摘要
复数项幂级数Σ∞n=1znn在有界区域 |z|<1内是收敛的 ,在无界多连通区域 |z|>1上是发散的 ,在边界 |z|=1上当 z =- 1时收敛 ,z =1时发散。而对其它点的收敛情况 ,一般的教材及参考文献均未涉及。本文利用级数收敛的定义得到了此级数在 |z|
Complex power series Σ∞n=1znn is convergent in the bounded region ｜z｜<1,and diverses on the unbounded region ｜z｜>1.On the edge points, the series diverses at z=1,and converses at z=-1.But for the other points,no references consider the convergence.This paper obtains the convergence set of this series on ｜z｜=1 by the definition of series convergence.
