C. F. Gauss algorithm usong matlab

Complete elliptic integral of the first kind in the Legendre form K(k2), 0 < k2 < 1,




/ 2
0
2 2
2
1 sin ( )
( )


k t
dt
K k
cannot be evaluated in terms of the elementary functions. The following algorithm, due to
C. F. Gauss, generates a sequence of the arithmetic means {an} and a sequence of the
geometric means {bn}, where
43
a0 = 1, b0 = 1
k 2
an = (an-1 + bn-1)/2, bn = 1 1 n n a b n = 1, 2, ? .
It is known that both sequences have a common limit g and that an  bn, for all n.
Moreover,
K(k2) =
2g


Write MATLAB function K = compK(k2) which implements this algorithm. The input
parameter k2 stands for k2. Use the loop while to generate consecutive members of both
sequences, but do not save all numbers generated in the course of computations. Continue
execution of the while loop as long as an ? bn  eps, where eps is the machine epsilon

Jadayuu sir..
Mee to want the solution