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Areas in developing laurent series

  1. Jul 12, 2010 #1
    [tex]f(x)=\frac{-2}{z-1}[/tex]+[tex]\frac{3}{z+2}[/tex]
    our distance is from -2 till 1
    we develop around 1
    so our distances are 3 and zeo
    so our areas are
    0<|z-1|<3
    0<|z-1|
    3>|z-1|
    but i was told to develop around

    0<|z-1|<1
    there is no such area
    ?
     
  2. jcsd
  3. Jul 12, 2010 #2

    HallsofIvy

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    0< |z- 1|< 1 is -1< z< 1 and also [itex]z\ne 0[/itex]- two separate intervals.
     
  4. Jul 12, 2010 #3

    vela

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    The region 0<|z-1|<1 lies completely within 0<|z-1|<3, right? So if you find the Laurent series that converges in 0<|z-1|<3, it will obviously converge when 0<|z-1|<1.
     
  5. Jul 12, 2010 #4
    thanks
    :)
     
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