广义Hersch-Pfluger偏差函数的单调性及不等式  

Monotonicity and inequalities for generalized Hersch-Pfluger distortion function

作　　者：王飞[1] 周培桂 WANG Fei;ZHOU Peigui(Teaching Section of Mathematics,Zhejiang Institute of Mechanical and Electrical Engineering,Hangzhou 310053,China;Keyi College of Zhejiang Sci-Tech University,Shangyu 312300,China)

机构地区：[1]浙江机电职业技术学院数学教研室,杭州310053 [2]浙江理工大学科技与艺术学院,浙江上虞312300

出　　处：《浙江理工大学学报（自然科学版）》2019年第4期517-521,共5页Journal of Zhejiang Sci-Tech University(Natural Sciences)

基　　金：浙江省教育厅科研项目(Y201635387,Y201840023);浙江机电职业技术学院科研项目(A027117021);浙江省高等学校访问学者项目(FX2018093)

摘　　要：借助单调性l’H?pital法则等分析工具,揭示广义Hersch-Pfluger偏差函数、反双曲正切函数、初等函数的组合单调性,并建立广义Hersch-Pfluger偏差函数精确不等式。此外,通过Hüber函数分析性质获得Hersch-Pfluger偏差函数的单调性和不等式,从而改进Ramanujan模方程解的已知估计。In this study,the monotonicity properties of combinations of generalized Hersch-Pfluger distortion function,inverse hyperbolic tangent function and elementary functions are mainly analyzed with monotone I’H?pital rule,and precise inequalities of generalized Hersch-Pfluger distortion function are established.Besides,the monotonicity properties and inequalities of Hersch-Pfluger distortion function are figured out via property analysis with Hüber function,so as to improve the known estimates of solutions of Ramanujan modular equations.

关 键 词：精确不等式 Ramanujan模方程 广义Hersch-Pfluger偏差函数 反双曲正切函数 

分 类 号：O174[理学—数学]