ThmDex – An index of mathematical definitions, results, and conjectures.
Result R4618 on D3754: Standard gaussian function
Riemann integral of standard basic real gaussian function on the real line
Formulation 0
Let $x \mapsto e^{- \pi x^2}$ be a D3754: Standard gaussian function on $\mathbb{R}$.
Then \begin{equation} \int_{\mathbb{R}} e^{- \pi x^2} \, d x = 1 \end{equation}