A generalized Meijer transformation

Abstract

In a series of papers [1-6], Kratzel studies a generalized version of the classical Meijer transformation with the Kernel function(st)νη(q,ν+1; (st)q). This transformation is referred to as GM transformation which reduces to the classical Meijer transform whenq=1. He also discussed a second generalization of the Meijer transform involving the Kernel functionλν(n)(x)which reduces to the Meijer function whenn=2and the Laplace transform whenn=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.