In mathematics, antiholomorphic functions (also called antianalytic functions) are a family of functionss closely related to but distinct from holomorphic functions.

defined on an open set in the complex plane is said to be antiholomorphic if its derivative is the complex conjugate.

A definition of antiholomorphic function follows: ."

is a holomorphic function. Moreover, any antiholomorphic function can be obtained in this manner from a holomorphic function. This implies that a function is antiholomorphic if and only if it can be expanded in a power series.

If a function is both holomorphic and antiholomorphic, then it is constant on any connected component of its domain.

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