Definition:Complete Elliptic Integral of the Second Kind/Definition 1

Special Function

 * $\ds \map E k = \int \limits_0^{\pi / 2} \sqrt {1 - k^2 \sin^2 \phi} \rd \phi$

is the complete elliptic integral of the second kind, and is a function of $k$, defined on the interval $0 < k < 1$.

Also see

 * Equivalence of Definitions of Complete Elliptic Integral of the Second Kind