Formula:7842

Digital Library of Mathematical Functions ID 22.16.E29

${\displaystyle{\displaystyle\mathcal{E}\left(x+2K,k\right)=\mathcal{E}\left(x,k\right)+2E\left(k\right).}}$

Symbols List

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

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