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What does the space $\overline{\mathbb{C}[z]}$ stands for? Does it contain all the analytic functions or there are something else? And what about the closure thing?

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    Don't you mean $\overline{\mathbb{C}[z]}$ in the title of the question as well?2011-11-21
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    Could it be the polynomials in the variable $\overline{z}$? As in [Antiholomorphic function](http://en.wikipedia.org/wiki/Antiholomorphic_function)?2011-11-21
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    It is impossible to know what that notation means if you do not tell us at least where you found it...2011-11-22

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$\mathbb{C}[z]$ is the space of polynomial functions. I'm not sure what the bar does to it. What context does this appear in? Perhaps $\overline{\mathbb{C}[z]}$ stands for the space of entire functions because they are the limits of polynomials since they have series expansions. Other notations for the space of entire functions are $\mathcal O(\mathbb C)$ and $\mathcal H(\mathbb C)$.

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    I was reading an article about entire functions.2011-11-21
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    @Vanessa: Perhaps you could include a reference to the article in your question?2011-11-21
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    So it is the biggest space of entire functions; contains all complex polynomials, and all other forms of entire functions!2011-11-21
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    @Vanessa, we'd have to see that paper...2011-11-21
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    I would expect that something like $1+(1/2)z+(1/4)z^2+(1/8)z^3+\dots$ would be in the set, and that's not an entire function. It would really, really be good if we could see the article.2011-11-22
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    @Gerry, I meant *globally convergent* series. Perhaps, as you suggest, that space is just the space of holomorphic functions near 0.2011-11-22
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    I know that's what you meant - trouble is, neither one of us knows what the author meant. All I'm saying is that if *I* were to use that symbol, I would mean for it to include anything that looked like a limit of a sequence of polynomials. I might even mean for it to include things like $1+x+2x^2+6x^3+24x^4+120x^5+\dots$, which doesn't converge anywhere but at zero.2011-11-22