singularity and residue


by pivoxa15
Tags: residue, singularity
pivoxa15
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#1
Nov1-07, 04:53 AM
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1. The problem statement, all variables and given/known data
Do residues exist only for holomorphic function?

Classify the singularity and calculate the residue of tanh(z) and tan(z)




3. The attempt at a solution
For both
Essential isolated singularity because the numerator has an infinite number of terms.

Residue = 0.
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HallsofIvy
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Nov1-07, 06:00 AM
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Quote Quote by pivoxa15 View Post
1. The problem statement, all variables and given/known data
Do residues exist only for holomorphic function?

Classify the singularity and calculate the residue of tanh(z) and tan(z)




3. The attempt at a solution
For both
Essential isolated singularity because the numerator has an infinite number of terms.

Residue = 0.
What are the definitions of "residue" and "holomorphic function"?

At what point do tanh(z) and tan(z) have an isolated singularity? It doesn't make sense to talk about the "residue" of a function. A function may have a "residue" at a specific point.


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