Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/inequalities-for-generalized-gr-tzsch-ring-function-btF4OMTzcB
References (40)
-
(1998)
Pi and theAGM,AStudy inAnalyticNumberTheory andComputational Complexity, Reprint of the 1987 Original -
(1995)
Some properties of quasiconformal distortion functions -
B. Bhayo, M. Vuorinen (2011)
On generalized complete elliptic integrals and modular functionsProceedings of the Edinburgh Mathematical Society, 55
-
G. Anderson, M. Vamanamurthy, M. Vuorinen (1997)
Conformal Invariants, Inequalities, and Quasiconformal Maps -
Fei Wang, Jian-hui He, L. Yin, Feng (祁锋) (2019)
Monotonicity properties and inequalities related to generalized Grötzsch ring functionsOpen Mathematics, 17
-
Miao-Kun Wang, Y. Chu, S. Qiu (2015)
Sharp bounds for generalized elliptic integrals of the first kindJournal of Mathematical Analysis and Applications, 429
-
B. Berndt, S. Bhargava, F. Garvan (1995)
Ramanujan’s Theories of Elliptic Functions to Alternative BasesTransactions of the American Mathematical Society, 347
-
Y. Chu, Miao-Kun Wang (2011)
Optimal Lehmer Mean Bounds for the Toader MeanResults in Mathematics, 61
-
S. Takeuchi (2014)
A new form of the generalized complete elliptic integralsarXiv: Classical Analysis and ODEs
-
Zhen-Hang Yang, Y. Chu (2017)
A monotonicity property involving the generalized elliptic integral of the first kindMathematical Inequalities & Applications
-
Zhen-Hang Yang, Wei-Mao Qian, Y. Chu (2018)
Monotonicity properties and bounds involving the complete elliptic integrals of the first kindMathematical Inequalities & Applications
-
Tie-hong Zhao, Zai-Yin He, Y. Chu (2020)
On some refinements for inequalities involving zero-balanced hypergeometric function, 5
-
Miao-Kun Wang, Y. Chu, S. Qiu (2015)
Sharp bounds for generalized elliptic integrals of the first kindarXiv: Classical Analysis and ODEs
-
J. Thomas (1926)
Conformal Invariants.Proceedings of the National Academy of Sciences of the United States of America, 12 6
-
Miao-Kun Wang, Yong-min Li, Y. Chu (2018)
Inequalities and infinite product formula for Ramanujan generalized modular equation functionThe Ramanujan Journal, 46
-
V. Heikkala, M. Vamanamurthy, M. Vuorinen (2007)
Generalized Elliptic IntegralsComputational Methods and Function Theory, 9
-
T-R Huang, S-Y Tan, X-Y Ma, Y-M Chu (2018)
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 integralsJ. Inequal. Appl., 239
-
G. Anderson, S. Qiu, M. Vamanamurthy (1998)
Elliptic Integral Inequalities, with ApplicationsConstructive Approximation, 14
-
Y. Chu, Miao-Kun Wang, S. Qiu (2012)
Optimal combinations bounds of root-square and arithmetic means for Toader meanProceedings - Mathematical Sciences, 122
-
Miao-Kun Wang, S. Qiu, Y. Chu (2018)
Infinite series formula for Hübner upper bound function with applications to Hersch-Pfluger distortion functionMathematical Inequalities & Applications
-
Miao-Kun Wang, Y. Chu, Y. Qiu, S. Qiu (2011)
An optimal power mean inequality for the complete elliptic integralsAppl. Math. Lett., 24
-
Zhen-Hang Yang, Wei-Mao Qian, Y. Chu, Wen Zhang (2017)
Monotonicity rule for the quotient of two functions and its applicationJournal of Inequalities and Applications, 2017
-
G. Anderson, S. Qiu, M. Vamanamurthy, M. Vuorinen (2000)
Generalized elliptic integrals and modular equationsPacific Journal of Mathematics, 192
-
H. Alzer, Kendall Richards (2015)
A note on a function involving complete elliptic integrals: monotonicity, convexity, inequalitiesAnalysis Mathematica, 41
-
Y. Chu, Miao-Kun Wang, S. Qiu, Yue-Ping Jiang (2012)
Bounds for complete elliptic integrals of the second kind with applicationsComput. Math. Appl., 63
-
Guo-Jing Hai, Tie-hong Zhao (2020)
Monotonicity properties and bounds involving the two-parameter generalized Grötzsch ring functionJournal of Inequalities and Applications, 2020
-
Tie-hong Zhao, Miao-Kun Wang, Y. Chu (2021)
Monotonicity and convexity involving generalized elliptic integral of the first kindRevista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 115
-
Y. Chu, Y. Qiu, Miao-Kun Wang (2012)
Hölder mean inequalities for the complete elliptic integralsIntegral Transforms and Special Functions, 23
-
Xiaohui Zhang (2017)
On the generalized modulusThe Ramanujan Journal, 43
-
T. Huang, Shenyang Tan, Xiao-Yan Ma, Y. Chu (2018)
Monotonicity properties and bounds for the complete p-elliptic integralsJournal of Inequalities and Applications, 2018
-
Tie-hong Zhao, Zai-Yin He, Y. Chu (2020)
Sharp Bounds for the Weighted Hölder Mean of the Zero-Balanced Generalized Complete Elliptic IntegralsComputational Methods and Function Theory, 21
-
Miao-Kun Wang, Y. Chu (2017)
Refinements of transformation inequalities for zero-balanced hypergeometric functionsActa Mathematica Scientia, 37
-
Wei-Mao Qian, Y. Chu (2017)
Sharp bounds for a special quasi-arithmetic mean in terms of arithmetic and geometric means with two parametersJournal of Inequalities and Applications, 2017
-
Xiaohui Zhang (2015)
Solution to a conjecture on the Legendre M-function with an application to the generalized modulusJournal of Mathematical Analysis and Applications, 431
-
Miao-Kun Wang, Y. Chu (2018)
Landen inequalities for a class of hypergeometric functions with applicationsMathematical Inequalities & Applications
-
M. Abramowitz, I. Stegun, David Miller (1965)
Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables (National Bureau of Standards Applied Mathematics Series No. 55)Journal of Applied Mechanics, 32
-
Zhen-Hang Yang, Wei-Mao Qian, Y. Chu, Wen Zhang (2018)
On approximating the arithmetic-geometric mean and complete elliptic integral of the first kindJournal of Mathematical Analysis and Applications
-
J. Wendel (1948)
Note on the Gamma FunctionAmerican Mathematical Monthly, 55
-
H. Alzer, S. Qiu (2004)
Monotonicity theorems and inequalities for the complete elliptic integralsJournal of Computational and Applied Mathematics, 172
-
Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations
- Publisher
- Springer Journals
- Copyright
- Copyright © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021
- ISSN
- 1617-9447
- eISSN
- 2195-3724
- DOI
- 10.1007/s40315-021-00415-3
- Publisher site
- See Article on Publisher Site
Abstract
In this paper, we deal with the generalized Grötzsch ring function μa(r)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mu _a(r)$$\end{document} for r∈(0,1)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$r\in (0,1)$$\end{document} in the theory of the Ramanujan generalized modular equation and present new inequalities for μa(r)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mu _a(r)$$\end{document}.
Journal
Computational Methods and Function Theory – Springer Journals
Published: Sep 1, 2022
Keywords: Modular equation; Generalized elliptic integrals; Generalized Grötzsch ring function; Geometric function theory; 33E05; 33C05