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Monotonicity theorems and inequalities for the complete elliptic integrals. (English) Zbl 1059.33029
Summary: We prove monotonicity properties of certain combinations of complete elliptic integrals of the first and second kind, \(\mathcal K\) and \(\mathcal E\). These results lead to sharp symmetrical bounds for \(\mathcal K\) and \(\mathcal E \), which improve recently discovered inequalities.
Reviewer: Reviewer (Berlin)

MSC:
33E05 Elliptic functions and integrals
26D15 Inequalities for sums, series and integrals
33C05 Classical hypergeometric functions, \({}_2F_1\)
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