I am given the definition of the residue of a complex function $f$ at an isolated singularity $z_0$ to be the coefficient of $\frac{1}{z-z_0}$ in the Laurent series expansion of $f$ in some punctured ball $B^{\circ}(z_0,r)$ for some $r>0$.
In general, how would I find it for an essential singularity in general then? I can't find the laurent series expansion of $f$ at it s essential singularity and look at the coefficient can I? (as it's not the definition)
I ask because I saw @Daniel Fischer's answer to: What is the residue of this essential singularity?
where he used the Residue theorem but other answers considered the series expansion as well...