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Math Help - Complex Taylor Series

  1. #1
    Member Haven's Avatar
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    Complex Taylor Series

    I'm having troubles with this one problem.

    Derive the Taylor Series of  f(z) centered around z_{0} = 0 by multiplying the top and bottom by 1-z where f(z) = \frac{1}{1+z+z^2}
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  2. #2
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by Haven View Post
    I'm having troubles with this one problem.

    Derive the Taylor Series of  f(z) centered around z_{0} = 0 by multiplying the top and bottom by 1-z where f(z) = \frac{1}{1+z+z^2}
    Using the hint, we have:

    f(z)=\frac{1-z}{1-z}\cdot\frac{1}{1+z+z^2}=(1-z)\left[\frac{1}{1-z^3}\right]=(1-z)\left[1+z^3+\frac{z^6}{2}+\frac{z^9}{6}+\frac{z^{12}}{24  }+...\right]
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  3. #3
    Member Haven's Avatar
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    Oh my gosh, it's so obvious now. I was trying to do partial fractions or something stupid like that. Thanks alot, and nice joke in your signature
    Last edited by mr fantastic; November 15th 2009 at 04:25 AM. Reason: d --> sh
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  4. #4
    Super Member redsoxfan325's Avatar
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    You're welcome and thanks. I assume you were referring to the Hilbert quote I had (seeing as I changed my signature literally five minutes ago).
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by Haven View Post
    Oh my gosh, it's so obvious now. I was trying to do partial fractions or something stupid like that. Thanks alot, and nice joke in your signature
    You will find that there is a "thanks" button on the right at the bottom of the helpful post for you if you wish to thank the helpful poster.

    CB
    Last edited by mr fantastic; November 15th 2009 at 04:26 AM.
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