---
tag: 0D6KXBHKC0
kind: concept
name: Power series in the complex plane
aliases: [complex-power-series, power-series]
msc: [30B10]
sources:
  - url: https://en.wikipedia.org/wiki/Power_series
    locator: lead section
---

## Summary

A power series is a series $\sum_{n \ge 0} a_n (z - c)^n$ with complex coefficients $a_n$, a center $c$ and a complex variable $z$, see the [[definition|0VARVQ9ZW1]].
It converges on a disc, and its sum is holomorphic there.