\begin{definition}[Definition:Mellin Transform]
Let $\map f t: \R_{\ge 0} \to \C$ be a function of a real variable $t$.
The '''Mellin Transform''' of $f$, denoted $\map \MM f$ or $\phi$, is defined as:
:$\ds \map {\MM \set {\map f t} } s = \map \phi s = \int_0^{\to +\infty} t^{s - 1} \map f t \rd t$
wherever this improper integral exists.
Here $\map \MM f$ is a complex function of the variable $s$.
{{NamedforDef|Robert Hjalmar Mellin|cat = Mellin}}
\end{definition}