My question is

Find all Laurent series expansions of function

f(x)=z^4/(3+z^2) around 1.

Please help!! I will be thankful, if someone can tell me how to do this!!

Thanks!!

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- Jul 14th 2010, 01:32 AMroy240All Laurent series expansion around 1.
My question is

Find all Laurent series expansions of function

f(x)=z^4/(3+z^2) around 1.

Please help!! I will be thankful, if someone can tell me how to do this!!

Thanks!! - Jul 14th 2010, 03:34 AMchisigma
The function $\displaystyle \frac{z^{4}}{3+z^{2}}$ is analytic in $\displaystyle z=1$ so that here the Laurent series and the Taylor seriers are the same and is...

$\displaystyle \displaystyle f(z)= \sum_{n=0}^{\infty} f^{(n)} (1)\ \frac{(z-1)^{n}}{n!}$ (1)

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$