---
tag: 0QX19C7K1C
kind: concept
name: Order of a zero
aliases: [multiplicity-of-a-zero]
msc: [30C15]
sources:
  - url: https://en.wikipedia.org/wiki/Zeros_and_poles
    locator: Definitions
---

## Summary

The order of a zero $z_0$ of a holomorphic function $f$ is the smallest $m$ with $f^{(m)}(z_0) \neq 0$, see the [[definition|064N002TX4]].
Near such a zero, $f(z) = (z - z_0)^m g(z)$ with $g(z_0) \neq 0$.