Formula:7844

Digital Library of Mathematical Functions ID 22.16.E31

${\displaystyle{\displaystyle E\left(\operatorname{am}\left(x,k\right),k\right)=\mathcal{E}\left(x,k\right),}}$

Constraint(s)

${\displaystyle{\displaystyle-K\leq x\leq K}}$

Symbols List

• ${\displaystyle{\displaystyle\mathcal{E}\left(\NVar{x},\NVar{k}\right)}}$: Jacobi’s epsilon function
• ${\displaystyle{\displaystyle\operatorname{am}\left(\NVar{x},\NVar{k}\right)}}$: Jacobi’s amplitude function
• ${\displaystyle{\displaystyle K\left(\NVar{k}\right)}}$: Legendre’s complete elliptic integral of the first kind
• ${\displaystyle{\displaystyle E\left(\NVar{\phi},\NVar{k}\right)}}$: Legendre’s incomplete elliptic integral of the second kind
• ${\displaystyle{\displaystyle x}}$: real
• ${\displaystyle{\displaystyle k}}$: modulus
 

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