Laurent Series of a Polynomial

Question

I'm asked to write the Laurent series of $f(z) = z^2 - a^2. $ In any book that I read, it says that the expansion in Laurent series is done in a domain where $f(z)$ has singularities otherwise we can't expand in Laurent Series. Am I understanding, correctly, the definition of Laurent Series?

Can I expand $f(z) = z^2 - a^2$ in Laurent series?

Answer 1

The Laurent series around a removable singularity $z_0$ of $f$ is the power series of $f$ around $z_0$.