摘要:形如 = 的函数项级数称为幂级数.它是一类结构简单,应用广泛的级数,且有很多方便的运算性质.本文通过对幂级数的基础知识的学习,利用幂级数可逐项求导,逐项可积的性质,归纳总结了它在求导,求极限,级数求和,积分计算,不等式证明,欧拉公式推导等方面的应用,并结合例题阐述了它在这几种应用中的技巧和方法.22151 毕业论文关键词:幂级数;数学分析;应用
Application of Power Series in Mathematical Analysis
Abstract: Series expressed by function terms like = called power series. It is a kind of simple structure, wide application of the series, and there are a lot of convenient operation properties. In this paper, through study of the basic knowledge of power series, using the power series can be item by item, derivation, item by item, the nature of the integrable, summarized its derivation, limit, series summation, integral calculation, an inequation, euler's formula derivation of application, and combined with examples, the application of it in several of the techniques and methods.
Key words: Power series;Mathematical analysis;Application
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