ThmDex – An index of mathematical definitions, results, and conjectures.
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Real gaussian density function
Definition D2719
Standard real gaussian density function
Formulation 0
The standard real gaussian density function is the D4364: Real function \begin{equation} \mathbb{R} \to \mathbb{R}, \quad x \mapsto \frac{1}{\sqrt{2 \pi}} \exp \bigg( - \frac{1}{2} x^2 \bigg) \end{equation}
Formulation 1
The standard real gaussian density function is the D4364: Real function \begin{equation} \mathbb{R} \to \mathbb{R}, \quad x \mapsto (2 \pi)^{- 1/2} e^{- x^2 / 2} \end{equation}
Formulation 2
The standard real gaussian density function is the D4364: Real function \begin{equation} \mathbb{R} \to \mathbb{R}, \quad x \mapsto \frac{1}{\sqrt{2 \pi}} e^{- \frac{x^2}{2}} \end{equation}