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Math Help - All Laurent series expansion around 1.

  1. #1
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    Question All Laurent series expansion around 1.

    My question is

    Find all Laurent series expansions of function

    f(x)=z^4/(3+z^2) around 1.

    Please help!! I will be thankful, if someone can tell me how to do this!!

    Thanks!!
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  2. #2
    MHF Contributor chisigma's Avatar
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    The function \frac{z^{4}}{3+z^{2}} is analytic in z=1 so that here the Laurent series and the Taylor seriers are the same and is...

    \displaystyle f(z)= \sum_{n=0}^{\infty}  f^{(n)} (1)\ \frac{(z-1)^{n}}{n!} (1)

    Kind regards

    \chi \sigma
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