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

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Two mathematicians from the Byelorussian State University present new results on the theory of a class of integrals know as the H- function of two variables, first introduced in 1978. The self- contained study, for teachers, researchers, and graduate students working in special functions and integral transforms, discusses two variables with and without the third characteristic, one- dimensional H-transform and its composition structure, and general integral convolutions. Double spaced. Acidic paper. Annotation c. Book News, Inc., Portland, OR (
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Product Details

  • ISBN-13: 9789810206901
  • Publisher: World Scientific Publishing Company, Incorporated
  • Publication date: 5/28/1992
  • Series: Series on Soviet and East European Mathematics, #6
  • Pages: 308
  • Product dimensions: 6.38 (w) x 8.72 (h) x 0.82 (d)

Table of Contents

Ch. I General H-function of Two Variables
1 Historical background 1
2 Definition and notations 9
3 The convergence region of the general H-function of two variables 12
4 The H-function of two real positive variables 23
5 Simple contiguous relations for the H-function of two variables 47
6 Main properties for the H-function 51
7 The double Mellin transform 54
8 Series representations for the H-function of two variables 57
9 Characteristic of the general H-function of two variables 69
Ch. II The H-function of two variables with the third characteristic
10 Definition and notations 72
11 Convergence theorems 75
12 Reduction formulas for the H-function with the third characteristic 80
13 The G-function of two variables and its special cases 89
14 The double Kampe de Ferlet hypergeometric series 103
Ch. III One-dimensional H-transform and its composition structure
15 Spaces [actual symbols not reproducible] (L) and [actual symbols not reproducible] (L) 119
16 One-dimensional H-transform in the spaces [actual symbols not reproducible] (L) and [actual symbols not reproducible] (L) 129
17 The G-transform and its special cases 142
18 Composition structure of the H- and G- transforms 153
Ch. IV General integral convolutions for the H-transform
19 Classical Laplace convolution and its new properties 162
20 General integral convolution: definition, existence and factorization property 170
21 Typical examples of the general convolutions 181
22 Case of the same kernels: the general Laplace convolution 190
23 G-convolution and its typical examples 198
24 Convolutions for some classical integral transforms 209
25 Modified H-convolution 225
26 General Leibniz rules and their integral analogs 233
Bibliography 261
Author Index 279
Subject Index 285
Notations 291
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