## Finding Laurent Series

When finding a Laurent series it is important to specify the region on which the series is to converge. The function is analytic on each ofand

The Laurent series on each of the above regions is not the same however.

To find the Laurent series, start by writingin terms of its partial fractions.

To find the Laurent series onexpand each term aboutusing the binomial theorem.

The first series below will converge forand the second will converge forso the sum will converge for

To find the Laurent series on use the expansion above forvalid for and writeso that the binomial expansion will converge for

To find the Laurent series on writevalid for and writeso that the binomial expansion will converge forand the sum will converge for