---
tag: 07GJV36896
kind: concept
name: Complex exponential
aliases: [exponential-function, exp]
msc: [33B10]
sources:
  - url: https://en.wikipedia.org/wiki/Exponential_function
    locator: Complex exponential
---

## Summary

The complex exponential is the function $z \mapsto e^z = \sum_{n \ge 0} z^n / n!$ on $\mathbb{C}$, see the [[definition|054VXHMCA3]].
It extends the real exponential function, it is entire, and it has period $2\pi i$.