// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
// Copyright (C) INRIA - F.D
//
// Copyright (C) 2012 - 2016 - Scilab Enterprises
//
// This file is hereby licensed under the terms of the GNU GPL v2.0,
// pursuant to article 5.3.4 of the CeCILL v.2.1.
// This file was originally licensed under the terms of the CeCILL v2.1,
// and continues to be available under such terms.
// For more information, see the COPYING file which you should have received
// along with this program.
function [K]=%k(m)
//K=%k(m)
//Calculates Jacobi's complete elliptic integral
//of the first kind:
// K = integral from 0 to 1 of
// [(1-t**2)(1-m*t**2)]**(-1/2)
//m is allowed to be a vector
//Ref :Abramowitz and Stegun page 598
// m :Parameter used in calculating the elliptic
// :integral where 0 %eps,
an=0.5*(a+b);
bn=sqrt(a.*b);
cn=0.5*(a-b);
a=an;
b=bn;
c=cn;
end,
K=%pi*un./(2*a);
endfunction