Some General Families of Integral Transformations and Related Results

Abstract

This article is motivated essentially by several extensive developments on
the familiar Laplace and Hankel transforms as well as on their extensions
and generalizations. Our main object here is to present several (presumably
new) properties and characteristics as well as inter-relationships among
each of such general families of integral transforms as Srivastava’s generalized Whittaker transform, Hardy’s generalized Hankel transform and
Srivastava’s -generalized Hankel transform. Many trivial and inconsequential parametric and argument variations of the classical Laplace transform
and its s-multiplied version (or the Laplace-Carson transform), each of
which unfortunately is being referred to as a \new" integral transform in
the present-day obviously amateurish-type amateurish-type literature, are
pointed out. The Srivastava-Panda multidimensional integral transformations involving their multivariable H-function in the kernel as well as the
potentially useful process of association of variables in the theory and applications of the multidimensional Laplace transform are also considered
with a view to encouraging related further studies and revisits