Definition:Exponential Order

Definition
Let $f \left({t}\right): \R \to \R$ or $\R \to \C$ be a function.

Let $f$ be continuous on the real interval $\left [{0 \,.\,.\, \to} \right)$, except possibly for some finite number of discontinuities of the first kind in every finite subinterval of $\left [{0 \,.\,.\, \to} \right)$.

Then $f\left({t}\right)$ is said to be of exponential order, denoted $f \in \mathcal{E}$, it is of exponential order $a$ for some $a > 0$.