Sharp Power Mean Inequalities for the Generalized Elliptic Integral of the First Kind
We establish two sharp inequalities involving the power mean and generalized elliptic integral of the first kind. As applications, the analogous inequalities concerning the complete p -elliptic integral of the first kind are also derived.
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| Published in: | Computational methods and function theory Vol. 20; no. 1; pp. 111 - 124 |
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| Language: | English |
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| ISSN: | 1617-9447, 2195-3724 |
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| Abstract | We establish two sharp inequalities involving the power mean and generalized elliptic integral of the first kind. As applications, the analogous inequalities concerning the complete
p
-elliptic integral of the first kind are also derived. |
|---|---|
| AbstractList | We establish two sharp inequalities involving the power mean and generalized elliptic integral of the first kind. As applications, the analogous inequalities concerning the complete p-elliptic integral of the first kind are also derived. We establish two sharp inequalities involving the power mean and generalized elliptic integral of the first kind. As applications, the analogous inequalities concerning the complete p -elliptic integral of the first kind are also derived. |
| Author | Chu, Yu-Ming He, Zai-Yin Wang, Miao-Kun |
| Author_xml | – sequence: 1 givenname: Miao-Kun surname: Wang fullname: Wang, Miao-Kun organization: Department of Mathematics, Huzhou University – sequence: 2 givenname: Zai-Yin surname: He fullname: He, Zai-Yin organization: School of Mathematics, Hunan University – sequence: 3 givenname: Yu-Ming surname: Chu fullname: Chu, Yu-Ming email: chuyuming@zjhu.edu.cn organization: College of Science, Hunan City University, School of Mathematics and Statistics, Changsha University of Science and Technology |
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| Keywords | 26E60 Complete elliptic integral Generalized elliptic integral Complete 33E05 Gaussian hypergeometric function 33C05 elliptic integral Power mean |
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| References_xml | – reference: AndersonGDVamanmurthyMKVuorinenMFunctional inequalities for complete elliptic integrals and their ratiosSIAM J. Math. Anal.1990212536549103890610.1137/0521029 – reference: QianW-MYangY-YZhangH-WChuY-MOptimal two-parameter geometric and arithmetic mean bounds for the Sándor-Yang meanJ. Inequal. Appl.201920191210.1186/s13660-019-1962-5Article ID 287 – reference: BariczÁTurán type inequalities for generalized complete elliptic integralsMath. Z.20072564895911230889610.1007/s00209-007-0111-x – reference: WangM-KChuY-MZhangWMonotonicity and inequalities involving zero-balanced hypergeometric functionMath. Inequal. Appl.201922260161739345051416.33007 – reference: WangM-KChuY-MZhangWPrecise estimates for the solution of Ramanujan’s generalized modular equationRamanujan J.2019493653668397969610.1007/s11139-018-0130-8 – reference: BhayoBAVuorinenMOn generalized complete elliptic integrals and modular functionsProc. Edinb. Math. Soc. (2)2012553591611297524410.1017/S0013091511000356 – reference: WangM-KChuY-MQiuY-FQiuS-LAn optimal power mean inequality for the complete elliptic integralsAppl. Math. Lett.2011246887890277615510.1016/j.aml.2010.12.044 – reference: WangG-DZhangX-HChuY-MA power mean inequality involving the complete elliptic integralsRocky Mountain J. Math.201444516611667329564810.1216/RMJ-2014-44-5-1661 – reference: ChuY-MWangM-KOptimal Lehmer mean bounds for the Toader meanResults Math.2012613–4223229292511710.1007/s00025-010-0090-9 – reference: AndersonGDVamanamurthyMKVuorinenMConformal Invariants, Inequalities, and Quasiconformal Maps1997New YorkJohn Wiley & Sons0885.30012 – reference: ByrdPFFriedmanMDHandbook of Elliptic Integrals of Engineer and Physicists1971New YorkSpringer10.1007/978-3-642-65138-0 – reference: Yang, Zh.-H., Chu, Y.-M.: A monotonicity property involving the generalized elliptic integral of the first kind. Math. Inequal. 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| Title | Sharp Power Mean Inequalities for the Generalized Elliptic Integral of the First Kind |
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