\begin{definition}[Definition:Elliptic Integral of the First Kind/Incomplete/Amplitude]
Let $u = F \left({k, \phi}\right)$ denote the incomplete elliptic integral of the first kind.
The parameter $\phi = \operatorname{am} u$ of $u = F \left({k, \phi}\right)$ is called the '''amplitude''' of $u$.
\end{definition}