Difference between revisions of "Elliptic E"
From specialfunctionswiki
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=See Also= | =See Also= | ||
| − | [[ | + | [[Elliptic K]] <br /> |
[[Incomplete Elliptic E]] | [[Incomplete Elliptic E]] | ||
=References= | =References= | ||
[http://web.mst.edu/~lmhall/SPFNS/spfns.pdf "Special Functions" by Leon Hall] | [http://web.mst.edu/~lmhall/SPFNS/spfns.pdf "Special Functions" by Leon Hall] | ||
Revision as of 02:17, 6 January 2016
If $m=k^2$ we define the complete elliptic integral of the second kind, $E$, to be $$E(k)=E(m)=\displaystyle\int_0^{\frac{\pi}{2}} \sqrt{1-k^2\sin^2 \theta} d\theta.$$
Plot of $E(m)$ on $[-10,1]$.
- Domaincoloringelliptice.png
Domain coloring of $E(m)$.
See Also
Elliptic K
Incomplete Elliptic E
