Function: ellE
Section: transcendental
C-Name: ellE
Prototype: Gp
Help: ellE(k): Complete elliptic integral of the second kind for the
 complex parameter k using the agm.
Doc: Complete elliptic integral of the second kind
 $$E(k)=\int_{0}^{\pi/2}(1-k^{2}\sin(t)^{2})^{1/2}\,dt$$ for the
 complex parameter $k$ using the agm.

 In particular, the perimeter of an ellipse of semi-major and semi-minor axes
 $a$ and $b$ is given by
 \bprog
   e = sqrt(1 - (b/a)^2); \\ eccentricity
   4 * a * ellE(e)  \\ perimeter
 @eprog
