by Nguyen Thanh Hai (Byelorussian State University) & S B Yakubovich (Byelorussian State University)

This book presents new results in the theory of the double Mellin-Barnes integrals popularly known as the general H-function of two variables.

A general integral convolution is constructed by the authors and it contains Laplace convolution as a particular case and possesses a factorization property for one-dimensional H-transform. Many examples of convolutions for classical integral transforms are obtained and they can be applied for the evaluation of series and integrals.

• General H-Function of Two Variables and the Solution of its Convergence Problem
• Main Properties, Series Presentations and Characteristic of the H-Function
• H-Function with the Third Characteristic and its Particular Cases
• G-Function of Two Variables
• Table of Special Cases of the G-Function
• One-Dimensional H-Transform in Spaces M^-1(L) and M^-1_c,γ(L) and its Composition Structure
• Classical Laplace Convolution and its New Properties
• General Integral Convolution for H-Function Transform
• Existence and Factorization Property of the Convolution
• New Examples of Convolution for Classical Integral Transforms
• Generalized Integral Convolution
• General Leibniz Rules and Their Integral Analogs