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Is Cauchy's integral formula applicable to this type of integral?

  • #1

Homework Statement



I am trying to determine if Cauchy's integral formula will work on the following integral, where the contour C is the unit circle traversed in the counterclockwise direction.

[tex]\oint_{C}^{}{\frac{z^2+1}{e^{iz}-1}}[/tex]


Homework Equations


See Cauchy's Integral Formula - http://en.wikipedia.org/wiki/Cauchy_integral_formula" [Broken]

The Attempt at a Solution



I realize that there is a pole at z=0. I realize that if I could get this integral into the form

[tex]\frac{f(z)}{z}[/tex],

with f(z) being analytic in and on the contour C, then I could use the formula. However, I'm not sure how to get the integrand in that form. Is it even possible to use Cauchy's integral formula on this integral, or do I need to use a different method to evaluate this integral?
 
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Answers and Replies

  • #3
Ok, so it appears that I need to use the residue theorem in order to evaluate this integral. I was hoping I could just use the integral formula. I haven't got to study the residue theorem yet in my text. Thanks
 
  • #4
lurflurf
Homework Helper
2,432
132
The residue thorem is a simple use of the integral formula.
write f(z)=[z*f(z)]/z
 
  • #5
1,444
0
so are these the steps:

do a laurent expansion of denominator
cancel with stuff in the numerator
then the coefficient of the [itex]z^{-1}[/itex] term gives us the residue
multiply this by [itex]2 \pi i[/itex] to give the integral's value

im not too sure about the first of those two steps???
 

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