- #1

dykuma

- 56

- 7

## Homework Statement

and the solution (just to check my work)

## Homework Equations

None specifically. There seems to be many ways to solve these problems, but the one used in class seemed to be partial fractions and Taylor series.

## The Attempt at a Solution

The first step seems to be expanding this using partial fractions, giving me

Now, for 0 < |z| < 1, we expand each of the fractions in the parenthesis in powers of z.

This is the Laurent series for f (z) which is valid in the region 0 < |z| < 1. I then need to get the other two series, which the next one I should try to get is for the region |z| > 2. To get that, it is suggested that I write the two partial fractions as:

However I am not sure what to do with this. I have seen things saying I should expand these two functions, and then add them together, however this does not give me the answer for the region |z| > 2, (in fact, it just gives me the first series, but a degree higher, which makes sense).