holomorphic function

Complex functions differentiable everywhere on their domains

EntityQ207476

Also known as holomorphic functions · analytic function · analytic functions

Subclass of: function of a complex variable
, meromorphic function

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From Wikipedia, the free encyclopedia · Read full article · Text CC BY-SA 4.0

In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighbourhood of each point in a domain in complex coordinate space ⁠⁠. The existence of a complex derivative in a neighbourhood is a very strong condition: It implies that a holomorphic function is infinitely differentiable and locally equal to its own Taylor series. Holomorphic functions are the central objects of study in complex analysis.

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Studied by: complex analysis

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Source last edited September 14, 2026. AIDB refreshes this page daily.

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AIDB. (2026). holomorphic function (Q207476). Retrieved from https://aidb.si/e/holomorphic-function-Q207476