Elliptic E
From specialfunctionswiki
If $m=k^2$ we define the complete elliptic integral of the second kind, $E$, to be $$E(k)=E(m)=\displaystyle\int_0^{\frac{\pi}{2}} \sqrt{1-k^2\sin^2 \theta} d\theta.$$ The incomplete elliptic integral of the second kind is $$E(\phi|k)=E(\phi|m)=\displaystyle\int_0^{\phi} \sqrt{1-m\sin^2 \theta}d\theta.$$
