Monotonicity theorems and inequalities for the complete elliptic integrals

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摘要

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.

论文关键词：primary,33E05,secondary,26D15,33C05,Complete elliptic integrals,Monotonicity,Inequalities,Mean values,Arc length of an ellipse

论文评审过程：Received 6 November 2003, Revised 29 January 2004, Available online 7 October 2004.

论文官网地址：https://doi.org/10.1016/j.cam.2004.02.009