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Homework Help: Laurent series

  1. Jul 22, 2014 #1
    I need explanation about this Laurent series.

    The question is:
    Let {##z\inℂ|0<|z|##}, expand ##\frac{e^{z^2}}{z^3}## where the centre z=0 into Laurent series.

    And the solution is:

    I don't understand the solution because isn't the formula for Laurent series


  2. jcsd
  3. Jul 22, 2014 #2
    Why is this a laurent series? This looks like a maclaurin expansion of the exponential function.
  4. Jul 22, 2014 #3


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    Does a MacLaurin expansion have negative exponents?
  5. Jul 22, 2014 #4
    No it doesn't but that definitely is a power series of the exponential function. Is Laurent series the same as power series? I am confused.
  6. Jul 22, 2014 #5

    Ray Vickson

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    Just write out the first 3 or 4 terms of your series. Does that not look like a Laurent series to you?
  7. Jul 22, 2014 #6
    Aha, now I see it. So, can I conclude that a Taylor/maclaurin series is a Laurent series with only positive exponents?
  8. Jul 23, 2014 #7


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    Yes, of course. But what does that have to do with this problem? This series has negative powers.
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