functions in ellipse.i -

             EllipticE(k)  
 
     return E(k), the complete Elliptic Function  
     integral from 0 to pi/2 of  sqrt(1-k^2 *(sin(x))^2) dx  
     k must lie in -1<= k <=1  
     Uses the arithmetic/geometric mean method. (Abramowitz & Stegun p598)   

             EllipticK(k)  
 
   return E(k), the complete Elliptic Function   
   integral from 0 to pi/2 of  1/sqrt(1-k^2 *(sin(x))^2) dx  
   uses the arithmetic/geometric mean method. (Abramowitz & Stegun p598)  
   k must lie in   -1 < k <1.  
   E(k) diverges as log(4/sqrt(1-k^2)) as k->1