The aerodynamics of it are mostly beyond me, but I note that the "lifting Line Theory (3D Wings)" section in
http://www.aeromech.usyd.edu.au/aero/contents.html
states that
"The span-wise lift distribution is assumed to be elliptical with a small modification due to wing planform geometry. The assumed vortex line strength is thus a Fourier series approximation. "
Then goes on to give a function which looks rather like the Glauert approximation quoted earlier.
Regards
ET