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Zbl 1059.33029
Alzer, Horst; Qiu, Songliang
Monotonicity theorems and inequalities for the complete elliptic integrals. (English)
[J] J. Comput. Appl. Math. 172, No. 2, 289-312 (2004). ISSN 0377-0427

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

MSC 2000:: *33E05 Elliptic functions and integrals
26D15 Inequalities for sums, series and integrals of real functions
33C05 Classical hypergeometric functions

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

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Zentralblatt MATH Berlin [Germany]