Mellin Barnes Integrals

Author : Nguyen Thanh Hai
Publisher : World Scientific
ISBN 13 : 9814506141
Total Pages : 308 pages
Book Rating : 4.44/5 ( download)

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Download or read book The Double Mellin-Barnes Type Integrals and Their Applications to Convolution Theory written by Nguyen Thanh Hai and published by World Scientific. This book was released on 1992-05-26 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. keywords:Mellin Transform of the One and Two Variables;Mellin-Barnes Integrals;Convolutions;Meijer's G-Function of Two Variables;Fox's H-Function of Two Variables;Fourier Transform;Laplace Transform;Gamma Function;Double Kampe de Feriet Hypergeometric Series;Leibniz Rules and Integral Analogs“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

Author : R. B. Paris
Publisher : Cambridge University Press
ISBN 13 : 9781139430128
Total Pages : 452 pages
Book Rating : 4.22/5 ( download)

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Download or read book Asymptotics and Mellin-Barnes Integrals written by R. B. Paris and published by Cambridge University Press. This book was released on 2001-09-24 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotics and Mellin-Barnes Integrals, first published in 2001, provides an account of the use and properties of a type of complex integral representation that arises frequently in the study of special functions typically of interest in classical analysis and mathematical physics. After developing the properties of these integrals, their use in determining the asymptotic behaviour of special functions is detailed. Although such integrals have a long history, the book's account includes recent research results in analytic number theory and hyperasymptotics. The book also fills a gap in the literature on asymptotic analysis and special functions by providing a thorough account of the use of Mellin-Barnes integrals that is otherwise not available in other standard references on asymptotics.

Author : R. B. Paris
Publisher :
ISBN 13 : 9780511069192
Total Pages : 422 pages
Book Rating : 4.97/5 ( download)

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Download or read book Asymptotics and Mellin-Barnes Integrals written by R. B. Paris and published by . This book was released on 2001 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotics and Mellin-Barnes Integrals provides an account of the use and properties of a type of complex integral representation that arises frequently in the study of special functions typically of interest in classical analysis and mathematical physics.

Author : Ievgen Dubovyk
Publisher : Springer Nature
ISBN 13 : 3031142721
Total Pages : 296 pages
Book Rating : 4.27/5 ( download)

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Download or read book Mellin-Barnes Integrals written by Ievgen Dubovyk and published by Springer Nature. This book was released on 2022-12-15 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, the authors discuss the Mellin-Barnes representation of complex multidimensional integrals. Experiments frontiered by the High-Luminosity Large Hadron Collider at CERN and future collider projects demand the development of computational methods to achieve the theoretical precision required by experimental setups. In this regard, performing higher-order calculations in perturbative quantum field theory is of paramount importance. The Mellin-Barnes integrals technique has been successfully applied to the analytic and numerical analysis of integrals connected with virtual and real higher-order perturbative corrections to particle scattering. Easy-to-follow examples with the supplemental online material introduce the reader to the construction and the analytic, approximate, and numeric solution of Mellin-Barnes integrals in Euclidean and Minkowskian kinematic regimes. It also includes an overview of the state-of-the-art software packages for manipulating and evaluating Mellin-Barnes integrals. The book is meant for advanced students and young researchers to master the theoretical background needed to perform perturbative quantum field theory calculations.

Author : Isabella Bierenbaum
Publisher :
ISBN 13 :
Total Pages : 6 pages
Book Rating : 4.46/5 ( download)

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Download or read book Evaluating two-loop massive operator matrix elements with Mellin Barnes integrals written by Isabella Bierenbaum and published by . This book was released on 2006 with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : J. Usovitsch
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.30/5 ( download)

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Download or read book MBnumerics written by J. Usovitsch and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : S.B. Yakubovich
Publisher : Springer Science & Business Media
ISBN 13 : 9401111960
Total Pages : 335 pages
Book Rating : 4.66/5 ( download)

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Download or read book The Hypergeometric Approach to Integral Transforms and Convolutions written by S.B. Yakubovich and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to develop a new approach which we called the hyper geometric one to the theory of various integral transforms, convolutions, and their applications to solutions of integro-differential equations, operational calculus, and evaluation of integrals. We hope that this simple approach, which will be explained below, allows students, post graduates in mathematics, physicists and technicians, and serious mathematicians and researchers to find in this book new interesting results in the theory of integral transforms, special functions, and convolutions. The idea of this approach can be found in various papers of many authors, but systematic discussion and development is realized in this book for the first time. Let us explain briefly the basic points of this approach. As it is known, in the theory of special functions and its applications, the hypergeometric functions play the main role. Besides known elementary functions, this class includes the Gauss's, Bessel's, Kummer's, functions et c. In general case, the hypergeometric functions are defined as a linear combinations of the Mellin-Barnes integrals. These ques tions are extensively discussed in Chapter 1. Moreover, the Mellin-Barnes type integrals can be understood as an inversion Mellin transform from the quotient of products of Euler's gamma-functions. Thus we are led to the general construc tions like the Meijer's G-function and the Fox's H-function.

Author : George Fikioris
Publisher : Springer Nature
ISBN 13 : 3031016971
Total Pages : 67 pages
Book Rating : 4.74/5 ( download)

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Download or read book Mellin-Transform Method for Integral Evaluation written by George Fikioris and published by Springer Nature. This book was released on 2022-05-31 with total page 67 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the Mellin-transform method for the exact calculation of one-dimensional definite integrals, and illustrates the application if this method to electromagnetics problems. Once the basics have been mastered, one quickly realizes that the method is extremely powerful, often yielding closed-form expressions very difficult to come up with other methods or to deduce from the usual tables of integrals. Yet, as opposed to other methods, the present method is very straightforward to apply; it usually requires laborious calculations, but little ingenuity. Two functions, the generalized hypergeometric function and the Meijer G-function, are very much related to the Mellin-transform method and arise frequently when the method is applied. Because these functions can be automatically handled by modern numerical routines, they are now much more useful than they were in the past. The Mellin-transform method and the two aforementioned functions are discussed first. Then the method is applied in three examples to obtain results, which, at least in the antenna/electromagnetics literature, are believed to be new. In the first example, a closed-form expression, as a generalized hypergeometric function, is obtained for the power radiated by a constant-current circular-loop antenna. The second example concerns the admittance of a 2-D slot antenna. In both these examples, the exact closed-form expressions are applied to improve upon existing formulas in standard antenna textbooks. In the third example, a very simple expression for an integral arising in recent, unpublished studies of unbounded, biaxially anisotropic media is derived. Additional examples are also briefly discussed.

Author : Michał Ochman
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.12/5 ( download)

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Download or read book MBsums - a Mathematics Package for the Representation of Mellin-Barnes Integrals by Multiple Sums written by Michał Ochman and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : A.M. Mathai
Publisher : Springer Science & Business Media
ISBN 13 : 1441909168
Total Pages : 276 pages
Book Rating : 4.69/5 ( download)

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Download or read book The H-Function written by A.M. Mathai and published by Springer Science & Business Media. This book was released on 2009-10-10 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: TheH-function or popularly known in the literature as Fox’sH-function has recently found applications in a large variety of problems connected with reaction, diffusion, reaction–diffusion, engineering and communication, fractional differ- tial and integral equations, many areas of theoretical physics, statistical distribution theory, etc. One of the standard books and most cited book on the topic is the 1978 book of Mathai and Saxena. Since then, the subject has grown a lot, mainly in the elds of applications. Due to popular demand, the authors were requested to - grade and bring out a revised edition of the 1978 book. It was decided to bring out a new book, mostly dealing with recent applications in statistical distributions, pa- way models, nonextensive statistical mechanics, astrophysics problems, fractional calculus, etc. and to make use of the expertise of Hans J. Haubold in astrophysics area also. It was decided to con ne the discussion toH-function of one scalar variable only. Matrix variable cases and many variable cases are not discussed in detail, but an insight into these areas is given. When going from one variable to many variables, there is nothing called a unique bivariate or multivariate analogue of a givenfunction. Whatever be the criteria used, there may be manydifferentfunctions quali ed to be bivariate or multivariate analogues of a given univariate function. Some of the bivariate and multivariateH-functions, currently in the literature, are also questioned by many authors.