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Inequalities for means. (English) Zbl 0802.26009
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 $$\infty$$.

##### MSC:
 26D15 Inequalities for sums, series and integrals 33E05 Elliptic functions and integrals 26D07 Inequalities involving other types of functions 26A24 Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems
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