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Is it true that "an infinite product of entire functions $\{ f_{n}(z) \}_{n=1}^{\infty}$ is again an entire function"?

$$\prod_{n=1}^{\infty}f_{n}(z)$$ (entire function is a function which is analytic in the complex plane).

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    If it converges locally uniformly, then yes.2012-10-10
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    @Lukas: I don't have any further information, I just have an infinite sequence of entire functions and want to see if the product is entire or not. So I understand that it is not true in general!2012-10-10
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    Maybe you should post the explicit product you are interested in? In general, like for series there is no reason that these products converge in the whole plane.2012-10-10
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    I already did..2012-10-10
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    What if $f_n(z)=z$ for all $n$?2012-10-10

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