Isolated singularities are classified as one of 3 types: f has a removable singularity at z0 if f(z) is bounded on some punctured disc about z0: |f(z)| ≤ M when 0 < |z − z0| < r , some M, r > 0. f has a pole at z0 if limz→z0 f(z) = ∞. Everything else: f has an essential singularity at z0.

What are the three types of singularities?

There are three types of isolated singularities: removable singularities, poles and essential singularities.

How do you find the singularity of a function?

The point a is a removable singularity of f if there exists a holomorphic function g defined on all of U such that f(z) = g(z) for all z in U \ {a}. The function g is a continuous replacement for the function f.