Let $\phi : \mathbb{R} \rightarrow \mathbb{R}$ be given by $$\phi(t) = \frac{1}{2} + \frac{e^{t^2}}{4e^{t^2} - 2}$$ Prove that $\phi$ is a characteristic function.
My attempt:
I know that there are certain criteria that say that a function is a characteristic function of distribution, eg the Bochner criterion, but I do not know how to prove that a function is positively defined. I also have the Polya criterion, but here the condition that $\phi (\infty) = 0$ is not satisfied. Could You give me some hints?