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A power mean inequality involving the complete elliptic integrals
Rocky Mountain Journal of Mathematics, 2014 In this paper the authors investigate a power mean inequality for a special function which is defined by the complete elliptic integrals.
Yuming Chu, Xiaohui Zhang, Gendi Wang
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Auxiliary Table of Complete Elliptic Integrals
Journal of Mathematics and Physics, 1946Zur Erleichterung der Interpolation der vollständigen elliptischen Integrale \(K\) und \(E\) für \(k^2\to 1\) werden diese mit dem Argument \(\log(1-k^2)\) vertafelt.
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Fast computation of complete elliptic integrals and Jacobian elliptic functions
Celestial Mechanics and Dynamical Astronomy, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Toshio Fukushima
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Inequalities for the ratio of complete elliptic integrals
Proceedings of the American Mathematical Society, 2016We present various inequalities for the complete elliptic integral of the first kind, \[ K (
Alzer, Horst, Richards, Kendall
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Number of zeros of complete elliptic integrals
Functional Analysis and Its Applications, 1984Translation from Funkts. Anal. Prilozh. 18, No.2, 73-74 (Russian) (1984; Zbl 0547.14003).
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Functional Inequalities for Hypergeometric Functions and Complete Elliptic Integrals
SIAM Journal on Mathematical Analysis, 1992The authors obtain a number of inequalities for the classical \(_ 2F_ 1\) hypergeometric functions and for two of its special cases, the complete elliptic integrals of the first and second kind.
Anderson, G. D. +2 more
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On a generalization of Barton's integral and related integrals of complete elliptic integrals
Mathematical Proceedings of the Cambridge Philosophical Society, 1987Let K(k) and E(k) denote respectively the complete elliptic integrals of the first and second kind with modulus k, as defined by Byrd and Friedman ([5] 110·06 and 110·07), and let k′ = √(1 − k2), the complementary modulus.
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Sharp inequalities for the complete elliptic integral of the first kind
Mathematical Proceedings of the Cambridge Philosophical Society, 1998The author offers an improvement on one of two inequalities for the complete elliptic integral of the first kind by \textit{S. L. Qiu} and \textit{M. K. Vamamurthy} [SIAM J. Math. Anal. 27, 823-834 (1996; Zbl 0860.33014)] and the statement that the constants in the improved inequality and in the remaining one are the best possible.
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Tables of Complete Elliptic Integrals
Journal of Mathematics and Physics, 1941openaire +2 more sources