高阶Cauchy中值定理“中间点”x→+∞时更广泛的渐近估计式  

More Extensive Asymptotic Estimation Formula of “Intermediate Point” for High Order Cauchy Mean Value Theorem x Is Near +∞

作　　者：张树义[1] 聂辉 丛培根 Zhang Shuyi;Nie Hui;Cong Peigen(College of Mathematics and Physics,Bohai University,Jinzhou 121013,China)

机构地区：[1]渤海大学数理学院,辽宁锦州121013

出　　处：《北华大学学报（自然科学版）》2019年第1期1-7,共7页Journal of Beihua University（Natural Science）

基　　金：国家自然科学基金项目(11371070);渤海大学研究生创新基金项目(YJC20170036)

摘　　要：利用无穷区间上的比较函数概念研究高阶Cauchy中值定理"中间点"x→+∞时的渐近性态,在一定条件下,建立高阶Cauchy中值定理"中间点"x→+∞时更广泛的渐近估计式,统一并改进了相关结果.The purpose of this paper is to study the asymptotic behavior of“intermediate point”of high order Cauchy mean value theorem by using the concept of comparison function in infinite interval when x is near+∞.Under certain conditions,a more extensive asymptotic estimation formula of“intermediate point”for high order Cauchy mean value theorem is established when x is near+∞.Thus the corresponding results in some references are unified and developed.

关 键 词：比较函数 高阶Cauchy中值定理 无穷区间 中间点 

分 类 号：O171[理学—数学]