# Homework Help: Complex Analysis- Singularities

1. Mar 8, 2010

### TheForumLord

1. The problem statement, all variables and given/known data
Let f be analytic at the complex plane excapt for z= -1 and z=3 which are simple poles of f.

Let $$\Sigma_{-\infty}^{-1} a_{n}(z-2)^{n}$$ be the Laurent series of f.
In part A I've found that the series converges at 1<|z-2|<3 .
B is: Find the coeefficients $$a_{n}$$ of the given Laurent series.
Hint: Look at $$g(z) = (z+1)(z-3)f(z)$$

2. Relevant equations
3. The attempt at a solution
We know that g(z) has no poles or singularities whatsoever. So Laurent series of g is actually a Taylor series... But how can we find from this data the given coeefficients?

2. Mar 8, 2010

### vela

Staff Emeritus
Are you sure that's a correct Laurent series for f(z)? Doesn't it have an essential singularity at z=2?

3. Mar 8, 2010

### TheForumLord

I'm sure indeed...I had no typos in this one... But the an's can be also zero or something...