Difference between revisions of "Elliptic E"
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If $m=k^2$ we define the complete elliptic integral of the second kind, $E$, to be | If $m=k^2$ we define the complete elliptic integral of the second kind, $E$, to be | ||
$$E(k)=E(m)=\displaystyle\int_0^{\frac{\pi}{2}} \sqrt{1-k^2\sin^2 \theta} d\theta.$$ | $$E(k)=E(m)=\displaystyle\int_0^{\frac{\pi}{2}} \sqrt{1-k^2\sin^2 \theta} d\theta.$$ | ||
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Revision as of 18:10, 25 July 2015
If $m=k^2$ we define the complete elliptic integral of the second kind, $E$, to be $$E(k)=E(m)=\displaystyle\int_0^{\frac{\pi}{2}} \sqrt{1-k^2\sin^2 \theta} d\theta.$$
Plot of $E(m)$ on $[-10,1]$.
- Domaincoloringelliptice.png
Domain coloring of $E(m)$.
