Mellin transform

The Mellin transformDlmfMathworldPlanetmath is an integral transformDlmfMathworld defined as follows:


Intuitively, it may be viewed as a continuousMathworldPlanetmath analogue of a power series — instead of synthetizing a functionMathworldPlanetmath by summing multiples of integer powers, we integrate over all real powers. This transform is closely related to the Laplace transformDlmfMathworldPlanetmath — if we make a change of variables t=e-r and define g by f(e-r)=g(r), then the above integralDlmfPlanetmath becomes


which is a bilateral Laplace transform.

(more to come)

Title Mellin transform
Canonical name MellinTransform
Date of creation 2015-02-17 15:10:57
Last modified on 2015-02-17 15:10:57
Owner rspuzio (6075)
Last modified by pahio (2872)
Numerical id 7
Author rspuzio (2872)
Entry type Definition
Classification msc 44A15