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 | ||
| − | $$E(k)=E(m)=\displaystyle\int_0^{\frac{\pi}{2}} \sqrt{1-k^2\sin^2 \theta} d\theta.$$ | + | $$E(k)=E(m)=\displaystyle\int_0^{\frac{\pi}{2}} \sqrt{1-k^2\sin^2 \theta} \mathrm{d}\theta.$$ |
<div align="center"> | <div align="center"> | ||
Revision as of 16:58, 25 May 2016
If $m=k^2$ we define the complete elliptic integral of the second kind, $E$, to be $$E(k)=E(m)=\displaystyle\int_0^{\frac{\pi}{2}} \sqrt{1-k^2\sin^2 \theta} \mathrm{d}\theta.$$
Plot of $E(m)$ on $[-10,1]$.
Domain coloring of $E$.
See Also
Elliptic K
Incomplete Elliptic E
