Two dimensional Laplace transforms of generalized hypergeometric functions

New Laplace transforms of Kummer's confluent hypergeometric functions

In this paper we aim to show how one can obtain so far unknown Laplace transforms of three rather general cases of Kummer’s confluent hypergeometric function 1F1(a; b; x) by employing generalizations of Gauss’s second summation theorem, Bailey’s summation theorem and Kummer’s summation theorem obtained earlier by Lavoie, Grondin and Rathie. The results established may be useful in theoretical p...

HYPERgeometric functions DIfferential REduction: MATHEMATICA based packages for differential reduction of generalized hypergeometric functions: Horn hypergeometric functions of two variables

The HYPERDIRE is a project devoted to creation of a set of Mathematica based programs for differential reduction of hypergeometric functions. The current version allow to manipulate with full set of Horn hypergeometric functions of two variables (34 functions). PROGRAM SUMMARY Title of program: HYPERDIRE Version: 1.0.0 Release: 1.0.0 Catalogue number : Program obtained from: https://sites.googl...

An axiomatic approach to the non-linear theory of generalized functions and consistency of Laplace transforms

We offer an axiomatic definition of a differential algebra of gen­ eralized functions over an algebraically closed non-Archimedean field. This algebra is of Colombeau type in the sense that it contains a copy of the space of Schwartz distributions. We study the uniqueness of the objects we define and the consistency of our axioms. Next, we identify an inconsistency in the conventional Laplace t...

Generalized Ageing Classes in Terms of Laplace Transforms

Kebir (1994) (see also Shaked and Shanthikumar, 1994) has characterized likelihood ratio (LR) ordering, failure rate (FR) ordering, reversed hazard rate ordering and stochastic (ST) ordering with the help of Laplace transform. Using Laplace transform, Nanda (1995) has characterized, by means of necessary and sufficient conditions, the property that two life distributions are ordered in the s-FR...

Hypergeometric transforms in certain classes of analytic functions