A Generalized Meijer Transformation

In a series of papers [1–6], Kratzel studies a generalized version of the classical Meijer transformation with the Kernel function (st)v n (q, v + 1; (st)^). This transformation is referred to as GM transformation which reduces to the classical Meijer transform when q = 1. He also discussed a second generalization of the Meijer transform involving the Kernel function (x) which reduces to the Meijer function when n = 2 and the Laplace transform when n * 1. This is called the Meijer–Laplace (or ML) transformation. This paper is concerned with a study of both GM and ML transforms in the distributional sense. Several properties of these transformations including inversion, uniqueness, and analyticity are discussed in some detail. © 1985, Hindawi Publishing Corporation. All rights reserved