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Homework Help: Pole of a function, as a geometric series

  1. Apr 22, 2017 #1
    1. The problem statement, all variables and given/known data
    Determine the order of the poles for the given function.
    [itex] f(z)=\frac{1}{1+e^z} [/itex]

    2. Relevant equations

    3. The attempt at a solution
    I know if you set the denominator equal to zero
    you get z=ln(-1)
    But if you expand the function as a geometric series ,
    [itex] 1-e^{z}+e^{2z}...... [/itex]
    I dont see how there is a pole in the geometric series expansion , there is no division by zero.
  2. jcsd
  3. Apr 22, 2017 #2


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    Staff Emeritus
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    You want to expand as a series consisting of powers of ##z-z_0## about the point ##z_0 = i\pi##.
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