1. The problem statement, all variables and given/known data Question is= Find all Laurent series expansion of f(z)=z^4/(3+z^2) around 1. I will be very very thankful if someone can help me to do this question. 2. Relevant equations 3. The attempt at a solution can I assume (z-1=u) here and change the function in terms of $u$. then i will have f(u+1)=(u+1)^4/(u+2)^2 It should have singularity at $u=-2$. now I m big confuse about in what regions I should compute Laurent series. I have trouble of thinking that how many laurent series I will have and what will be the conditions on $z$. Thanks !!!!