Compositional Structure of Classical Integral Transforms

Explore the compositional structure of classical integral transforms in this 29-minute Wolfram video. Delve into the recently implemented fractional order integro-differentiation operator, FractionalD, and its relation to more general integral transforms. Learn how most classical integral transforms can be represented as compositions of modified direct and inverse Laplace transforms with power multipliers. Discover how to construct two main classes of integral transforms using MellinTransform: convolution type and transforms with respect to indices. Examine definitions, inversions, compositional structures, and representations of various transforms, including FourierSinTransform, FourierExpTransform, HankelTransform, Stieltjes transform, G-transform, Kontorovich–Lebedev transform, Mehler–Fock transform, and Wimp transform. Understand how these transforms can be applied to rational functions and those representable through MeijerG functions. Cover topics such as integral representations, major functions, merge functions, relations between integral transforms, and associated problems.

Introduction
Definition
Properties
Definitions
Integral Transforms
Merlin Transform
Wim Transform
monograph
kernel
integral representation
major function
merge function
relations between integral transforms
problems with integral transforms
conclusion