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Math Help - Small question on order of poles

  1. #1
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    Small question on order of poles

    If you have a function thats

    f(z) = g(w)/(z^2-2i) and you want the residue at z = 1+i, z^2 = 2i and g(w) analytic at the point

    would the order of the pole still be 1 even though its z^2?

    or would this require the laurent series to determine properly?

    thanks for any help
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Re: Small question on order of poles

    Quote Originally Posted by Daniiel View Post
    If you have a function thats

    f(z) = g(w)/(z^2-2i) and you want the residue at z = 1+i, z^2 = 2i and g(w) analytic at the point

    would the order of the pole still be 1 even though its z^2?

    or would this require the laurent series to determine properly?

    thanks for any help
    Well think about it, if you wanted to figure out the order of the ple at z=1+i you need to figure out what is the minimum n such that \displaystyle \lim_{z\to 1+i}(z-(1+i))^n\frac{g(z)}{z^2-2i} exists.
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  3. #3
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    Re: Small question on order of poles

    g(w)/(z-(1+i))(z+(1+i)) n=1

    I had troubling seeing that it could be split apart into that.

    iz all good,

    thanks! =]
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