I evaluate the complete elliptic integral of first kind as the sum of two Gauss hypergeometric functions.
Bulletin of Mathematical Sciences and Applications (Volume 6)
E. Guedes and R. R. Gandhi, "On the Complete Elliptic Integrals and Babylonian Identity IV: The Complete Elliptic Integral of First Kind as Sum of Two Gauss Hypergeometric Functions", Bulletin of Mathematical Sciences and Applications, Vol. 6, pp. 60-63, 2013