$D := U(z_0,r)\setminus \bigcup_{n=1}^{\infty} \{z_n\}$, $z_n$ poles, prove $f(D)$ is dense in $\mathbb{C}$.

Asked Nov 11 '13 at 00:10

Active Nov 11 '13 at 01:48

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I'm looking at the following complex analysis problem.

Suppose that $f$ is analytic in $D := U(z_0,r)\setminus \bigcup_{n=1}^\infty \{z_n\}$, all the points $z_n$ are poles, and $z_n \to z_0$. Prove $f(D)$ is dense in $\mathbb{C}$.

I feel like I have to define some function and manipulate it somehow, but I haven't been able to come up with a function that works. Can you help?

edited Nov 11 '13 at 01:48

Michael Hardy

asked Nov 11 '13 at 00:10

Numbersandsoon

2,910

This question basically asks the same thing: http://math.stackexchange.com/questions/135458/limit-point-of-poles-is-essential-singularity-am-i-speaking-nonsense – Beni Bogosel Nov 11 '13 at 00:26

$D := U(z_0,r)\setminus \bigcup_{n=1}^{\infty} \{z_n\}$, $z_n$ poles, prove $f(D)$ is dense in $\mathbb{C}$.

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