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## Homework Statement

Let f be analytic at the complex plane excapt for z= -1 and z=3 which are simple poles of f.

Let [tex] \Sigma_{-\infty}^{-1} a_{n}(z-2)^{n} [/tex] 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 [tex] a_{n} [/tex] of the given Laurent series.

Hint: Look at [tex] g(z) = (z+1)(z-3)f(z) [/tex]

## Homework Equations

## 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?

Thanks in advance