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Which sets are removable for holomorphic functions?
Prove analyticity by Morera’s theorem

Let $f$ be a continuous complex-valued function on $\mathbb{C}$ such that it is analytic everywhere outside $[-a,a] \subset \mathbb{R}$. Show that it is in fact entire.

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marked as duplicate by Jonas Meyer, Henry T. Horton, Austin Mohr, rschwieb, 5PM Jan 22 '13 at 2:47

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When you say strip, do you mean an actual strip $[-a+it,a+it]$, as $t\in\mathbb R$ varies, or you really want the subset $[-a,a]\subset\mathbb R$? –  M Turgeon Sep 26 '12 at 16:02
The latter one. Sorry for any confusion! –  Char Sep 26 '12 at 16:06
This has been answered several times already. Search for "Morera" and you'll find some answers. –  WimC Sep 26 '12 at 16:19
Thanks! I can see how that could be used to solve this problem! –  Char Sep 26 '12 at 16:28
I started to type an answer but @WimC was faster.(+1) –  vesszabo Sep 26 '12 at 16:45

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