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Singularity and residue 
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#1
Nov107, 04:53 AM

P: 2,268

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. 


#2
Nov107, 06:00 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,363

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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