线性微分方程解的存在唯一性在幂级数中的应用  

The Application of Existence and Uniqueness Theorem of the Solution to Linear Differential Equation in Power Series

作　　者：彭娟[1] 范周田[1] PENG Juan;FAN Zhou-tian(College of Science,Beijing University of Technology,Beijing 10024,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》2018年第5期77-80,共4页College Mathematics

摘　　要：在幂级数的学习中,如何将函数展开成幂级数和求幂级数的和函数这两类问题是学习的重点和难点.利用线性微分方程解的存在唯一性,分别给出了求函数的麦克劳林展开式和计算幂级数和函数的一般步骤.There are two kinds of important issues in the study of power series.One is the expansion of power series,the other is to find the sum function of power series.By using the existence and uniqueness theorem of the solution to linear differential equation,the general steps to solve the above two problems are given.

关 键 词：线性微分方程解的存在唯一 麦克劳林级数 幂级数 和函数 

分 类 号：O172.1[理学—数学]