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Laurent series

  1. May 24, 2010 #1
    1. The problem statement, all variables and given/known data
    Find the Laurent series for f(z)=1/(z(z-1)) valid on 1<|z-1|<infinity


    2. Relevant equations
    1/(1+a)=1-a+a^2-a^3... where |a|<1
    we are not supposed to use integrals for this problem

    3. The attempt at a solution
    I want 1/(z-1) to be in my final answer, so I have 1/(z(z-1))=(1/(z-1))(1/(z-1))(1/(1+1/(z-1))=(*)
    I can then expand the last of the three terms in (*) as 1/(1-1/(z-1))=1-(z-1)^-1+(z-1)^-2 etc.
    Is this right? can I then multiply it by the first two (multiplicative) terms in (*) to get an extra (z-1)^-2 in each term of the series
     
  2. jcsd
  3. May 24, 2010 #2

    vela

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    Yes, that's right.
     
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