Elliptic K

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The Elliptic $K$ function is also known as the complete Elliptic integral of the first kind. If $m=k^2$ we define the complete elliptic integral of the first kind, $K$ to be $$K(k)=K(m)=\displaystyle\int_0^{\frac{\pi}{2}} \dfrac{1}{\sqrt{1-k^2\sin^2 \theta}} \mathrm{d}\theta.$$

See Also[edit]

Elliptic E
Incomplete Elliptic K

References[edit]

"Special Functions" by Leon Hall