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Expansion of power series

  1. Jul 25, 2009 #1
    Hi,

    I have 2 questions regarding how to expand power series.

    1). Find the power series expansion of Log z about the point z= i - 2

    2). Expand the function 1/(z^2 + 1) in power series about infinity

    Any help will be greatly appreciated. This is because I am totally unsure about what to do when they asked for an expansion of complex function or power series. And if possible, can you show me a somewhat detailed step by step explanation? I'm really sorry for the trouble. This is because I'm really clueless on how to even start.

    Thank you so much:smile:
     
  2. jcsd
  3. Jul 25, 2009 #2
    Do it the same way as you would if z wasn't complex. Just watch your algebra with regards to any simplifications you might make.
     
  4. Jul 25, 2009 #3

    HallsofIvy

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    For the second one, write 1/(z^2+ 1) as
    [tex]\frac{1}{1- (iz)^2}[/tex]
    and express it as a geometric series.
     
  5. Jul 25, 2009 #4
    I would do that to expand at zero. But at infinity, probably I would do
    [tex]\frac{1}{z^2+ 1} = \frac{1}{z^2}\left(\frac{1}{1+(1/z^2)}\right)[/tex],
    then expand as a geometric series.
     
  6. Jul 25, 2009 #5

    HallsofIvy

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    Absolutely right. I did not see that "about infinity". Thanks.
     
  7. Jul 25, 2009 #6
    thank you so much for all of your help! :) i really appreciate that..

    Does anyone of you know how to do number 1 though?
     
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