The Double Mellin-Barnes Type Integrals and Their Application to Convolution Theory

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.More Description

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.
Contents: General H-Function of Two Variables and the Solution of its Convergence ProblemMain Properties, Series Presentations and Characteristic of the H-FunctionH-Function with the Third Characteristic and its Particular CasesG-Function of Two VariablesTable of Special Cases of the G-FunctionOne-Dimensional H-Transform in Spaces M-1(L) and M-1c,γ(L) and its Composition StructureClassical Laplace Convolution and its New PropertiesGeneral Integral Convolution for H-Function TransformExistence and Factorization Property of the ConvolutionNew Examples of Convolution for Classical Integral TransformsGeneralized Integral ConvolutionGeneral Leibniz Rules and Their Integral Analogs
Readership: Researchers and students in mathematics, mechanics and physics.