# Definition talk:Analytic Function

## Analytic vs. holomorphic

It is fairly standard terminology these days to say that an **analytic** function is one that can be expressed by a power series, while a **holomorphic** function is one that is complex differentiable (on an open set). The two definitions are equivalent, but this is not trivial - it requires the development of Cauchy's integral theorem.

I would suggest defining analytic and holomorphic separately, with a note of course that these two definitions coincide, with a reference to Analytic Functions are Holomorphic, an article that is yet to be created.

As an aside, I believe Bers used to refer to the equivalence of these definitions, and some others, as the **Fundamental Theorem of Complex Analysis**, as in the recent book 'Complex Analysis in the spirit of Lipman Bers', by Kra et al. lasserempe 09:13, 16 February 2009 (UTC)

All sounds sensible to me. Go for it. --prime mover (talk) 19:05, 16 February 2009 (UTC)