幂级数和函数的求法探究  

On the Solving Process of the Summation Function of Power Series

作　　者：赵金虎 Zhao Jinhu(School of Mathematics and Statistics,Fuyang Normal University,Fuyang 236037,China)

机构地区：[1]阜阳师范大学数学与统计学院,安徽阜阳230637

出　　处：《黑河学院学报》2024年第2期181-182,184,共3页Journal of Heihe University

基　　金：国家自然科学基金青年项目“基于分数阶本构关系的多孔介质流动与传热传质数值研究”(12102093)。

摘　　要：通过幂级数的运算求和函数是《数学分析》学习中的难点之一。通过分类列举的方式,根据幂级数的两个性质:在收敛域内的任何闭区间上是一致收敛的;逐项求导、逐项积分后收敛半径不变,但收敛域有可能改变,对幂级数和函数的求法在四个角度进行归纳总结,形成比较全面的解题策略,有利于帮助学习者熟练掌握幂级数的运算。Solving summation function through power series operation is one of the diffi cult points in the study of Mathematical Analysis.By the way of classifi cation and enumeration and according to two properties of power series,it is uniformly convergent in any closed interval in the convergence domain;the radius of convergence remains the same after derivation and integration term by term,but the convergence domain may change.Summarizing the solution of fi nding power series and functions from four perspectives can form a more comprehensive problem-solving strategy,which is conducive to helping learners to master the operation of power series.

关 键 词：幂级数的运算 收敛域 和函数 

分 类 号：O173[理学—数学]