$f: \mathbb{C} \to \mathbb{C}$ is continuous (here $\mathbb{C}$ is the complex plane) and $f$ is analytic everywhere on $\mathbb{C}$ except possibly on the interval $[-1,1]$. Is $f$ an entire function?
Is $f$ an entire function?
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complex-analysis
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1[This](http://math.stackexchange.com/questions/201312/prove-analyticity-by-moreras-theorem) answers your question in more generality. – 2012-11-23