论文 杨朋.docx

天津师范大学本科毕业论文(设计) 题目: 幂级数求和的简便方法学院:数学科学学院学生姓名:杨朋学号: 09505057 专业:数学与应用数学年级: 2009 级完成日期: 2013 年5月 13日指导教师:许贵桥Ⅰ幂级数求和的简便方法摘要: 幂级数求和在高等数学中对于初学者来讲是一个难点同时又是一个重点,,但当遇到一些具体的幂级数求和的问题时,,介绍了利用微分方程、通项公式、定义法、代数法来求幂级数的和函数,从而拓宽对幂级数求和的认识及对它有更深一步的了解. 关键词: 幂级数求和;微分方程;通项公式Ⅱ Some Simple Methods of Power Series Summation Ab stract: The summing power series isa difficult and important for beginne rs in high mathematics,its summing method isa lot first,the general method is itemizd integral and itemzd differential,however when we encounter some specific problems of power series , itemizd integral and itemzd differential,ar not always simple and this article on the basis of itemizd integral and itemzd differential draw into differential equation ,general term formula ,defined method and algebraic method to solve the power series summation .Thus we broaden the understanding of power serier summation and the same time have a deeper understanding of it. Key words: power series summation ; differential equation; general term formula Ⅲ目录 1引言...................................................................................................................................... 1 幂级数及幂级数的和函数的基本概念...................................................................... 1 幂级数的基本性质...................................................................................................... 1 .............................................................................. 2 2幂级数求和的几种方法...................................................................................................... 3 、逐项微分和逐项积分球幂级数的和函数...................................... 3 .............................................................................. 4 对于求幂级数的和函数.............................................................................................. 8 预备知识..........................