Calculating residuals

  • Thread starter Tosh5457
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  • #1

Homework Statement

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]

Homework Equations

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)?
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  • #2
Try expressing the exponential by its taylor series.

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