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Thread: Laurent series question

  1. #1
    MHF Contributor
    Nov 2008

    Laurent series question

    find the laurent series of $\displaystyle f(x)=\frac{-2}{z-1}$+$\displaystyle \frac{3}{z+2}$
    i was by my teacher that the radius of convergence
    is what smaller then the number which makes the denominator 0.
    $\displaystyle f(x)=\frac{1}{1-z}$
    the radius is 1 and
    because 1-1=0
    it is analitical on
    so if i apply the same logic
    $\displaystyle f(x)=\frac{-2}{z-1}$

    1 still makes denominator 0
    it is analitical on
    but the correct answer is
    it is analitical on
    $\displaystyle f(x)=\frac{3}{z+2}$
    -2 makes denominator 0
    so |z|<-2 (but its illogical because |z| is a positive numbe)
    where is my mistake?
    Last edited by transgalactic; Jul 10th 2010 at 11:45 AM.
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