1. The problem statement, all variables and given/known data Hello friends, 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. 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 have to obtain the residues to proceed to the next steps. 2. Relevant equations The function has the following form: f(z)=exp(A*Z^N+B*Z^-N)/Z where A, B and N are real constants (N>=3). 3. The attempt at a solution I want to compute the resiude at z=0. I wrote the Laurent serie 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.