Difference between revisions of "Elliptic E"
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| − | File:Ellipticeplot.png| | + | File:Ellipticeplot.png|Graph of $E$. |
File:Complexellipticeplot.png|[[Domain coloring]] of $E$. | File:Complexellipticeplot.png|[[Domain coloring]] of $E$. | ||
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| + | =Properties= | ||
| + | [[E(m)=(pi/2)2F1(-1/2,1/2;1;m)]]<br /> | ||
=See Also= | =See Also= | ||
Latest revision as of 04:54, 21 December 2017
If $m=k^2$ we define the complete elliptic integral of the second kind, $E$, to be $$E(k)=E(m)=\displaystyle\int_0^{\frac{\pi}{2}} \sqrt{1-k^2\sin^2 \theta} \mathrm{d}\theta.$$
Graph of $E$.
Domain coloring of $E$.
Properties
See Also
Elliptic K
Incomplete Elliptic E
