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Sharp Estimates for Complete Elliptic Integrals
SIAM Journal on Mathematical Analysis, 1996Summary: Monotonicity and convexity properties of certain functions defined in terms of complete elliptic integrals are studied and sharp functional inequalities for these functions are obtianed, thus answering some open questions.
Qiu, S.-L., Vamanamurthy, M. K.
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ON THE SEMI-DIFFERENTIALS OF SOME COMPLETE ELLIPTIC INTEGRALS AND THEIR DIFFERENCES
Jnanabha, 2022In this article we aim at obtaining the semi-differentials of Complete Elliptic integrals of different kinds and their differences in terms of algebraic functions by using series manipulation technique and Pfaff-Kummer linear ¨ transformation.
Qureshi, M. I., Majid, Javid, Ara, Jahan
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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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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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Functional inequalities for the ratio of complete p-elliptic integrals
Journal of Mathematical Analysis and Applications, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gu, Xiaoyan, Zhang, Xiaohui
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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.
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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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Asymptotically sharp bounds for the complete $p$-elliptic integral of the first kind
Hokkaido Mathematical Journal, 2022Yuming Chu
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