# All Laurent series expansion around 1.

• July 14th 2010, 01:32 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.

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)
$\chi$ $\sigma$