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# 重新发明复数 篇六 复数域上的收敛性上篇

## 从一些例子引入收敛半径

### I. 例子A

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## A way lead to Complex Region

\frac{1}{a-x}=\frac{1}{a-(X+k)}=\frac{1}{a-k}\frac{1}{[1-\frac{X}{a-k}]} \\
=\sum^{\infty}_{j=0}{\frac{X^j}{(a-k)^{j+1}}} \\
\textbf{where}\space |X|<|a-k|

\frac{1}{1/x^2}=\frac{1}{2}[\frac{1}{1-x}-\frac{1}{-1-x}]\\
=\frac{1}{2}\sum^{\infty}_{j=0}{[\frac{1}{(1-k)^{j+1}}-\frac{1}{(-1-k)^{j+1}}]X^j}\\
\textbf{where}\space |X|<|1-k|\space \textbf{and} \space |X|>|1+k|

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## Reference

Visual Complex Analysis

## 2条评论

1. 哒哒

哇噢，such a big amazing !

1. 下篇则是更大的amazing!