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Math Help - Laurent Series

  1. #1
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    Laurent Series

    Hello, i got this question in a exam:

    Get the Laurent Series of

    {\sqrt{(z-1)(z-2)}}


    i think he said we could do the expansion at the point of our choice

    can you help me out?
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  2. #2
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    Quote Originally Posted by PanZerOlas View Post
    Hello, i got this question in a exam:

    Get the Laurent Series of

    {\sqrt{(z-1)(z-2)}}


    i think he said we could do the expansion at the point of our choice

    can you help me out?
    Notice that (z-1)(z-2) = z^2 - 3z + 2 = z^2 - 3z + \tfrac{9}{4} - \tfrac{9}{4} + 2 = \left( z - \tfrac{3}{2} \right)^2 + \tfrac{17}{4}.
    Thus, I think the most conveint point is \tfrac{3}{2} to exand the series.

    Now, you can almost finish the problem by applying the binomial series.
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