Suppose $E{|X|^{2}}<\infty$ and $E{X}=0$. Show that Var(X)$= \sigma^{2}<\infty$ (done), and that $\varphi_{X}(u)=1-\frac{1}{2}u^{2}\sigma^{2}+o(u^{2})$ (what I can't figure out how to find, especially since we're not given a distribution).
I'm really at my wits' end; please help!
Also, FYI: a function is $o(t)$ if $\lim_{t\to 0}\frac{|g(t)|}{t}=0$.