---
tag: 0SYR10HD4R
kind: concept
name: Cauchy principal value
aliases: [principal-value-integral]
msc: [26A42]
sources:
  - url: https://en.wikipedia.org/wiki/Cauchy_principal_value
    locator: lead section
same_as:
  wikidata: Q769374
  wikipedia: Cauchy principal value
---

## Summary

The Cauchy principal value gives a value to some improper integrals that do not converge in the usual sense, see the [[definition|0V3RDQV3ZX]].
It removes a symmetric neighborhood of the singular point, or integrates over a symmetric interval $[-R, R]$, and then takes the limit.