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Homework Help: Complex Analysis- Singularities

  1. Mar 8, 2010 #1
    1. The problem statement, all variables and given/known data
    Let f be analytic at the complex plane excapt for z= -1 and z=3 which are simple poles of f.

    Let [tex] \Sigma_{-\infty}^{-1} a_{n}(z-2)^{n} [/tex] be the Laurent series of f.
    In part A I've found that the series converges at 1<|z-2|<3 .
    B is: Find the coeefficients [tex] a_{n} [/tex] of the given Laurent series.
    Hint: Look at [tex] g(z) = (z+1)(z-3)f(z) [/tex]


    2. Relevant equations
    3. The attempt at a solution
    We know that g(z) has no poles or singularities whatsoever. So Laurent series of g is actually a Taylor series... But how can we find from this data the given coeefficients?

    Thanks in advance
     
  2. jcsd
  3. Mar 8, 2010 #2

    vela

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    Are you sure that's a correct Laurent series for f(z)? Doesn't it have an essential singularity at z=2?
     
  4. Mar 8, 2010 #3
    I'm sure indeed...I had no typos in this one... But the an's can be also zero or something...
     
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