Isolated singularity

In the context of Complex Analysis, given the function $f$ we would say that $z_{0} \in C$ is a isolated singularity if there exists $r > 0$ such that $f$ is holomorphic in

B (z_{0}, r) - {z_{0}} .

We can define therefore the Laurent series for $f$ around $z_{0}$

f (z) = \sum_{n = 0}^{\infty} a_{n} (z - z_{0})^{n} + \sum_{n = 1}^{\infty} \frac{b_{n}}{(z - z_{0})^{n}}

It is said that the singularity is removable if $b_{n} = 0$ for $n \geq 1$ . Another special case: pole.