Let α_(n + 1) | = | (2α_n β_n)/(α_n + β_n) β_(n + 1) | = | sqrt(α_n β_n), then H(α_0, β_0) congruent lim_(n->∞) a_n = 1/(M(α_0^(-1), β_0^(-1))), where M is the arithmetic-geometric mean.

arithmetic-geometric mean | arithmetic mean | geometric mean | harmonic mean