Monotonicity, convexity, and inequalities for the generalized elliptic integrals

Abstract We provide the monotonicity and convexity properties and sharp bounds for the generalized elliptic integrals K a ( r ) $\mathscr{K}_{a}(r)$ and E a ( r ) $\mathscr {E}_{a}(r)$ depending on a parameter a ∈ ( 0 , 1 ) $a\in(0,1)$ , which contains an earlier result in the particular case a = 1...

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Main Authors:	Tiren Huang, Shenyang Tan, Xiaohui Zhang
Format:	Article
Language:	English
Published:	SpringerOpen 2017-11-01
Series:	Journal of Inequalities and Applications
Subjects:	generalized elliptic integrals of the first and second kinds Gaussian hypergeometric function monotonicity convexity inequality
Online Access:	http://link.springer.com/article/10.1186/s13660-017-1556-z

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spelling	doaj-66d297802959440e995e33dcbe9588142020-11-25T01:53:24ZengSpringerOpenJournal of Inequalities and Applications1029-242X2017-11-01201711910.1186/s13660-017-1556-zMonotonicity, convexity, and inequalities for the generalized elliptic integralsTiren Huang0Shenyang Tan1Xiaohui Zhang2Department of Mathematics, Zhejiang Sci-Tech UniversityTaizhou Institute of Sci. & Tech., NUSTDepartment of Mathematics, Zhejiang Sci-Tech UniversityAbstract We provide the monotonicity and convexity properties and sharp bounds for the generalized elliptic integrals K a ( r ) $\mathscr{K}_{a}(r)$ and E a ( r ) $\mathscr {E}_{a}(r)$ depending on a parameter a ∈ ( 0 , 1 ) $a\in(0,1)$ , which contains an earlier result in the particular case a = 1 / 2 $a=1/2$ .http://link.springer.com/article/10.1186/s13660-017-1556-zgeneralized elliptic integrals of the first and second kindsGaussian hypergeometric functionmonotonicityconvexityinequality
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Tiren Huang Shenyang Tan Xiaohui Zhang
spellingShingle	Tiren Huang Shenyang Tan Xiaohui Zhang Monotonicity, convexity, and inequalities for the generalized elliptic integrals Journal of Inequalities and Applications generalized elliptic integrals of the first and second kinds Gaussian hypergeometric function monotonicity convexity inequality
author_facet	Tiren Huang Shenyang Tan Xiaohui Zhang
author_sort	Tiren Huang
title	Monotonicity, convexity, and inequalities for the generalized elliptic integrals
title_short	Monotonicity, convexity, and inequalities for the generalized elliptic integrals
title_full	Monotonicity, convexity, and inequalities for the generalized elliptic integrals
title_fullStr	Monotonicity, convexity, and inequalities for the generalized elliptic integrals
title_full_unstemmed	Monotonicity, convexity, and inequalities for the generalized elliptic integrals
title_sort	monotonicity, convexity, and inequalities for the generalized elliptic integrals
publisher	SpringerOpen
series	Journal of Inequalities and Applications
issn	1029-242X
publishDate	2017-11-01
description	Abstract We provide the monotonicity and convexity properties and sharp bounds for the generalized elliptic integrals K a ( r ) $\mathscr{K}_{a}(r)$ and E a ( r ) $\mathscr {E}_{a}(r)$ depending on a parameter a ∈ ( 0 , 1 ) $a\in(0,1)$ , which contains an earlier result in the particular case a = 1 / 2 $a=1/2$ .
topic	generalized elliptic integrals of the first and second kinds Gaussian hypergeometric function monotonicity convexity inequality
url	http://link.springer.com/article/10.1186/s13660-017-1556-z
work_keys_str_mv	AT tirenhuang monotonicityconvexityandinequalitiesforthegeneralizedellipticintegrals AT shenyangtan monotonicityconvexityandinequalitiesforthegeneralizedellipticintegrals AT xiaohuizhang monotonicityconvexityandinequalitiesforthegeneralizedellipticintegrals
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Monotonicity, convexity, and inequalities for the generalized elliptic integrals

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