Monotonicity theorems and inequalities for the complete elliptic integrals

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Abstract

We prove monotonicity properties of certain combinations of complete elliptic integrals of the first and second kind, K and E. These results lead to sharp symmetrical bounds for K and E, which improve recently discovered inequalities.

MSC

primary
33E05
secondary
26D15
33C05

Keywords

Complete elliptic integrals
Monotonicity
Inequalities
Mean values
Arc length of an ellipse

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