Re: Second derivative of analytic function.

From: David C. Ullrich (ullrich_at_math.okstate.edu)
Date: 03/06/05 

Date: Sun, 06 Mar 2005 07:56:05 -0600

On Sat, 05 Mar 2005 16:17:26 -0500, "G. A. Edgar"
<edgar@math.ohio-state.edu.invalid> wrote:

>In article <422A15FB.674EBECB@ANTISPAMbtinternet.com.invalid>, Jim
>Spriggs <jim.sprigs@ANTISPAMbtinternet.com.invalid> wrote:
>
>> The only proofs I have seen that an analytic function has a second
>> derivative use contour integration. Is there a proof of this that
>> doesn't?
>
>There is such a proof, but it is much more difficult than the proofs
>using integration. This is from a comment made in the text COMPLEX
>ANALYSIS by Ahlfors. Or maybe it was just a comment Ahlfors made in
>his lecture on that day (around 1971 when I was in his class).
>
>For Jose Carlos Santos: The question in your language would
>be: if f' exists in an open set, then why is f' analytic?

Or possibly "if f' exists in an open set, then why is f analytic?"

************************

David C. Ullrich