I'm a student of mechanical engineering and I have a problem with computing residues of a complex function. I've read some useful comments in the other threads. Now I've got some ideas about essential singularity and series expansion in computing the residue. However, I still can't find the solution to my problem. I arrived at a complex function in the process of finding a solution to a mechanical problem. Then I had to obtain the residues to proceed to the next steps. The function has the following form:
where $A$, $B$ and $N$ are real constants $(N \geq 3)$.
I want to compute the resiude at $z=0$. I wrote the Laurent series of $f$, but got an infinite sum. I do not even know if I am at the right direction. I would be really thankful if someone could give me a hint on this and put me back in the right direction.