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单词 Holomorphic
释义

holomorphic


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

limzz0f(z)-f(z0)z-z0

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).

Titleholomorphic
Canonical nameHolomorphic
Date of creation2013-03-22 12:04:33
Last modified on2013-03-22 12:04:33
Ownerdjao (24)
Last modified bydjao (24)
Numerical id12
Authordjao (24)
Entry typeDefinition
Classificationmsc 30D20
Classificationmsc 32A10
Synonymholomorphic function
Synonymregular function
Synonymcomplex differentiable
Related topicCauchyRiemannEquations
Related topicAnalytic
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