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Math Help - Finding Laurent Series

  1. #1
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    Finding Laurent Series

    Hi sorry to trouble you but I've been to find the singular terms in the Laurent expansion of

    <br />
f(z) = \exp(-\frac{1}{z}) at z=0

    Am I correct in saying that because there is an essential singularity here it's undefined or am I completely wrong?
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  2. #2
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    Why not just use the Taylor series for e^w and then substitute w=-1/z.
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  3. #3
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    Quote Originally Posted by shawsend View Post
    Why not just use the Taylor series for e^w and then substitute w=-1/z.
    That would work if I were taking the series about the point  z= \infty

    but the series is about z=0 which was the issue
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  4. #4
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    Quote Originally Posted by thelostchild View Post
    Hi sorry to trouble you but I've been to find the singular terms in the Laurent expansion of

    <br />
f(z) = \exp(-\frac{1}{z}) at z=0

    Am I correct in saying that because there is an essential singularity here it's undefined or am I completely wrong?
    There is an essential singularity but all that means is that the principal part of the Laurent series in an infinite series. The suggestion given in post #2 is what you should do to get this series.
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