A generalized Meijer transformation. (1985)

• Record Type: Journal Article
• Authors: Rao, G. L. N.; Debnath, L.
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 8:Number 2(1985)
• Page Start: 359
• Page End: 365
• Publication Date: 1985
• Subjects: distributional GM and ML transforms -- Meijer transform; Mathematics -- Periodicals; 510.5
• DOI: 10.1155/S0161171285000370
• Languages: English
• ISSNs: 0161-1712

Abstract

Abstract : In a series of papers [1-6], Kratzel studies a generalized version of the classical Meijer transformation with the Kernel function( st ) ν η ( 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 functionλ ν ( n ) ( x ) which reduces to the Meijer function whenn = 2 and 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.