# All Laurent series expansion around 1.

• July 14th 2010, 02:32 AM
roy240
All 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!!
• July 14th 2010, 04:34 AM
chisigma
The function $\frac{z^{4}}{3+z^{2}}$ is analytic in $z=1$ so that here the Laurent series and the Taylor seriers are the same and is...

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

Kind regards

$\chi$ $\sigma$