# $z_{0}$ is a pole of $f$

Let $f$ be an analytic function on a punctured neighborhood of $x_{0}\in\mathbf{C}$, that is, $f$ analytic on

 $\{z\in C:0<|z-x_{0}|<\varepsilon\}$

for some $\varepsilon>0$ and such that

 $\lim_{z\rightarrow z_{0}}|f(z)|=\infty.$

We say then that $x_{0}$ is a pole for $f$.

Title $z_{0}$ is a pole of $f$ Z0IsAPoleOfF 2013-03-22 14:00:55 2013-03-22 14:00:55 drini (3) drini (3) 7 drini (3) Definition msc 30A99