power series expansion of the function $ e^{-\frac {1}{x^2}} $ about $0 $ I know that the function $e^{-\frac {1}{x^2}}$ is infinite  differentiable in a neighborhood of $0$ in $\mathbb{R}$. Does a power series representation exist for this function? If it does not exist, please provide some explanation. 

It does have a nice Laurent series about zero, doesn't it? That is a power series representation, isn't it? (Just substitute $z=-\frac1{x^2}$ in the Maclaurin series for $e^z$).
