# Differences

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 — pole_of_a_complex_function [2014/03/21 11:11] (current) 2014/02/21 18:17 nikolaj created 2014/02/21 18:17 nikolaj created Line 1: Line 1: + ===== Pole of a complex function ===== + ==== Set ==== + | @#55CCEE: context ​    | @#55CCEE: $\mathcal O$ ... open subset of $\mathbb C$ | + | @#55CCEE: context ​    | @#55CCEE: $f:\mathcal O\to \mathbb C$ | + | @#FFBB00: definiendum | @#FFBB00: $a\in\mathrm{it}$ | + + | @#DDDDDD: range       | @#DDDDDD: $U$ ... open subset of $\mathbb O$ | + | @#DDDDDD: range       | @#DDDDDD: $g:\mathcal O\to \mathbb C$ | + | @#DDDDDD: range       | @#DDDDDD: $n\in\mathbb N, n>0$ | + + | @#55EE55: postulate ​  | @#55EE55: $\exists U,g,n.\ \left(z\in U\right)\land \left(f\ \mathrm{holomorphic\ on}\ U\setminus\{z\}\right)\land \left(g\ \mathrm{holomorphic\ on}\ U\right)\land \left(f(z)=\frac{g(z)}{(z-a)^n}\right)$ | + + ==== Discussion ==== + The natural number $n$ associated with $a$ is called the order of the pole. + + === Reference === + Wikipedia: [[http://​en.wikipedia.org/​wiki/​Pole_%28complex_analysis%29|Pole (complex analysis)]] + ==== Parents ==== + === Context === + [[ℂ valued function]]