Mellin Barnes Integrals
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Asymptotics And Mellin Barnes Integrals
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Author : R. B. Paris
language : en
Publisher: Cambridge University Press
Release Date : 2001-09-24
Asymptotics And Mellin Barnes Integrals written by R. B. Paris and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-09-24 with Mathematics categories.
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.
The Double Mellin Barnes Type Integrals And Their Applications To Convolution Theory
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Author : Nguyen Thanh Hai
language : en
Publisher: World Scientific
Release Date : 1992-05-26
The Double Mellin Barnes Type Integrals And Their Applications To Convolution Theory written by Nguyen Thanh Hai and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-05-26 with Science categories.
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
Asymptotics And Mellin Barnes Integrals
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Author : R. B. Paris
language : en
Publisher:
Release Date : 2001
Asymptotics And Mellin Barnes Integrals written by R. B. Paris and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Asymptotic expansions categories.
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.
Mellin Barnes Integrals
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Author : Ievgen Dubovyk
language : en
Publisher: Springer Nature
Release Date : 2022-12-15
Mellin Barnes Integrals written by Ievgen Dubovyk and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-15 with Science categories.
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.
Mellin Barnes Integrals Related To The Lie Algebra U N
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Author : Alexander N. Manashov
language : en
Publisher:
Release Date : 2021
Mellin Barnes Integrals Related To The Lie Algebra U N written by Alexander N. Manashov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.
Evaluating Two Loop Massive Operator Matrix Elements With Mellin Barnes Integrals
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Author : Isabella Bierenbaum
language : de
Publisher:
Release Date : 2006
Evaluating Two Loop Massive Operator Matrix Elements With Mellin Barnes Integrals written by Isabella Bierenbaum and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.
Mbnumerics
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Author : J. Usovitsch
language : en
Publisher:
Release Date : 2018
Mbnumerics written by J. Usovitsch and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.
Mbsums A Mathematics Package For The Representation Of Mellin Barnes Integrals By Multiple Sums
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Author : M. Ochman
language : en
Publisher:
Release Date : 2015
Mbsums A Mathematics Package For The Representation Of Mellin Barnes Integrals By Multiple Sums written by M. Ochman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
Mellin Transform Method For Integral Evaluation
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Author : George Fikioris
language : en
Publisher: Springer Nature
Release Date : 2022-05-31
Mellin Transform Method For Integral Evaluation written by George Fikioris and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-31 with Technology & Engineering categories.
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.
The Stokes Phenomenon Borel Summation And Mellin Barnes Regularisation
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Author : Victor Kowalenko
language : en
Publisher: Bentham Science Publishers
Release Date : 2009
The Stokes Phenomenon Borel Summation And Mellin Barnes Regularisation written by Victor Kowalenko and has been published by Bentham Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
The Stokes phenomenon refers to the emergence of jump discontinuities in asymptotic expansions at specific rays in the complex plane. This book presents a radical theory for the phenomenon by introducing the concept of regularization. Two methods of regularization, Borel summation and Mellin-Barnes regularization, are used to derive general expressions for the regularized values of asymptotic expansions throughout the complex plane. Though different, both yield identical values, which, where possible, agree with the original functions. Consequently, asymptotics has been elevated to a true disc