ThmDex – An index of mathematical definitions, results, and conjectures.
Result R2254 on D5634: Standard real gaussian function
Riemann integral of standard real gaussian function
Formulation 0
Let $x \mapsto e^{- x^2}$ be a D5634: Standard real gaussian function on $\mathbb{R}$.
Then \begin{equation} \int_{\mathbb{R}} e^{- x^2} \, d x = \sqrt{\pi} \end{equation}