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Math Help - Help! Laurent series

  1. #1
    janfg67
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    Help! Laurent series

    Hi everyone... I need help with a Laurent series. The problem is finding the finite Laurent series for (1 + z^2) / (z-2) for |z-2| > 2. I'm having trouble getting the algebraic manipulation of some form of: 1/(1 + g(z-2) ) or 1/(1 - g(z-2)). The finite part is also throwing me off. Thanks for any help you can give!
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    Quote Originally Posted by janfg67 View Post
    Hi everyone... I need help with a Laurent series. The problem is finding the finite Laurent series for (1 + z^2) / (z-2) for |z-2| > 2. I'm having trouble getting the algebraic manipulation of some form of: 1/(1 + g(z-2) ) or 1/(1 - g(z-2)). The finite part is also throwing me off. Thanks for any help you can give!
    \frac{z^2 + 1}{z-2} = \frac{(z^2 - 4)+5}{z-2} = \frac{(z-2)(z+2)}{z-2} + \frac{5}{z-2}
    So,
    (z+2) + 5(z-2)^{-1} = 5(z-2)^{-1} + 4 +(z-2)
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