摘要
本文总结了求幂级数和函数的四种方法。一种方法是将待求级数分解成己知和函数的级数的运算(一般是加减)表达形式,然后逐一求和新的级数;第二种方法是“先求导,再积分”或“先积分,再求导”;第三种方法是把待求级数用基本初等函数的幂级数展开式表示出来;第四种方法是列写出和函数满足的微分方程,解此微分方程得到和函数。
This paper summarizes some kinds of solutions of sum functions of power series. （ 1 ） The first sdution is to let series be decomposed into operative expression of function series whose sum functions are known; （2）＂The second solution is the method of first derivation, second quadrature＂ or ＂first quadrature, second derivation＂;（3）The third one is to let series be expressed by basic elementary function＇s power series expansion; （4）The fourth one is to determine differential equations which sum functions sat- isfy, then solve the differential equations.
关键词
函数项级数
幂级数
和函数
series of functions
power series
sum functions
