1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    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!

Homework Help: Find residue of exp(1/(z+i))

  1. Jun 14, 2012 #1
    Hi, I want to know how you find the residue of z=-i for the function exp(1/(z+i)). Clearly, the function has an essential singularity at z=-i so the good ol' formula for the residue for a pole of order m, doesn't really work here. What do I do? :)
     
  2. jcsd
  3. Jun 14, 2012 #2
    You expand the function as a Laurent series around the pole and recall that the residue at that point is the coefficient in front of term proportional to [itex]\frac{1}{z+i} [/itex]
     
  4. Jun 14, 2012 #3
    okay, can you help me how that is done. My book's section os Laurent series is quite poor. The only thing I know about expanding functions as them, is that you can sometimes use geometric series. You don't need to say how I should do it, just hint me at where to start.
     
  5. Jun 14, 2012 #4
    Just expand e^x as a usual Taylor series, then plug in x=1/(z+i) and it's done!
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook