ThmDex – An index of mathematical definitions, results, and conjectures.
F9552
Formulation 0
Let $x_1, \ldots, x_N \in [0, \infty)$ each be a D993: Real number such that
(i) $a \in \mathbb{R}$ is a D2455: Real geometric mean of $x_1, \ldots, x_N$
Then \begin{equation} a = \left( \prod_{n = 1}^N x_n \right)^{1 / N} \end{equation}