How can the arithmetic-geometric mean be derived using Elliptic Integration?

[yanshu]

hello every,how to get the arithmetic-geometric mean? sorry,i can't find it in other place.and my english is poor. arithmetic-geometric mean is: the limit of An,A1=a,B1=b,A(n+1)=(An+Bn)/2,B(n+1)=(AnBn)^1/2 GAUSS got it. a form of Elliptic Integration. Thanks~

 

[mathman]

http://en.wikipedia.org/wiki/Arithmetic-geometric_mean

See above

 

[yanshu]

there isn't the proof... how to get it to form of Elliptic Integration?