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ENgez

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- Thread starter ENgez
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- #1

ENgez

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- #2

spamiam

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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.

- #3

mathwonk

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- #4

Landau

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well, it has negative powers. E.g. you might want to consider rational functions, or e^/z/z, or e^(1/z), or ... just any quotient of holomorphic functions, as mathwonk says.But i fail to see its purpose - what does it do that the taylor series can't?

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