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Complex Analysis: Special Power Series

  1. Feb 24, 2015 #1
    1. The problem statement, all variables and given/known data
    Give an example of a power series with [itex]R=1[\itex] that converges uniformly for [itex]|z|\le 1[\itex], but such that its derived series converges nowhere for [itex]|z=1|[\itex].

    2. Relevant equations
    R is the radius of convergence and the derived series is the term by term derivative.

    3. The attempt at a solution
    I've tried a bunch of stuff but at the moment I'm leaning towards some variation of the power series for the sin function.
    It would be nice if there was a way to solve this without guessing and checking a bunch of times.
     
  2. jcsd
  3. Feb 24, 2015 #2
    It's OK to delete this. Posted it on accident.
     
    Last edited: Feb 25, 2015
  4. Feb 24, 2015 #3
    Sorry, I'm not sure why my latex commands aren't taking.
     
  5. Feb 25, 2015 #4

    BvU

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    You want a forward slash to terminate, not a backslash.
     
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