算术平均的正弦与正切平均确界的改进  

Improvements of Bounds for the Arithmetic Mean in Terms of the Sine and Tangent Means

作　　者：杨月英[1] YANG Yue-ying(School of Mechatronics and Automobile Engineering,Huzhou Vocational and Technological College,Huzhou 313000,China)

机构地区：[1]湖州职业技术学院机电与汽车工程学院,浙江湖州313000

出　　处：《湖州职业技术学院学报》2020年第3期59-61,共3页Journal of Huzhou Vocational and Technological College

基　　金：2018年度湖州市自然科学资金项目“完全椭圆积分、拟算术平均及其不等式研究”(2018YZ07)的研究成果之一.

摘　　要：研究了算术平均A与正弦平均M sin和正切平均M tan组合的序关系,运用单调性L’Hospital法则等分析工具得到了一个算术平均A关于正弦平均M sin和正切平均M tan的精确不等式.所得结论加强了已知结果.The article discusses the combinations of the sine mean M sin and tangent mean M tan for the arithmetic mean A by using the method of the monotone L’Hospital rule and other analytical tools.The main result obtained is a sharp inequality for the arithmetic mean A in terms of the sine mean M sin and tangent mean M tan.The conclusion is an improvement of some previously known results.

关 键 词：正弦平均 正切平均 算术平均 

分 类 号：O174[理学—数学]