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Mellin transform

In mathematics, the Mellin transform is a kind of multiplicative analogue of the Fourier transform. It is closely connected to the theory of Dirichlet series

The Mellin transform of a function f is

The inverse transform is

The notation implies this is a contour integral taken over a vertical line in the complex plane.

The transform is named after the Finnish mathematician Robert Hjalmar Mellin (1854 - 1933).