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Let $L\in \mathbb{C}$ be a line. Assume $f:U\to\mathbb{C}$ is continuous and holomorphic on $U\setminus{L}$. Show that $f$ is holomorphic on $U$ I think I have to use Morera`s theorem and it is enough to consider only cases when line intersects the triangle, but then there might be differant types of these cases( such a line intersects one side in one point, or in infinitely many many points,...) Is there a way to group all of them such that we cover all cases?

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I'd consider two cases: $L$ intersecting the interior of the triangle, or not. –  martini Oct 9 '12 at 11:04
    
Why is this true? If $f(z)=\log(z),U=\Bbb C$ and $L$ is some line through the origin, then the hypotheses are satisfied. –  Andrew Oct 9 '12 at 18:43
    
Ah, maybe you are missing a comma after "Assume $f$ is continuous"? –  Andrew Oct 9 '12 at 18:45

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