---
tag: 0NAHXR1FRH
kind: concept
name: Holomorphic function
aliases: [holomorphic, complex-analytic-function]
msc: [30A99]
sources:
  - url: https://en.wikipedia.org/wiki/Holomorphic_function
    locator: lead section
same_as:
  wikidata: Q207476
  wikipedia: Holomorphic function
---

## Summary

A holomorphic function is a complex function that is complex differentiable at each point of an open subset of $\mathbb{C}$, see the [[definition|0DG0Z72CQD]].
Holomorphic functions are the main objects of complex analysis.
They are infinitely differentiable and they are equal to their Taylor series near each point.