---
tag: 0N288P2TB5
kind: concept
name: Radius of convergence
msc: [30B10]
sources:
  - url: https://en.wikipedia.org/wiki/Radius_of_convergence
    locator: lead section
same_as:
  wikidata: Q1428097
  wikipedia: Radius of convergence
---

## Summary

Each power series with center $c$ has a unique $R$ in $[0, \infty]$ such that it converges for $|x - c| < R$ and diverges for $|x - c| > R$. This $R$ is its radius of convergence. The node [[radius of convergence|0660QX1VPR]] gives the precise definition.