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Residue of sin(1/z)/cos(z)

  1. Apr 15, 2016 #1
    1. The problem statement, all variables and given/known data
    Hello guys, I need to find the orders of each pole as well as the residue of the function sin(1/z)/cos(z).

    2. Relevant equations
    I imagine that this is a simple pole so I will either find the Laurent series and get the coefficient of [tex](z-z_0)^{-1}[/tex] or use the simpler limiting case.

    3. The attempt at a solution
    So far, I think that there is clearly a pole at [tex]n\pi-\frac{\pi}{2}[/tex] due to the z in the cosine term, although I'm not sure whether it's considered a pole when the value of z causes the term sin(1/z) to go to zero. Any help here and further direction on calculating the residue from there would be awesome. Thank you very much.
     
  2. jcsd
  3. Apr 15, 2016 #2
    What is the name of this chapter ?
     
  4. Apr 15, 2016 #3
    Calculus of Residues? No particular book.
     
  5. Apr 15, 2016 #4
    Alright. I have not heard about it before.
     
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