Sharp Bounds for the Weighted Hölder Mean of the Zero-Balanced Generalized Complete Elliptic Integrals
In the article, we present the best possible bounds for the weighted Hölder mean of the zero-balanced generalized complete elliptic integrals of the first and second kinds, which are the generalizations of previous results for complete p -elliptic integrals.
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| Published in | Computational methods and function theory Vol. 21; no. 3; pp. 413 - 426 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.09.2021
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1617-9447 2195-3724 |
| DOI | 10.1007/s40315-020-00352-7 |
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| Abstract | In the article, we present the best possible bounds for the weighted Hölder mean of the zero-balanced generalized complete elliptic integrals of the first and second kinds, which are the generalizations of previous results for complete
p
-elliptic integrals. |
|---|---|
| AbstractList | In the article, we present the best possible bounds for the weighted Hölder mean of the zero-balanced generalized complete elliptic integrals of the first and second kinds, which are the generalizations of previous results for complete
p
-elliptic integrals. In the article, we present the best possible bounds for the weighted Hölder mean of the zero-balanced generalized complete elliptic integrals of the first and second kinds, which are the generalizations of previous results for complete p-elliptic integrals. |
| Author | Zhao, Tie-Hong Chu, Yu-Ming He, Zai-Yin |
| Author_xml | – sequence: 1 givenname: Tie-Hong surname: Zhao fullname: Zhao, Tie-Hong organization: Department of Mathematics, Hangzhou Normal 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: Department of Mathematics, Huzhou University, Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science and Technology |
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| Cites_doi | 10.1186/s13660-017-1484-y 10.1155/2010/493058 10.2140/pjm.2000.192.1 10.1007/s13398-020-00784-9 10.1155/2011/896483 10.1186/s13660-018-1828-2 10.7153/jca-09-04 10.1007/s00209-007-0111-x 10.1007/s11139-018-0061-4 10.1016/j.aml.2010.12.044 10.1090/proc/13337 10.1007/s12044-012-0062-y 10.1017/S0305004198002692 10.1186/s13660-020-02327-7 10.1007/s00025-010-0090-9 10.2298/AADM190924020W 10.2996/kmj/1458651700 10.1007/s40315-020-00298-w 10.1007/BF03321716 10.1016/j.jmaa.2015.04.035 10.2298/AADM171015001Y 10.1016/j.jmaa.2015.03.043 10.1007/s11139-018-9993-y 10.1016/j.jmaa.2019.123388 10.1007/s13398-020-00825-3 10.1016/j.cam.2018.08.027 10.3934/math.2020290 10.3934/math.2020418 10.1186/s13660-018-1711-1 10.1016/j.jmaa.2018.03.005 |
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| Keywords | Complete elliptic integrals Weighted Hölder mean 33E05 Gaussian hypergeometric function Zero-balanced 33C05 |
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| References | AlzerHSharp inequalities for the complete elliptic integral of the first kindMath. Proc. Camb. Philos. Soc.19881242309314163113510.1017/S0305004198002692 BariczÁTurán type inequalities for generalized complete elliptic integralsMath. Z.20072564895911230889610.1007/s00209-007-0111-x AndersonGDQiuS-LVamanamurthyMKVuorinenMGeneralized elliptic integrals and modular equationsPacific J. Math.20001921137174103110.2140/pjm.2000.192.1 YangZ-HTianJ-FSharp inequalities for the generalized elliptic integrals of the first kindRamanujan J.201948191116390249710.1007/s11139-018-0061-4 YangZ-HChuY-MWangM-KMonotonicity criterion for the quotient of power series with applicationsJ. Math. Anal. Appl.20154281587604332700510.1016/j.jmaa.2015.03.043 AndersonGDVamanamurthyMKVuorinenMConformal invariants, inequalities, and quasiconformal maps1997New YorkWiley0885.30012 ZhaoT-HWangM-KChuY-MA sharp double inequality involving generalized complete elliptic integral of the first kindAIMS Math.20205545124528414746210.3934/math.2020290 Qi, F.: Bounds for the ratio of two gamma functions. J. Inequal. Appl., 2010, Article ID 493058, 84 pages (2010) WangM-KChuH-HLiY-MChuY-MAnswers to three conjectures on convexity of three functions involving complete elliptic integrals of the first kindAppl. Anal. Discrete Math.2020141255271409341710.2298/AADM190924020W WangM-KChuY-MQiuS-LSharp bounds for generalized elliptic integrals of the first kindJ. Math. Anal. Appl.20154292744757334249010.1016/j.jmaa.2015.04.035 YangZ-HChuY-MZhangWHigh accuracy asymptotic bounds for the complete elliptic integral of the second kindAppl. Math. Comput.2019348552564389417910.1016/j.cam.2018.08.027 TakeuchiSLegendre-type relations for generalized complete elliptic integralsJ. Class. Anal.2016913542358008410.7153/jca-09-04 Qian, W.-M., He, Z.-Y., Chu, Y.-M.: Approximation for the complete elliptic integral of the first kind, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. 114(2), Article ID 57, 12 pages (2020) Zhao, T.-H., Chu, Y.-M., Wang, H.: Logarithmically complete monotonicity properties relating to the gamma function, Abstr. Appl. Anal., 2011, Article ID 896483, 13 pages (2011) Yang, Z.-H., Qian, W.-M., Chu, Y.-M., Zhang, W.: On rational bounds for the gamma function, J. Inequal. Appl., 2017, Article ID 210, 17 pages (2017) Hai, G.-J., Zhao, T.-H.: Monotonicity properties and bounds involving the two-parameter generalized Grötzsch ring function. J. Inequal. Appl., 2020, Article ID 66, 17 pages (2020) WangM-MChuY-MQiuY-FQiuS-LAn optimal power mean inequality for the complete elliptic integralsAppl. Math. Lett.2011246887890277615510.1016/j.aml.2010.12.044 WangM-KHeZ-YChuY-MSharp power mean inequalities for the generalized elliptic integral of the first KindComput. Methods Funct. Theory2020201111124407186510.1007/s40315-020-00298-w ShenJ-MYangZ-HQianW-MZhangWChuY-MSharp rational bounds for the gamma functionMath. Inequal. Appl.202023384385341289561455.33002 WangM-KChuY-MJiangY-PRamanujan’s cubic transformation inequalities for zero-balanced hypergeometric functionsRocky Mountain J. Math.201646267969135290871350.33007 Huang, T.-R., Tan, S.-Y., Ma, X.-Y., Chu, Y.-M.: Monotonicity properties and bounds for the complete p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p$$\end{document}-elliptic integrals. J. Inequal. Appl., 2018, Article ID 239, 11 pages (2018) ChuY-MWangM-KQiuS-LOptimal combinations bounds of root-square and arithmetic means for Toader meanProc. Indian Acad. Sci. Math. Sci.201212214151290958210.1007/s12044-012-0062-y TakeuchiSA new form of the generalized complete elliptic integralsKodai Math. J.2016391202226347827910.2996/kmj/1458651700 YangZ-HQianW-MChuY-MZhangWOn approximating the arithmetic-geometric mean and complete elliptic integral of the first kindJ. Math. Anal. Appl.2018462217141726377431310.1016/j.jmaa.2018.03.005 YangZ-HQianW-MZhangWChuY-MNotes on the complete elliptic integral of the first kindMath. Inequal. Appl.2020231779340615261440.33020 ChuY-MWangM-KOptimal Lehmer mean bounds for the Toader meanResults. Math.2012613–4223229292511710.1007/s00025-010-0090-9 AlzerHRichardsKInequalities for the ratio of complete elliptic integralsProc. Am. Math. Soc.2017145416611670360155710.1090/proc/13337 Huang, T.-R., Han, B.-W., Ma, X.-Y., Chu, Y.-M.: Optimal bounds for the generalized Euler-Mascheroni constant. J. Inequal. Appl., 2018, Article ID 118, 9 pages (2018) Wang, M.-K., Chu, H.-H., Chu, Y.-M.: Precise bounds for the weighted Hölder mean of the complete p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p$$\end{document}-elliptic integrals, J. Math. Anal. Appl., 480(2), Article ID 123388, 9 pages (2019) YangZ-HTianJ-FConvexity and monotonicity for elliptic integrals of the first kind and applicationsAppl. Anal. Discrete Math.2019131240260394805410.2298/AADM171015001Y ZhaoT-HHeZ-YChuY-MOn some refinements for inequalities involving zero-balanced hypergeometric functionAIMS Math.20205664796495414896210.3934/math.2020418 TakeuchiSComplete p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p$$\end{document}-elliptic integrals and a computation formula of πp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi _p$$\end{document} for p=4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p=4$$\end{document}Ramanujan J.2018462309321380396210.1007/s11139-018-9993-y Zhao, T.-H., Shi, L., Chu, Y.-M.: Convexity and concavity of the modified Bessel functions of the first kind with respect to Hölder means, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat., 114(2), Article ID 96, 14 pages (2020) AbramowitzMStegunIAHandbook of mathematical functions with formulas, graphs, and mathematical tables1964WashingtonU. S. Government Printing Office0171.38503 WangM-KChuY-MLiY-MZhangWAsymptotic expansion and bounds for complete elliptic integralsMath. Inequal. Appl.202023382184141289551455.33013 HeikkalaVVamanamurthyMKVuorinenMGeneralized elliptic integralsComput. Methods Funct. 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| References_xml | – reference: YangZ-HTianJ-FSharp inequalities for the generalized elliptic integrals of the first kindRamanujan J.201948191116390249710.1007/s11139-018-0061-4 – reference: ZhaoT-HWangM-KChuY-MA sharp double inequality involving generalized complete elliptic integral of the first kindAIMS Math.20205545124528414746210.3934/math.2020290 – reference: BariczÁTurán type inequalities for generalized complete elliptic integralsMath. Z.20072564895911230889610.1007/s00209-007-0111-x – reference: ChuY-MWangM-KOptimal Lehmer mean bounds for the Toader meanResults. Math.2012613–4223229292511710.1007/s00025-010-0090-9 – reference: AbramowitzMStegunIAHandbook of mathematical functions with formulas, graphs, and mathematical tables1964WashingtonU. S. Government Printing Office0171.38503 – reference: YangZ-HChuY-MWangM-KMonotonicity criterion for the quotient of power series with applicationsJ. Math. Anal. Appl.20154281587604332700510.1016/j.jmaa.2015.03.043 – reference: YangZ-HQianW-MZhangWChuY-MNotes on the complete elliptic integral of the first kindMath. Inequal. Appl.2020231779340615261440.33020 – reference: AndersonGDQiuS-LVamanamurthyMKVuorinenMGeneralized elliptic integrals and modular equationsPacific J. Math.20001921137174103110.2140/pjm.2000.192.1 – reference: Wang, M.-K., Chu, H.-H., Chu, Y.-M.: Precise bounds for the weighted Hölder mean of the complete p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p$$\end{document}-elliptic integrals, J. Math. Anal. Appl., 480(2), Article ID 123388, 9 pages (2019) – reference: WangM-KChuY-MQiuS-LSharp bounds for generalized elliptic integrals of the first kindJ. Math. Anal. Appl.20154292744757334249010.1016/j.jmaa.2015.04.035 – reference: WangM-KHeZ-YChuY-MSharp power mean inequalities for the generalized elliptic integral of the first KindComput. Methods Funct. Theory2020201111124407186510.1007/s40315-020-00298-w – reference: Yang, Z.-H., Qian, W.-M., Chu, Y.-M., Zhang, W.: On rational bounds for the gamma function, J. Inequal. Appl., 2017, Article ID 210, 17 pages (2017) – reference: Hai, G.-J., Zhao, T.-H.: Monotonicity properties and bounds involving the two-parameter generalized Grötzsch ring function. J. Inequal. Appl., 2020, Article ID 66, 17 pages (2020) – reference: AndersonGDVamanamurthyMKVuorinenMConformal invariants, inequalities, and quasiconformal maps1997New YorkWiley0885.30012 – reference: TakeuchiSLegendre-type relations for generalized complete elliptic integralsJ. Class. Anal.2016913542358008410.7153/jca-09-04 – reference: Zhao, T.-H., Shi, L., Chu, Y.-M.: Convexity and concavity of the modified Bessel functions of the first kind with respect to Hölder means, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat., 114(2), Article ID 96, 14 pages (2020) – reference: Qi, F.: Bounds for the ratio of two gamma functions. J. Inequal. Appl., 2010, Article ID 493058, 84 pages (2010) – reference: YangZ-HChuY-MZhangWHigh accuracy asymptotic bounds for the complete elliptic integral of the second kindAppl. Math. Comput.2019348552564389417910.1016/j.cam.2018.08.027 – reference: AlzerHRichardsKInequalities for the ratio of complete elliptic integralsProc. Am. Math. Soc.2017145416611670360155710.1090/proc/13337 – reference: TakeuchiSA new form of the generalized complete elliptic integralsKodai Math. J.2016391202226347827910.2996/kmj/1458651700 – reference: AlzerHSharp inequalities for the complete elliptic integral of the first kindMath. Proc. Camb. Philos. Soc.19881242309314163113510.1017/S0305004198002692 – reference: WangM-KChuY-MJiangY-PRamanujan’s cubic transformation inequalities for zero-balanced hypergeometric functionsRocky Mountain J. Math.201646267969135290871350.33007 – reference: ShenJ-MYangZ-HQianW-MZhangWChuY-MSharp rational bounds for the gamma functionMath. Inequal. Appl.202023384385341289561455.33002 – reference: YangZ-HQianW-MChuY-MZhangWOn approximating the arithmetic-geometric mean and complete elliptic integral of the first kindJ. Math. Anal. Appl.2018462217141726377431310.1016/j.jmaa.2018.03.005 – reference: WangM-KChuH-HLiY-MChuY-MAnswers to three conjectures on convexity of three functions involving complete elliptic integrals of the first kindAppl. Anal. Discrete Math.2020141255271409341710.2298/AADM190924020W – reference: ChuY-MWangM-KQiuS-LOptimal combinations bounds of root-square and arithmetic means for Toader meanProc. Indian Acad. Sci. Math. Sci.201212214151290958210.1007/s12044-012-0062-y – reference: ZhaoT-HHeZ-YChuY-MOn some refinements for inequalities involving zero-balanced hypergeometric functionAIMS Math.20205664796495414896210.3934/math.2020418 – reference: Zhao, T.-H., Chu, Y.-M., Wang, H.: Logarithmically complete monotonicity properties relating to the gamma function, Abstr. Appl. Anal., 2011, Article ID 896483, 13 pages (2011) – reference: WangM-MChuY-MQiuY-FQiuS-LAn optimal power mean inequality for the complete elliptic integralsAppl. Math. Lett.2011246887890277615510.1016/j.aml.2010.12.044 – reference: Huang, T.-R., Tan, S.-Y., Ma, X.-Y., Chu, Y.-M.: Monotonicity properties and bounds for the complete p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p$$\end{document}-elliptic integrals. J. Inequal. Appl., 2018, Article ID 239, 11 pages (2018) – reference: TakeuchiSComplete p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p$$\end{document}-elliptic integrals and a computation formula of πp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi _p$$\end{document} for p=4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p=4$$\end{document}Ramanujan J.2018462309321380396210.1007/s11139-018-9993-y – reference: WangM-KChuY-MLiY-MZhangWAsymptotic expansion and bounds for complete elliptic integralsMath. Inequal. Appl.202023382184141289551455.33013 – reference: YangZ-HTianJ-FConvexity and monotonicity for elliptic integrals of the first kind and applicationsAppl. Anal. Discrete Math.2019131240260394805410.2298/AADM171015001Y – reference: Huang, T.-R., Han, B.-W., Ma, X.-Y., Chu, Y.-M.: Optimal bounds for the generalized Euler-Mascheroni constant. J. Inequal. Appl., 2018, Article ID 118, 9 pages (2018) – reference: HeikkalaVVamanamurthyMKVuorinenMGeneralized elliptic integralsComput. Methods Funct. Theory20099175109247826510.1007/BF03321716 – reference: Qian, W.-M., He, Z.-Y., Chu, Y.-M.: Approximation for the complete elliptic integral of the first kind, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. 114(2), Article ID 57, 12 pages (2020) – ident: 352_CR28 doi: 10.1186/s13660-017-1484-y – ident: 352_CR13 doi: 10.1155/2010/493058 – volume: 192 start-page: 1 issue: 1 year: 2000 ident: 352_CR4 publication-title: Pacific J. Math. doi: 10.2140/pjm.2000.192.1 – ident: 352_CR14 doi: 10.1007/s13398-020-00784-9 – ident: 352_CR33 doi: 10.1155/2011/896483 – ident: 352_CR12 doi: 10.1186/s13660-018-1828-2 – volume: 9 start-page: 35 issue: 1 year: 2016 ident: 352_CR17 publication-title: J. Class. Anal. doi: 10.7153/jca-09-04 – volume-title: Conformal invariants, inequalities, and quasiconformal maps year: 1997 ident: 352_CR5 – volume: 256 start-page: 895 issue: 4 year: 2007 ident: 352_CR6 publication-title: Math. Z. doi: 10.1007/s00209-007-0111-x – volume: 46 start-page: 679 issue: 2 year: 2016 ident: 352_CR20 publication-title: Rocky Mountain J. Math. – volume: 48 start-page: 91 issue: 1 year: 2019 ident: 352_CR32 publication-title: Ramanujan J. doi: 10.1007/s11139-018-0061-4 – volume: 24 start-page: 887 issue: 6 year: 2011 ident: 352_CR24 publication-title: Appl. Math. Lett. doi: 10.1016/j.aml.2010.12.044 – volume: 145 start-page: 1661 issue: 4 year: 2017 ident: 352_CR3 publication-title: Proc. Am. Math. Soc. doi: 10.1090/proc/13337 – volume: 122 start-page: 41 issue: 1 year: 2012 ident: 352_CR8 publication-title: Proc. Indian Acad. Sci. Math. Sci. doi: 10.1007/s12044-012-0062-y – volume: 124 start-page: 309 issue: 2 year: 1988 ident: 352_CR2 publication-title: Math. Proc. Camb. Philos. Soc. doi: 10.1017/S0305004198002692 – ident: 352_CR9 doi: 10.1186/s13660-020-02327-7 – volume: 61 start-page: 223 issue: 3–4 year: 2012 ident: 352_CR7 publication-title: Results. Math. doi: 10.1007/s00025-010-0090-9 – volume: 14 start-page: 255 issue: 1 year: 2020 ident: 352_CR21 publication-title: Appl. Anal. Discrete Math. doi: 10.2298/AADM190924020W – volume: 23 start-page: 77 issue: 1 year: 2020 ident: 352_CR30 publication-title: Math. Inequal. Appl. – volume-title: Handbook of mathematical functions with formulas, graphs, and mathematical tables year: 1964 ident: 352_CR1 – volume: 39 start-page: 202 issue: 1 year: 2016 ident: 352_CR16 publication-title: Kodai Math. J. doi: 10.2996/kmj/1458651700 – volume: 20 start-page: 111 issue: 1 year: 2020 ident: 352_CR27 publication-title: Comput. Methods Funct. Theory doi: 10.1007/s40315-020-00298-w – volume: 9 start-page: 75 issue: 1 year: 2009 ident: 352_CR10 publication-title: Comput. Methods Funct. Theory doi: 10.1007/BF03321716 – volume: 429 start-page: 744 issue: 2 year: 2015 ident: 352_CR23 publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2015.04.035 – volume: 13 start-page: 240 issue: 1 year: 2019 ident: 352_CR31 publication-title: Appl. Anal. Discrete Math. doi: 10.2298/AADM171015001Y – volume: 23 start-page: 843 issue: 3 year: 2020 ident: 352_CR15 publication-title: Math. Inequal. Appl. – volume: 428 start-page: 587 issue: 1 year: 2015 ident: 352_CR25 publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2015.03.043 – volume: 46 start-page: 309 issue: 2 year: 2018 ident: 352_CR18 publication-title: Ramanujan J. doi: 10.1007/s11139-018-9993-y – ident: 352_CR19 doi: 10.1016/j.jmaa.2019.123388 – volume: 23 start-page: 821 issue: 3 year: 2020 ident: 352_CR22 publication-title: Math. Inequal. Appl. – ident: 352_CR35 doi: 10.1007/s13398-020-00825-3 – volume: 348 start-page: 552 year: 2019 ident: 352_CR26 publication-title: Appl. Math. Comput. doi: 10.1016/j.cam.2018.08.027 – volume: 5 start-page: 4512 issue: 5 year: 2020 ident: 352_CR36 publication-title: AIMS Math. doi: 10.3934/math.2020290 – volume: 5 start-page: 6479 issue: 6 year: 2020 ident: 352_CR34 publication-title: AIMS Math. doi: 10.3934/math.2020418 – ident: 352_CR11 doi: 10.1186/s13660-018-1711-1 – volume: 462 start-page: 1714 issue: 2 year: 2018 ident: 352_CR29 publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2018.03.005 |
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| Title | Sharp Bounds for the Weighted Hölder Mean of the Zero-Balanced Generalized Complete Elliptic Integrals |
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