关于幂级数收敛半径求法的注记  

A Note on the Method of Finding the Radius of Convergence of Power Series

作　　者：彭娟[1] 范周田[1] 杨蓉 PENG Juan;FAN Zhou-tian;YANG Rong(College of Applied Science,Beijing University of Technology,Beijing 100124,China)

机构地区：[1]北京工业大学应用数理学院,北京100124

出　　处：《大学数学》2019年第2期106-109,共4页College Mathematics

摘　　要：幂级数是微积分应用的重要理论基础,其中收敛半径的求法是学习相关内容的重点和难点.面向工科的高等数学教学中,通常限于介绍求比较简单的幂级数的收敛半径的方法,对于一般的幂级数,由于涉及上极限的理论,高等数学中不做讨论.本文从有界的角度讨论幂级数的收敛半径问题,避开了上极限问题的困难,所得结果可用于求任意幂级数的收敛半径.Power series is an important theoretical basis for calculus application,in which the way to find the convergence radius is both the key point and difficult point.In the higher Mathematics teaching for engineering students,it is usually limited to the method of a relatively simple power series.For the general power series,it is not discussed in higher mathematics because of the theory involving the upper limit.In this paper,the convergence radius of power series is discussed from the point of view of boundedness,avoiding the difficulty of upper limit problem.The result can be used to find the convergence radius of any power series.

关 键 词：幂级数 收敛半径 上极限 有界 

分 类 号：O173.1[理学—数学]