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, PDF,    科研立项经费支持
作者: 王 飞*：浙江机电职业技术学院数学教研室，浙江 杭州；周培桂, 王晓宇：浙江理工大学科技与艺术学院，浙江 上虞
关键词: 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
摘要: 本文研究广义Grötzsch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。
Abstract: In this paper, we study some monotonicity properties of certain functions defined in term of gen-eralized Grötzsch 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.
文章引用：王飞, 周培桂, 王晓宇. 广义GrO¨tzsch环函数的精确界及应用[J]. 理论数学, 2019, 9(3): 254-258. https://doi.org/10.12677/PM.2019.93032

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