Difference between revisions of "Elliptic K"
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(Created page with "If $m=k^2$ we define the complete elliptic integral of the first kind, $K$ to be $$K(k)=K(m)=\displaystyle\int_0^{\frac{\pi}{2}} \dfrac{1}{\sqrt{1-k^2\sin^2 \theta}} d\theta.$...") |
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Revision as of 07:10, 10 March 2015
If $m=k^2$ we define the complete elliptic integral of the first kind, $K$ to be $$K(k)=K(m)=\displaystyle\int_0^{\frac{\pi}{2}} \dfrac{1}{\sqrt{1-k^2\sin^2 \theta}} d\theta.$$ The incomplete elliptic integral of the first kind is $$K(\phi |k) = K(\phi |m) = \displaystyle\int_0^{\phi} \dfrac{1}{\sqrt{1-k^2\sin^2 \theta}} d\theta.$$
