# Why use a laurent series in complex analysis?

ENgez
In complex analysis, what exactly is the purpuse of the luarent series, i mean, i know that it apporximates the function like a taylor series, an if the function is analytic in the whole domain it simplifies in to a taylor series. But i fail to see its purpose - what does it do that the taylor series can't?

spamiam
Hello!

In complex analysis, we're often interested in functions that are not holomorphic/analytic, but are meromorphic: http://en.wikipedia.org/wiki/Meromorphic_function.

In this case, Laurent series are a generalization of Taylor series, since now we can approximate functions that have poles using a series. Take a look at this article: http://en.wikipedia.org/wiki/Residue_(complex_analysis).

Also, just like power series, the collection of Laurent series has a rich algebraic structure as well.