= Solution
The <classification of isolated singularities> can be stated through the Laurent expansion of $f$ about $a$:
* The singularity is removable when $f$ extends holomorphically to $a$, equivalently when every negative-power Laurent coefficient is zero.
* It is a pole of order $k$ when $(z-a)^kf(z)$ extends holomorphically to a <function> nonzero at $a$. Equivalently, the <Laurent series> starts with a nonzero $(z-a)^{-k}$ term and has no more negative power.
* It is essential when it is neither removable nor a pole, equivalently when infinitely many negative-power coefficients are nonzero.
Back to article page
