# Laurent Series

1. Jan 25, 2010

### csnsc14320

1. The problem statement, all variables and given/known data
Say whether the indicated point is regular, an essential singularity, or a pole, and if a pole of what order it is.

$$\frac{z^2-1}{(z-1)^2}, z = 1$$

2. Relevant equations

3. The attempt at a solution
Right now I'm just sort of stuck on how to put this into a laurent series - I can't seem to expand the denominator in a series about 1 because I keep getting infinity :(

any hints or suggestions?

Last edited: Jan 25, 2010
2. Jan 25, 2010

### Dick

You don't have to do a full Laurent series. Just factor the numerator and denominator and simplify.

3. Jan 25, 2010

### csnsc14320

i found that it reduces to $$\frac{z+1}{z-1}$$ but again don't I have to expand this and i have the same problem?

4. Jan 25, 2010

### Dick

I don't believe it reduces to (z+1)/(z-1). Did you enter the problem wrong? If not, try that again and show you did it.

5. Jan 25, 2010

### csnsc14320

$$\frac{z^2-1}{(z-1)^2}$$