Antiholomorphic function

In mathematics, a function on the complex plane is antiholomorphic at a point if its derivative with respect to z* exists, where here, z* 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(z*) is an antiholomorphic function.

A function

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

is antianalytic if f(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 z* − a..