Complex Analysis Question

Main Question or Discussion Point

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?

Answers and Replies

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.
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. :smile:

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