The standard natural real exponential function is the D5482: Positive real function $$\begin{equation} \mathbb{R} \to (0, \infty), \quad x \mapsto \lim_{N \to \infty} \sum_{n = 0}^N \frac{x^n}{n!} \end{equation}$$

The standard natural real exponential function is the D5482: Positive real function $$\begin{equation} \mathbb{R} \to (0, \infty), \quad x \mapsto \frac{x^0}{0!} + \frac{x^1}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + \frac{x^4}{4!} + \frac{x^5}{5!} + \frac{x^6}{6!} + \dots \end{equation}$$

The standard natural real exponential function is the D5482: Positive real function $$\begin{equation} \mathbb{R} \to (0, \infty), \quad x \mapsto \sum_{n = 0}^{\infty} \frac{x^n}{n!} \end{equation}$$