Definition:Characteristic Function of Random Variable

Definition
Let $X$ be a random variable on a probability space $\left({\Omega, \Sigma, \Pr}\right)$. The Characteristic Function of $X$ is a function $\phi:\R \to \C $ defined by
 * $ \displaystyle \phi(t) = \mathbb{E}\left[e^{itX}\right]$

where $i=\sqrt{-1}$ and $\mathbb{E}$ is the operator for expectation