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Trouble with an index change in Laurent series

  1. Mar 6, 2016 #1
    1. The problem statement, all variables and given/known data
    Hey guys, I'm just going through a Laurent series example and I'm having trouble understanding how they switched the index on a summation from n=0 to n=1 and then switched the argument from z^(-n-1) to z^n as well as changing the upper limit to -infinity. If anyone could shed some light on that for me I would really appreciate it.



    2. Relevant equations
    http://imgur.com/0PkgLim

    3. The attempt at a solution
    I thought that if you changed the index to n=1 then the power on z should just move up one erasing the ^(-1) and i'm not sure how switching the limit to negative infinity changes anything. Thanks for any help.
     

    Attached Files:

  2. jcsd
  3. Mar 6, 2016 #2

    vela

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    Try rewriting the summation in terms of ##k = -n-1##. What values does ##k## cover when ##n## goes from ##0## to ##\infty##?
     
  4. Mar 25, 2016 #3
    Thank you very much :)
     
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