An isolated singularity in a complex-valued function at which the function’s Laurent series has a finite principal part. For example,

respectively have an order 1 pole, or simple pole, at 0 and a pole of order 4 at 2. Note that the second function does not have a pole at π‎, as the numerator has a simple zero at π‎.

If a function f(z) has a pole at a, then f(z) →∞ as z→a. See meromorphic function.