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Laurent expansion of principal root

  1. May 2, 2009 #1
    How do I find the Laurent expansion of a function containing the principal branch cut of the nth root?

    Example:
    [tex]f(z)=-iz\cdot\sqrt[4]{1-\frac{1}{z^{4}}}[/tex]
     
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  3. May 2, 2009 #2

    Hurkyl

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    In exactly the same way you would any other function. What's giving you trouble?

    (p.s. about what point are you trying to find an expansion?)
     
  4. May 2, 2009 #3
    Around any point a with |a|>1.

    As far as I know, the principal nth root of z is defined as [tex]\sqrt[n]{|z|}e^{\frac{1}{n}i\mathrm{Arg}z}[/tex], which doesn't seem very helpful; how would you expand [tex]\sqrt{z}[/tex] around a point where it is defined?

    Perhaps these are silly questions; my book is very vague on Laurent expansions...

    EDIT: I think I've got it... or maybe not...
     
    Last edited: May 2, 2009
  5. May 20, 2011 #4
    is there any common and simple procedure to find the Laurent expansion of any function? If any then please reply me soon. Thanks
     
  6. May 20, 2011 #5

    HallsofIvy

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    It's essential Taylor's series, allowing negative powers.
     
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