ThmDex – An index of mathematical definitions, results, and conjectures.
Homomorphism property of the standard natural real exponential function
Formulation 0
Let $x_1, \dots, x_N \in \mathbb{R}$ each be a D993: Real number.
Then \begin{equation} \exp \left( \sum_{n = 1}^N x_n \right) = \prod_{n = 1}^N \exp(x_n) \end{equation}
Formulation 1
Let $x_1, x_2, \dots, x_N \in \mathbb{R}$ each be a D993: Real number.
Then \begin{equation} \exp(x_1 + x_2 + \cdots + x_N) = \exp(x_1) \exp(x_2) \cdots \exp(x_N) \end{equation}