Let $X \in \text{Poisson}(\lambda)$ be a D2854: Poisson random natural number.
Let $t \in \mathbb{R}$ be a D993: Real number.
Let $t \in \mathbb{R}$ be a D993: Real number.
Then
\begin{equation}
\mathbb{E}(e^{i t X})
= e^{\lambda (e^{i t} - 1)}
\end{equation}