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## Main Question or Discussion Point

Does anyone know of any examples of the explicit calculation of the Laurent series of a complex function? Any information would be appreciated.

- Thread starter rick1138
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Does anyone know of any examples of the explicit calculation of the Laurent series of a complex function? Any information would be appreciated.

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HallsofIvy

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As simple example: f(x)= e

f(x)= e

x

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Excellent. Exactly what I was looking for. Thanks.

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I know this was six years ago, but would you believe it is the clearest explanation of Laurent series on the internet.Construct the Taylor's series for (x-a)^{n}f(x) and multiply each term by (x-a)^{-n}.

- #5

Hurkyl

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In pure algebra, though, they usually limit Laurent series to ones that only have finitely many negative powers.

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my question about Laurent is this

let be the Taylor series [tex] f(1/x)= \sum_{n=0}^{\infty}c_{n}x^{n} [/tex] valid for |x| <1

then , if i make a change of variable [tex] x=1/y [/tex]

[tex] f(y)= \sum_{n=0}^{\infty}c_{n}y^{-n} [/tex] is a LAURENT series for the fucntion f(y) valid for |x| >1 ??

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