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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Series: | Journal of Inequalities and Applications |
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Online Access: | http://link.springer.com/article/10.1186/s13660-017-1556-z |
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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 |
_version_ |
1724991184186638336 |