Definition:Exponential Order

Definition
Let $\map f t: \R \to \mathbb F$ be a function, where $\mathbb F \in \set {\R, \C}$.

Let $f$ be continuous on the real interval $\hointr 0 \to$, except possibly for some finite number of discontinuities of the first kind in every finite subinterval of $\hointr 0 \to$.

Then $\map f t$ 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.

Also see

 * Definition:Big-O Notation