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Legendre's Elliptic Integrals of the Third Kind

Syntax	ellipi(phi, n, k)
See Also	elliprf

Description
Computes an element-by-element approximation of the elliptic integral defined by
                phi
                /           2    -1        2   2    -1/2 
Pi(phi, n, k) = | [1 + n sin (x) ]  [ 1 - k sin (x) ]   dx
                /
                0
where the arguments phi n and k are real or double-precision matrices. If both of these arguments is not a scalar, they must have the same dimension. For each (i, j),

     | phi(i, j) | < pi/2  and  | k(i, j) | < 1

Example
                      phi
                      /   
     Phi(phi, 0, 0) = | dx = phi
                      /
                      0
If you enter
     phi = rand(2, 3)
     print ellipi(phi, 0., 0.)
     print phi
O-Matrix will print two matrices with the same values.