Analytic Functions and Complex Analysis: Understanding the Relationship

[ultimateceej]

I don't really know which forum to post this in but I just have a quick question:

Is it sufficient to say that a function is analytic on a domain if it has a derivative and the derivative is continuous?

 

[Diffy]

I believe this from Wikipedia answers your question:

Any analytic function is smooth, that is, infinitely differentiable. The converse is not true; in fact, in a certain sense, the analytic functions are rather sparse compared to the infinitely differentiable functions.

 

[ultimateceej]

Thanks for the reply. I went to the wikipedia page and saw your post, but also came across this:

It can be proved that any complex function differentiable (in the complex sense) in an open set is analytic.

So it's not true in general, but in a complex context it is (according to wikipedia). Thanks for replying and pointing me to the answer.