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An inequality for generalized complete elliptic integral [PDF]
Journal of Inequalities and Applications, 2017 In this paper, we show an elegant inequality involving the ratio of generalized complete elliptic integrals of the first kind and generalize an interesting result of Alzer.
Li Yin +3 more
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Monotonicity properties and bounds for the complete p-elliptic integrals [PDF]
Journal of Inequalities and Applications, 2018 We generalize several monotonicity and convexity properties as well as sharp inequalities for the complete elliptic integrals to the complete p-elliptic integrals.
Ti-Ren Huang +3 more
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A Natural Approximation to the Complete Elliptic Integral of the First Kind
Mathematics, 2022 Let K(r) be the complete elliptic integral of the first kind. Then, the inequality 2K(r)/π>tanh−1(r)/sin−1r holds for all r∈(0,1). This conclusion does not match those in the existing literature.
Ling Zhu
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Monotonicity of the ratio for the complete elliptic integral and Stolarsky mean
Journal of Inequalities and Applications, 2016 In the article, we prove that the function r ↦ E ( r ) / S 9 / 2 − p , p ( 1 , r ′ ) $r\mapsto \mathcal{E}(r)/S_{9/2-p, p}(1, r')$ is strictly increasing on ( 0 , 1 ) $(0, 1)$ for p ≤ 7 / 4 $p\leq7/4$ and strictly decreasing on ( 0 , 1 ) $(0, 1)$ for p ∈
Zhen-Hang Yang, Yu-Ming Chu, Wen Zhang
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On Generalized Complete (p, q)-Elliptic Integrals [PDF]
Acta Mathematica Scientia, 2021 In this paper, authors study the generalized complete $(p,q)$-elliptic integrals of the first and the second kind as an application of generalized trigonometric functions with two parameters, and establish the Turán type inequalities of these functions.
Yin, Li +2 more
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Optimal bounds for Seiffert-like elliptic integral mean by harmonic, geometric, and arithmetic means
Journal of Inequalities and Applications, 2022 In this article, we present the optimal bounds for a special elliptic integral mean in terms of the harmonic combinations of harmonic, geometric, and arithmetic means.
Fan Zhang, Weimao Qian, Hui Zuo Xu
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Calculation of integrals in MathPartner
Discrete and Continuous Models and Applied Computational Science, 2021 We present the possibilities provided by the MathPartner service of calculating definite and indefinite integrals. MathPartner contains software implementation of the Risch algorithm and provides users with the ability to compute antiderivatives for ...
Gennadi I. Malaschonok +1 more
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Extended elliptic-type integrals with associated properties and Turán-type inequalities
Advances in Difference Equations, 2021 Our aim is to study and investigate the family of ( p , q ) $(p, q)$ -extended (incomplete and complete) elliptic-type integrals for which the usual properties and representations of various known results of the (classical) elliptic integrals are ...
Rakesh K. Parmar +3 more
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On epsilon factorized differential equations for elliptic Feynman integrals
Journal of High Energy Physics, 2022 In this paper we develop and demonstrate a method to obtain epsilon factorized differential equations for elliptic Feynman integrals. This method works by choosing an integral basis with the property that the period matrix obtained by integrating the ...
Hjalte Frellesvig
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Analytical Solution for the Cubic-Quintic Duffing Oscillator Equation with Physics Applications
Complexity, 2022 The nonlinear differential equation governing the periodic motion of the one-dimensional, undamped, and unforced cubic-quintic Duffing oscillator is solved exactly by obtaining the period and the solution.
Alvaro H. Salas +2 more
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