Let $G \in \text{Gaussian}(\mu, \sigma)$ be a D210: Gaussian random real number.
Let $n \in \mathbb{N}$ be a D996: Natural number.
Let $n \in \mathbb{N}$ be a D996: Natural number.
Then
\begin{equation}
\mathbb{E}[(G - \mu)^n]
=
\begin{cases}
\sigma^n (n - 1) !!, \quad & n \in \{ 0, 2, 4, \ldots \} \\
0, \quad & n \in \{ 1, 3, 5, \ldots \}
\end{cases}
\end{equation}