Inequalities for means (Q1329320)

The authors prove inequalities for power means, Stolarsky means, the geometric mean, and Gauss's arithmetic-geometric mean and establish connections to elliptic integrals. A typical result is that \(((x^ t - y^ t)/(\ln (x/y)t))^{1/t}\) is a continuous function of \(t\) and strictly increases from \((xy)^{1/2}\) to \(\max (x,y)\) as \(t\) grows from 0 to \(\infty\).