When finding a residue, how am I to know which coefficient to choose? For instance, if I have, let's say three poles, which coefficients of the Laurent series do I choose to calculate the residue? Does it just go by the number of poles? 3 poles, the first, second, and third coefficients of the series?
I know the Residue of f(z) @ z=z_o is the first coeffiient, b_1, of the Laurent series. But after that, things get fuzzy. It does not matter what the value of z_o is, it is always the first coefficient? And if there are several poles... then what?