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Inequalities and bounds for elliptic integrals. II. (English) Zbl 1185.33025
Dominici, Diego (ed.) et al., Special functions and orthogonal polynomials. AMS special session, Tucson, AZ, USA, April 21--22, 2007. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4650-6/pbk). Contemporary Mathematics 471, 127-138 (2008).
Summary: Inequalities involving Legendre’s elliptic integrals of the first, second, and third kind are derived. Bounds for some functions involving Legendre’s complete integrals $K$ and $E$ are proven. Main results of this paper are obtained using logarithmic convexity and total positivity of integrals under discussion. New inequalities for the symmetric elliptic integrals are obtained. For the entire collection see [Zbl 1148.33001].

33E05Elliptic functions and integrals
26D15Inequalities for sums, series and integrals of real functions