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}