---
tag: 050F2FMTKF
kind: concept
name: Harmonic conjugate
aliases: [conjugate-harmonic-function]
msc: [31A05]
sources:
  - url: https://en.wikipedia.org/wiki/Harmonic_conjugate
    locator: lead section
same_as:
  wikidata: Q5659251
  wikipedia: Harmonic conjugate
---

## Summary

A harmonic conjugate of a real harmonic function $u$ is a real function $v$ such that $u + iv$ is holomorphic, see the [[definition|0CC56MJ4FG]].
On a domain, it is unique up to an additive constant when it exists.