Given a random variable X, then its characteristic function is φ‎_X(t) = E(e^itX), where E denotes the expectation. If the probability density function is f_X:ℝ → ℝ, then note that ${\text{φ}}_X\left(t\right)={\widehat{f}}_X(–t)$, where ${\widehat{f}}_X$ denotes the Fourier transform. Characteristic functions have the merit of converging, which is not always the case for moment generating functions (see cauchy distribution).