International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 2, Pages 359-365
doi:10.1155/S0161171285000370
A generalized Meijer transformation
1Department of Mathematics, Jamshedpur Co-operative College of the Ranchi University, Jamshedpur, India
2Department of Mathematics, University of Central Florida, Orlando 32816, Florida, USA
Received 13 May 1983; Revised 15 January 1985
Copyright © 1985 G. L. N. Rao and L. Debnath. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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 when q=1. He also discussed a second generalization of the Meijer transform involving the Kernel function λν(n)(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.