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If $f$ is an entire function, then is the radius of convergence of its Taylor series, centered at any point $z_0$, equal to infinity?

I tend to think that this is true, because the series converges to $f$ at any point. Is this incorrect?

rookie
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    Basically, the radius of convergence of a complex power series extends until it encounters a pole or essential singularity of the function. An entire function has no poles or essential singularities. – Doc Dec 13 '13 at 03:50
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    See the proof in http://en.wikipedia.org/wiki/Analyticity_of_holomorphic_functions – Moishe Kohan Dec 13 '13 at 03:52

1 Answers1

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You are absolutely correct. But I had too few characters, so am using filler now.

Igor Rivin
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