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Another Laurent Expansion Question

  1. Dec 9, 2009 #1
    1. The problem statement, all variables and given/known data
    Find all possible Laurent expansions centered at 0 for
    (z - 1) / (z + 1)

    Find the Laurent Expansion centerd at z = -1 that converages at z = 1/2 and determine the largest opens et on which
    (z - 1) / (z + 1) converges



    2. Relevant equations



    3. The attempt at a solution

    (z - 1) / (z + 1) breaks down into [z / (z+1)] - [1 / (z+1)]

    For the first one divide out the z to obtain 1 / 1 + (1/z) I think? However not being in the form 1 / 1 - (1/z) would this be the same series but negative? That doens't seem right.

    For breaking down -1 / (z + 1) I didn't know how to attack that one.
     
  2. jcsd
  3. Dec 10, 2009 #2
    Anything?
     
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