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Laurent Series

  1. Nov 25, 2008 #1
    Hi. I am having trouble getting started on this problem.

    I need to find the Laurent series for: f(z) = exp[(a/2)*(z - 1/z)] in |z|>0.

    I know that the coefficients are: (1/2pi)*integral[cos(kx) - a*sin(x)]dx |(0 to 2pi)

    But I am having trouble seeing how to get started on showing that this is true.

    Thanks for any help anyone can offer.
  2. jcsd
  3. Dec 2, 2008 #2
    Maybe this helps: [tex]z = e^{ix} \Leftrightarrow \frac{1}{2}\left(z - \frac{1}{z}\right) = i \sin x[/tex]
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