Here is the derivation of an analytic formula by the author Mr H.C. Rajpoot in form of an infinite converging series to compute the circumference or perimeter of any ellipse given any two of major axis, minor axis & eccentricity. The series had been derived by using integration in polar co-ordinates, binomial expansion and β & γ-functions. This series is in form of discrete summation of infinite terms which converge to a finite value hence this is extremely useful in case studies & practical applications to compute the perimeter of an ellipse to the desired accuracy.