Let U be a domain in the complex numbersMathworldPlanetmathPlanetmath. A function f:U is holomorphic if f has a complex derivativeMathworldPlanetmath at every point x in U, i.e. if


exists for all z0U.

More generally, if Ωn is a domain, then a function f:Ω is said to be holomorphic if f is holomorphic in each of the variables. The class of all holomorphic functions on Ω is usually denoted by 𝒪(Ω).

Title holomorphic
Canonical name Holomorphic
Date of creation 2013-03-22 12:04:33
Last modified on 2013-03-22 12:04:33
Owner djao (24)
Last modified by djao (24)
Numerical id 12
Author djao (24)
Entry type Definition
Classification msc 30D20
Classification msc 32A10
Synonym holomorphic function
Synonym regular function
Synonym complex differentiable
Related topic CauchyRiemannEquations
Related topic Analytic