I have two questions. The definition I learned defined a laurents for a function analytic in some annalus? I guess this question is asking annali centered at $1$? How do I determine all the annali?
Also, is there a quicker way to find coefficients $a_n$ of the laurent series without applying the definition directly (i.e $a_n = 1/2\pi i \int f(\zeta)/(\zeta - 1?)^{n+1} d\zeta$)