Definition:Holomorphic Function/Vector-Valued

Definition

This definition needs to be completed. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by adding or completing the definition. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{DefinitionWanted}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

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 an analytic (complex) function.

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

Sometimes the term regular function can be seen, which means the same thing.

Also see

• Results about holomorphic functions can be found here.