Formula:7826

Digital Library of Mathematical Functions ID 22.16.E14

${\displaystyle{\displaystyle\mathcal{E}\left(x,k\right)=\int_{0}^{\operatorname{sn}\left(x,k\right)}\sqrt{\frac{1-k^{2}t^{2}}{1-t^{2}}}\mathrm{d}t;}}$

Symbols List

• ${\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}$: 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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