Definition:Elliptic Integral of the Second Kind/Complete
Jump to navigation
Jump to search
Special Function
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 $0 < k < 1$.
Also see
- Results about the complete elliptic integral of the second kind can be found here.