An extension of Gauss's arithmetic-geometric mean (AGM) to three variables iteration scheme

Kiyoshi Sogo

Gauss's arithmetic-geometric mean (AGM) which is described by two variables iteration $(a_n,b_n)\to (a_{n+1},b_{n+1})$ by $a_{n+1}=(a_n+b_n)/2,b_{n+1}=\sqrt{a_n{b}_n}$. W…