广义Lagrange型和Cauchy型Taylor公式  

Generalized Lagrange type and Cauchy type Taylor formulas

作　　者：于林[1] YU Lin(School of Science,China Three Gorges University,Yichang 443002,China)

机构地区：[1]三峡大学理学院,湖北宜昌443002

出　　处：《高师理科学刊》2023年第9期1-3,共3页Journal of Science of Teachers＇College and University

基　　金：国家自然科学基金项目(11871195);三峡大学教学改革研究项目(J2023052)。

摘　　要：通过引入适当的辅助函数,并以单侧导数替换双侧导数,以高阶导数替换一阶导数,证明了一类广义的Lagrange型和Cauchy型Taylor公式.所得结论既是Lagrange中值定理和Cauchy中值定理的推广,同时也是一种新型的Taylor公式.With the help of some suitable auxiliary functions,the generalized Lagrange type and Cauchy type Taylor formulas are proved by replacing bilateral derivatives with unilateral derivatives and replacing first order derivatives with higher order derivatives.The result obtained here is not only a generalization of Lagrange′s mean value theorem and Cauchy′s mean value theorem,but also a new type of Taylor′s formula.

关 键 词：微分中值定理 TAYLOR公式 单侧导数 

分 类 号：O172.1[理学—数学]