The
real gaussian density function with parameters $\mu \in \mathbb{R}$ and $\sigma \in (0, \infty)$ is the
D4364: Real function
\begin{equation}
\mathbb{R} \to \mathbb{R}, \quad
x \mapsto \frac{1}{\sqrt{2 \pi \sigma^2}} e^{- \frac{1}{2} \big( \frac{x - \mu}{\sigma} \big)^2}
\end{equation}