Characteristic Function

A function \(\hat{f}\) associated with a random variable \(X\) that equals the expected value of \(e^{itX}\).
Given the probability density function, \(f\), it is given by
\[ \hat{f}(t) = E\left[e^{itX}\right] = \int_{-\infty}^{+\infty} e^{itx} f(x) \mathrm{d}x \]