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Complex Analysis: Entire Function Series

  1. Feb 16, 2012 #1
    1. The problem statement, all variables and given/known data
    I need to prove that [tex]\sum_{n=1}^{∞}[1−Cos(n−1z)][/tex] is entire.

    2. Relevant equations

    3. The attempt at a solution
    I know that I need to show that the series is differentiable for its whole domain, but I am not sure how to do that. Should I try to use the ratio test?
  2. jcsd
  3. Feb 16, 2012 #2


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    You probably mean 1-cos(z/n). Yes, expand the cos in a power series and try to say something about the convergence of the summed series using the ratio test.
  4. Feb 17, 2012 #3
    Oops, that is what I mean. Thank you very much.
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