This is consistent with the characteristic function of formula_21 being a Wick rotation of formula_15 when the moment generating function exists, as the characteristic function of a continuous random variable formula_21 is the Fourier transform of its probability density function formula_23, and in general when a function formula_31 is of exponential order, the Fourier transform of formula_32 is a Wick rotation of its two-sided Laplace transform in the region of convergence. See the relation of the Fourier and Laplace transforms for further information.