# Series and singularities of complex functions

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]

https://brainmass.com/math/complex-analysis/series-singularities-complex-functions-532096

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