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In mathematics, **antiholomorphic functions** (also called **antianalytic functions**^{[1]}) are a family of functions closely related to but distinct from holomorphic functions.

A function of the complex variable z defined on an open set in the complex plane is said to be **antiholomorphic** if its derivative with respect to *z* exists in the neighbourhood of each and every point in that set, where *z* is the complex conjugate.

A definition of antiholomorphic function follows:^{[1]}

"[a] function of one or more complex variables [is said to be anti-holomorphic if (and only if) it] is the complex conjugate of a holomorphic function ."

One can show that if *f*(*z*) is a holomorphic function on an open set *D*, then *f*(*z*) is an antiholomorphic function on *D*, where *D* is the reflection against the *x*-axis of *D*, or in other words, *D* is the set of complex conjugates of elements of *D*. 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 in *z* in a neighborhood of each point in its domain. Also, a function *f*(*z*) is antiholomorphic on an open set *D* if and only if the function *f*(*z*) is holomorphic on *D*.

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