Singularity and residue

1. Nov 1, 2007

pivoxa15

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.

Last edited: Nov 1, 2007
2. Nov 1, 2007

HallsofIvy

Staff Emeritus
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.