1. Find the series representations for the function
f(z) = z/[(z-2)(z^2-1)]
in powers of z that is valid when
1) |z| < 1
2) 1 < |z| < 2
3) |z| > 2
2. Fine all singularities of the function f in C, and determine whether it is a pole (find its order), a removable singularity, or an essential singularity.
1) f(z) = ze^(3/z)
2) f(z) = (cos z)/[(z - (pi/2))(sin z)]
3) f(z) = (cos z)/[(z^2)(z - pi)^3]
We give a detailed solution to the problems.