Category:Definitions/Complete Elliptic Integral of the Second Kind

This category contains definitions related to Complete Elliptic Integral of the Second Kind.
Related results can be found in Category:Complete Elliptic Integral of the Second Kind.

Definition 1

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

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

Definition 2

$\ds \map E k = \int \limits_0^1 \dfrac {\sqrt {1 - k^2 v^2} } {\sqrt {1 - v^2} } \rd v$

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