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Complex analysis

  1. Nov 24, 2005 #1
    hi there
    im confused with this question..
    Integrate 1) Sin(1/z) dz
    and 2) Z sin (1/Z^3)

    where Z is any complex number., over C which is a circle of radius 1 centred at 0

    i tried using the cauchy integral formula and stuff but somehow the answer always comes infinity...is that right ..please help..got exam tomorrow!
  2. jcsd
  3. Nov 25, 2005 #2

    matt grime

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    Where are the poles and what are its residues at each pole?
  4. Nov 25, 2005 #3


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    Use Laurent series
  5. Nov 27, 2005 #4


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    Presumably, you know the Taylor's series for sin(z). Replace z in that series by 1/z and 1/z3 to get the Laurent Series for sin(1/z) and sin(1/z3) respectively. Then the integrals should be easy.
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