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

  • Thread starter saybrook1
  • Start date
  • #1
101
4

Homework Statement


Hello guys, I need to find the orders of each pole as well as the residue of the function sin(1/z)/cos(z).

Homework 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.

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.
 

Answers and Replies

  • #2
6
0
What is the name of this chapter ?
 
  • #3
101
4
What is the name of this chapter ?
Calculus of Residues? No particular book.
 
  • #4
6
0
Alright. I have not heard about it before.
 

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