Re: Region of convergence



On Wed, 12 Sep 2007 19:09:46 +0300, "I.N. Galidakis"
<morpheus@xxxxxxxxxxxx> wrote:

Is anyone aware of a convergent series sum(a_n*z^n,n=1..oo) in complex analysis
which has a non-circular region of convergence?

Any shape other than a disk would be acceptable.

My instinct (which is often wrong) tells me that it can't happen, but it never
hurts to ask.

Doesn't the ratio test imply that the region of convergence must be a
disk?

quasi
.



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