asymptotic elliptic integral

I discover that y=ellip(1-t)-1; behaves like 0.25*(-t.*log(t)+t*v) in the neighborhood of t=0, for v=1.77259; where ellip(x)= complete elliptic integral of the second kind. (Later,) v= 4*log(2)-1 from expanding the function around t=1. With one pole out of the way, the function should be a little more amenable to Chebyshev approximation; however, there are still an infinite number of poles at t=1 at higher order.