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Legendre's Complete Elliptic Integrals (Mlmode)

Syntax	[K, E] = ellipke(m)
See Also	ellipf , ellipe

Description
Computes an element-by-element approximation of the elliptic integral K defined by
            pi/2
            /            2    -1/2 
     K(m) = | [ 1 - m sin (x) ]   dx
            /
            0
where the argument m is a real or double-precision matrix and for each (i, j),

     0 < | m   | < 1
            i,j


If the return value E is present, it is set to the element-by-element approximation of the elliptic integral E defined by
            pi/2
            /            2     1/2 
     E(m) = | [ 1 - m sin (x) ]   dx
            /
            0

Example
                   pi/2
                   /   
     K(0) = E(0) = | dx = pi/2
                   /
                   0
If in Mlmode you enter
     [K, E] = ellipke(0.);
     K
O-Matrix will reply
     1.5708
The variable E will also be set to this value.