Poles of a function are specific types of singularities where a function takes on infinite values. They occur in complex analysis when the function can be expressed in the form $$f(z) = \frac{g(z)}{(z - z_0)^n}$$, where $g(z)$ is analytic at $z_0$ and $n$ is a positive integer. The order of the pole corresponds to the value of $n$ and provides insight into the behavior of the function around that point.
congrats on reading the definition of poles of a function. now let's actually learn it.