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Calculating residuals

  1. Oct 26, 2011 #1
    1. The problem statement, all variables and given/known data

    Calculate the residuals of the following functions in the corresponding singularities:
    1) [tex]f(z) = z^{2}\exp (\frac{1}{z})[/tex]
    2) [tex]f(z) = exp(\frac{-1}{z^{2}})[/tex]


    2. Relevant equations



    3. The attempt at a solution
    I can't tell if these functions have poles or not, because I can't calculate [tex]lim z \to 0 (z^{m}f(z))[/tex], for any natural m. Is it even possible to calculate the residuals this way, or do i need to put the function in Laurent series (which I haven't studied yet)?
     
    Last edited: Oct 26, 2011
  2. jcsd
  3. Oct 27, 2011 #2
    Try expressing the exponential by its taylor series.
     
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