Definition:Holomorphic Function

Also defined as
A holomorphic function is sometimes defined as continuously differentiable.

By Holomorphic Function is Continuously Differentiable, the two are equivalent.

Also known as
Some authors refer to a holomorphic function on an open set of $\C$ as a (complex) analytic function.

This is because, by Holomorphic Function is Analytic, they are equivalent.

Also see

 * Definition:Meromorphic Function
 * Definition:Complex Analytic Function