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Homework Help: Singularities, residues

  1. Nov 4, 2006 #1
    does [tex] f(z)=\frac{ze^{iz}}{z^2+a^2} [/tex] have a singularity at infinity?

    if so, how do i get the residue there?
     
  2. jcsd
  3. Nov 4, 2006 #2

    quasar987

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    Does [tex]f(w):=f(1/z)[/tex] has a singularity at w=0 is what you must ask yourself.

    Btw - you're really not in the right forum.
     
    Last edited: Nov 4, 2006
  4. Nov 4, 2006 #3
    okay so i transform z -> 1/w then take lim w-> 0... if it blows up then i do have a singularity... how do i get lim w->0 of exp(i/w) ?

    well first, i think i need l'hopitals (for the whole function). then, can i use the fact that when taking a limit it can be approached along any line on the Z-plane? i.e. use the path along i-axis ?

    i think the conclusion will be that it blows up. three follow up questions. 1. how do i get the residue at infinity? 2. what is the conclusion in a case wherein the limit does not exist? 3. Is the singularity at infinity and/or its residue useful? (i mean i know the finite singularities are useful in integration, does this arise in some physical theory?)

    i am very sorry for posting in the wrong forum.. thanks for all the help
     
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