幂级数收敛域的论述

Discussion on the Convergence Domain of Power Series

级数研究的第一重要内容是收敛性,为了更好地研究级数的收敛性,作者通过研究幂级数加、减、柯西乘积运算以及幂级数逐项求导和逐项积分,探讨了幂级数的和、差、柯西乘积,以及幂级数求导和求积分后得到新的幂级数的收敛问题。最后通过实际例子进行验证,对今后研究幂级数收敛性是有一定的理论意义的。

The first important content of the series study is convergence.In order to better study the convergence of series,the author explores convergence of the new power series by studying power series addition,subtraction,Cauchy product operation and power series item-by-item derivation and item-by-item integration.Finally,verify knowledge points by practical examples and it is theoretical significance for studying power series convergence in the future.