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Math Help - Laurent series question

  1. #1
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    Laurent series question

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

    1 still makes denominator 0
    and
    it is analitical on
    |z|<1
    but the correct answer is
    it is analitical on
    |z|>1
    for
    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; July 10th 2010 at 12:45 PM.
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