By: Thanh Hai Nguyen, Semen B. IAkubovich

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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 facorization 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.

"The book gives a detailed and rigorous account of the theory of double Mellin-Barnes type integrals and contains new fundamental results and their applications to convolution theory. It is a valuable addition to the existing literature in the field of special functions and integral transforms." K M Saksena "In the areas of special functions and integral transforms, teachers, researchers and graduate students are advised to refer to this work." Siam Review, 1993

General H-function of Two Variables
Historical background	p. 1
Definition and notations	p. 9
The convergence region of the general H-function of two variables	p. 12
The H-function of two real positive variables	p. 23
Simple contiguous relations for the H-function of two variables	p. 47
Main properties for the H-function	p. 51
The double Mellin transform	p. 54
Series representations for the H-function of two variables	p. 57
Characteristic of the general H-function of two variables	p. 69
The H-function of two variables with the third characteristic
Definition and notations	p. 72
Convergence theorems	p. 75
Reduction formulas for the H-function with the third characteristic	p. 80
The G-function of two variables and its special cases	p. 89
The double Kampe de Ferlet hypergeometric series	p. 103
One-dimensional H-transform and its composition structure
Spaces [actual symbols not reproducible] (L) and [actual symbols not reproducible] (L)	p. 119
One-dimensional H-transform in the spaces [actual symbols not reproducible] (L) and [actual symbols not reproducible] (L)	p. 129
The G-transform and its special cases	p. 142
Composition structure of the H- and G- transforms	p. 153
General integral convolutions for the H-transform
Classical Laplace convolution and its new properties	p. 162
General integral convolution: definition, existence and factorization property	p. 170
Typical examples of the general convolutions	p. 181
Case of the same kernels: the general Laplace convolution	p. 190
G-convolution and its typical examples	p. 198
Convolutions for some classical integral transforms	p. 209
Modified H-convolution	p. 225
General Leibniz rules and their integral analogs	p. 233
Bibliography	p. 261
Author Index	p. 279
Subject Index	p. 285
Notations	p. 291
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9789810206901
ISBN-10: 9810206909
Series: Series on Soviet and East European Mathematics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 250
Published: 26th May 1992
Dimensions (cm): 22.149 x 16.205  x 2.083
Weight (kg): 0.558