1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    You want to expand as a series consisting of powers of ##z-z_0## about the point ##z_0 = i\pi##.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted