¨tzsch环函数，精确不等式，Ramanujan模方程，广义Hersch-Pfluger偏差函数
Generalized GrO¨tzsch Ring Function, Sharp Inequality, Ramanujan Modular Equations, Generalized Hersch-Pfluger Distortion Function, Open Access Library" />

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广义GrO¨tzsch环函数的精确界及应用
Sharp Inequalities and Application of the Generalized GrO¨tzsch Ring Function

DOI: 10.12677/PM.2019.93032, PP. 254-258

Keywords: 广义GrO">¨tzsch环函数，精确不等式，Ramanujan模方程，广义Hersch-Pfluger偏差函数
Generalized GrO">¨tzsch Ring Function, Sharp Inequality, Ramanujan Modular Equations, Generalized Hersch-Pfluger Distortion Function

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Abstract:

本文研究广义Gr？tzsch环函数与一些初等函数组合的单调性，并由此获得新的精确不等式。同时，将所得结果应用于Ramanujan模方程理论，获得广义Hersch-Pfluger偏差函数新的下界。
In this paper, we study some monotonicity properties of certain functions defined in term of gen-eralized Gr？tzsch ring function and some elementary functions, and get new sharp inequalities. Furthermore, we also obtain the lower bound of generalized Hersch-Pfluger distortion function by applying these results in Ramanujan modular equation theory.

References

[1]  Abramwitz, M. and Stegun, I.A. (1965) Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables. Dover Publications, New York, 253-294.
[2]  Qiu, S.L. and Vuorinen, M. (2005) Special Functions in Geometric Function Theory. In: Kühnau, R., Handbook of Complex Analysis: Geometric Function Theory, Elsevier, Amsterdam, 621-659.
https://doi.org/10.1016/S1874-5709(05)80018-6
[3]  Qiu, S.L., Ma, X.Y. and Huang, T.R. (2017) Some Proper-ties of the Difference between the Ramanujan Constant and Beta Function. Journal of Mathematical Analysis and Ap-plications, 40, 114-129.
https://doi.org/10.1016/j.jmaa.2016.08.043
[4]  Anderson, G.D., Vamanamurthy, M.K. and Vuorinen, M. (1997) Conformal Invariants, Inequalities, and Quasiconformal Maps. John Wiley & Sons, New York, 32-47.
[5]  Anderson, G.D., Qiu, S.L., Vamanamurthy, M.K., et al. (2000) Generalized Elliptic Integrals and Modular Equations. Pacific Journal of Mathematic, 192, 1-37.
https://doi.org/10.2140/pjm.2000.192.1
[6]  裘松良. Gr？tzsch环与Ramanujan模方程[J]. 数学学报, 2000, 43(2): 283-290.
[7]  Wang, G.D., Zhang, X.H. and Chu, Y.M. (2007) Ine-qualities for the Generalized Elliptic Integrals and Modular Functions. Journal of Mathematical Analysis and Applications, 331, 1275-1283.
https://doi.org/10.1016/j.jmaa.2006.09.070
[8]  Alzer, H. and Richards, K. (2015) On the Modulus of the Gr？tzsch Ring. Journal of Mathematical Analysis and Applications, 432, 134-141.
https://doi.org/10.1016/j.jmaa.2015.06.057
[9]  Zhang, X.H. (2017) On the Generalized Modulus. The Ramanu-jan Journal, 43, 405-413.
[10]  Ma, X.Y., Chu, Y.M. and Wang, F. (2013) Monotonicity and Inequalities for the Gen-eralized Distortion Function. Acta Mathematica Scientia, 33, 1759-1766.
https://doi.org/10.1016/S0252-9602(13)60121-6
[11]  张孝惠, 王根娣, 褚玉明, 等. 广义偏差函数的单调性和不等式[J]. 数学年刊, 2007, 28(2): 183-190.

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