaystyle\operatorname{cn}\left(\NVar{z},\NVar{k}\right)}}$: Jacobian elliptic function
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle x}}$: real
• ${\displaystyle{\displaystyle k}}$: modulus
• ${\displaystyle{\displaystyle k^{\prime}}}$: complementary modulus
 

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