幂级数和函数的求法及应用  

The Summation Method of Power Series and Its Application

作　　者：孟献青 MENG Xian-qing(School of Mathematics and Statistics,Shanxi Datong University,Datong Shanxi,037009;Institute of Quantum Information Science,Shanxi Datong University,Datong Shanxi,037009)

机构地区：[1]山西大同大学数学与统计学院,山西大同037009 [2]山西大同大学量子信息科学研究所,山西大同037009

出　　处：《山西大同大学学报（自然科学版）》2021年第6期8-11,共4页Journal of Shanxi Datong University(Natural Science Edition)

基　　金：山西大同大学校级科研项目[2020K2];湖南商学院北津学院教研教改项目[201904]。

摘　　要：幂级数的求和问题是高等数学的重要内容。讨论了如何通过四则运算、逐项积分、逐项求导把复杂的幂级数求和问题转化为三种最基本的类型进行求解,并介绍了幂级数的和函数在求数列极限,积分及数项级数求和中的应用。The summation of power series is an important content of higher mathematics.This paper discusses how to transform the complex power series summation problem into three most basic types for solution through the four fundamental operations of arith‐metic,term by term integration and term by term derivation,at the same time,introduces the application of the sum function of power series in solving the limit of series,integration and summation of series.

关 键 词：幂级数 和函数 数项级数 逐项积分 逐项求导 

分 类 号：O173[理学—数学]