Formula:7375

Digital Library of Mathematical Functions ID 19.30.E5

${\displaystyle{\displaystyle L(a,b)=4aE\left(k\right)=8aR_{G}\left(0,b^{2}/a^{2},1\right)=8R_{G}\left(0,a^{2},b^{2}\right)=8abR_{G}\left(0,a^{-2},b^{-2}\right),}}$

Symbols List

• ${\displaystyle{\displaystyle R_{G}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}$: symmetric elliptic integral of second kind
• ${\displaystyle{\displaystyle E\left(\NVar{k}\right)}}$: Legendre’s complete elliptic integral of the second kind
• ${\displaystyle{\displaystyle k}}$: real or complex modulus
• ${\displaystyle{\displaystyle L(a,b)}}$: length
 

Resources that cite this formula

No records found.