Monotonicity theorems and inequalities for the complete elliptic integrals

Authors:
Horst Alzer;Song-Liang Qiu
Affiliations:
Morsbacher Strasse 10, D-51545 Waldbröl, Germany;President's Office, Hangzhou Institute of Electronics Engineering, Hangzhou, Zhejiang 310037, People's Republic of China
Venue:
Journal of Computational and Applied Mathematics
Year:
2004

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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.