Definition:Mellin Transform

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Let $\map f t: \R_{\ge 0} \to \C$ be a function of a real variable $t$.

The Mellin transform of $f$ is defined and denoted as:

$\ds \map {\MM \set {\map f t} } s := \int_0^{\to +\infty} t^{s - 1} \map f t \rd t$

wherever this improper integral exists.

Here $\map \MM f$ is a complex function of the variable $s$.

Also denoted as

The Mellin transform can also be denoted $\phi$, hence:

$\map \phi s := \map {\MM \set {\map f t} } s$

Also see

  • Results about Mellin transforms can be found here.

Source of Name

This entry was named for Robert Hjalmar Mellin.