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Very easy and quick residue calculus question.

  • Thread starter car202
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  • #1
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Homework Statement



[tex]\oint_{\left|z\right|=3/2} \frac{e^{\frac{1}{z-1}}}{z} dz
[/tex]

Homework Equations



Using residue theorem, since there are two singularities withing the domain, evaluate residues at each singularity, and multiply by [tex]2\pi i[/tex]

The Attempt at a Solution



Here is the problem. The answer is [tex]2 \pi i[/tex] instead of [tex]2 \pi i + \frac{2\pi i}{e}[/tex]
I don't understand why singularity at zero is ignored.
FYI, if the domain it |z| = 1/2, the answer is 2pi*i/e.
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
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They didn't ignore the singularity at 0. The singularity at z=1 is not what you think it is. Try putting w=z-1 and expanding the power series around w=0. You'll find an infinite number of 1/w terms. Sum them.
 

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