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.