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Analytic function ( pole)

  1. Apr 12, 2010 #1
    1. The problem statement, all variables and given/known data

    Let r>1, let f be analytic in the disc (0,r)\{1}, and suppose that f has apole at 1.

    Let sum(a(k) *z(k)) be the power series expantion of f in the disc (0,r). Prove that there is a positive integer N so that a(k) not equal to zero for k>= N, and that

    lim (a(N+j+i)/a(N+1))=1

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Apr 18, 2010 #2
    no body replied on this problem

    is it so hard?
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