Let $X \in \text{Gaussian}(\mu, \sigma)$ be a D210: Gaussian random real number.
Let $t \in \mathbb{R}$ be a D993: Real number.

Then \begin{equation} \mathfrak{F}_X(t) = \exp \left( i \mu t - \frac{\sigma^2 t^2}{2} \right) \end{equation}