Using the Corollary 3 of previous paper (http://www.bmsa.us/admin/uploads/Mn95aZ.pdf), we evaluate the complete elliptic integral of the first kind in an approximately equal analytical closed form, by means of Bessel functions.
Bulletin of Mathematical Sciences and Applications (Volume 6)
E. Guedes and R. R. Gandhi, "On the Complete Elliptic Integrals and Babylonian Identity III: An Approximation for the Complete Elliptic Integral of the First Kind", Bulletin of Mathematical Sciences and Applications, Vol. 6, pp. 55-59, 2013