Cauchy–Riemann equations
Sign in to saveAlso known as d'Alembert–Euler conditions, Cauchy–Riemann conditions
system of linear partial differential equations characterizing holomorphic (complex differentiable) functions
Wikidata facts
- Subclass of
- partial differential equation
- Named after
- Bernhard Riemann
- Image
- Cauchy-Riemann.svg
Show 3 more facts
- discoverer or inventor
- Jean Le Rond d'Alembert
- time of discovery or invention
- 1752-00-00
- maintained by WikiProject
- WikiProject Mathematics
via Wikidata · CC0
~29 min read
Encyclopedic overview
A visual depiction of a vector X in a domain being multiplied by a complex number z, then mapped by df, versus being mapped by df then being multiplied by z afterwards. If both of these result in the point ending up in the same place for all X and z, then f satisfies the Cauchy–Riemann condition at the basepoint.
In mathematics, the Cauchy–Riemann equations are two partial differential equations that characterize differentiability of complex functions. The equations are
Excerpted from Wikipedia’s “Cauchy–Riemann equations” article, available under the CC BY-SA 4.0 licence.