Formula:7208

Digital Library of Mathematical Functions ID 19.25.E8

${\displaystyle{\displaystyle E\left(\phi,k\right)=R_{-\frac{1}{2}}\left(\tfrac{1}{2},-\tfrac{1}{2},\tfrac{3}{2};c-1,c-k^{2},c\right),}}$

Symbols List

• ${\displaystyle{\displaystyle R_{\NVar{-a}}\left(\NVar{b_{1}},\dots,\NVar{b_{n}};\NVar{z_{1}},\dots,\NVar{z_{n}}\right)}}$: multivariate hypergeometric function
• ${\displaystyle{\displaystyle E\left(\NVar{\phi},\NVar{k}\right)}}$: Legendre’s incomplete elliptic integral of the second kind
• ${\displaystyle{\displaystyle\phi}}$: real or complex argument
• ${\displaystyle{\displaystyle k}}$: real or complex modulus
 

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