Antiholomorphic function

In mathematics, a function on the complex plane is antiholomorphic at a point if its derivative with respect to z̅ exists, where here, z̅ is the complex conjugate. If the function is antiholomorphic at every point of some subset of the complex plane, then it is antiholomorphic on that set.

If f(z) is a holomorphic function, then f(z̅) is an antiholomorphic function.

A function

$f:\mathbb {C} \rightarrow \mathbb {C}$

is antianalytic if $f({\bar {z}})$ is an analytic function (i.e. holomorphic).

The local representation of analytic functions by means of power series shows that being antianalytic in a neighbourhood of a complex number a is the same condition as the existence of a power series in z̅ − a..