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!

Singularities and Laurent series

  1. Jun 11, 2016 #1
    1. The problem statement, all variables and given/known data
    Classify the singularities of

    ##\frac{1}{z^{1/4}(1+z)}##

    Find the Laurent series for

    ##\frac{1}{z^2-1}## around z=1 and z=-1

    2. Relevant equations


    3. The attempt at a solution
    So for the first bit there exists a singularity at ##z=0##, but I'm confused about the order of this since its fractional (I get that its a branch point, but does it 'act' as a singularity as well?)

    And there is also a pole at ##z=-1## of order 1.... ?

    (My problem with this is if I expand the ##\frac {1}{z^{\frac{1}{4}}}## about z=0 I get ##\frac{e^{\frac{i \pi}{4}}}{1+z} (1+\frac{1}{4}(z+1)+....)## and I don't know why these should be different?/ which one is wrong)

    And as for the Laurent series I'm afraid Im completely stuck.

    Many thanks- I really appreciate the help as I'm really struggling with these aspects
     
  2. jcsd
  3. Jun 16, 2016 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Singularities and Laurent series
  1. Laurent series (Replies: 6)

Loading...