Fox H-function transforms

Summary

A Fox H-function transform, or H-transform, is an integral transform on $(0, \infty)$ whose kernel is a Fox H-function of the product $xy$. The H-function generalizes the Meijer G-function by allowing positive scaling factors in front of the variable in each gamma factor of its Mellin–Barnes integral. So the H-transforms contain the Meijer G-function transforms and, through them, the Laplace, Stieltjes and Hankel-type transforms. They are a common framework for fractional calculus and for transforms with kernels of Mittag-Leffler or Wright type.