Definition:Exponential Order

Definition
Let $f \left({t}\right): \R \to \mathbb{F}$ be a function, where $\mathbb{F} \in \left \{{\R,\C}\right\}$.

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 $a > 0$.

Also known as
Such a function is also known as being of exponential type.