5
$\begingroup$

I want to construct a complex power series with the radius of convergence $R=1$ that diverges in:

1) $k$ points on the circle $\{|z|=1\}$.

2) countable number of points on the circle

I have already crafted series that converges on the whole circle and diverges on the whole circle.

Can anybody help with the problem?

Update: I have googled a series $\sum{\frac{z^{kn}}{kn}}$ that is an answer for 1). Though I still need help for the countable case.

  • 0
    Hint: Can you imagine a solution to 1) for $k=1$. It will help you for general $k$ (think about "rotating").2012-03-21
  • 0
    @martini, I have updated the question. My problem is about DIVergence.2012-03-21
  • 0
    what were your functions that converge and diverge on the whole circle?2012-03-21

2 Answers 2