K = ellipke
(m)
[K,E] = ellipke(m)
[K,E] = ellipke(m)
returns the complete elliptic integral of the first and second kinds for the elements of m. The complete elliptic integral of the first kind, K(m) = F(pi/2|m)
, is defined by
The complete elliptic integral of the second kind, E(m) = E(K(m)) =
, is defined by
E(pi/2|m)
Some definitions of K
and E
use the modulus k
instead of the parameter m
. They are related by
The accuracy of the result is eps
; the value of eps
can be changed for a less accurate, but more quickly computed answer.
Compute successive iterations of ai, bi, and ci with
stopping at iteration n when cn \xc5 0, within the tolerance specified by eps
. The complete elliptic integral of the first kind is then
ellipk
e is limited to the input domain 0 <= m<= 1.
ellipj
(c) Copyright 1994 by The MathWorks, Inc.