---
tag: 073MWACF1K
kind: concept
name: Order of a pole
aliases: [multiplicity-of-a-pole]
msc: [30D30]
sources:
  - url: https://en.wikipedia.org/wiki/Zeros_and_poles
    locator: Definitions
---

## Summary

The order of a pole $c$ of $f$ is the integer $m \ge 1$ with the following property. The function $(z - c)^m f(z)$ extends to a holomorphic function near $c$ that is not $0$ at $c$, see the [[definition|0YK27TJ4WF]].