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Complex Analysis Question

  1. Mar 27, 2008 #1
    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?
     
  2. jcsd
  3. Mar 27, 2008 #2
    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.
     
  4. Mar 27, 2008 #3
    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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