Asymptotics And 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.
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.
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
Asymptotics Of High Order Differential Equations
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Author : R. B. Paris
language : en
Publisher: Longman
Release Date : 1986
Asymptotics Of High Order Differential Equations written by R. B. Paris and has been published by Longman this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.
The Double Mellin Barnes Type Integrals And Their Applications To Convolution Theory
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Author : Thanh Hai Nguyen
language : en
Publisher: World Scientific
Release Date : 1992
The Double Mellin Barnes Type Integrals And Their Applications To Convolution Theory written by Thanh Hai Nguyen 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 with Mathematics 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.
Asymptotic Expansions Of Integrals
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Author : Norman Bleistein
language : en
Publisher: Ardent Media
Release Date : 1975
Asymptotic Expansions Of Integrals written by Norman Bleistein and has been published by Ardent Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Mathematics categories.
Coherent, systematic coverage of standard methods: integration by parts, Watson's lemma, LaPlace's method, stationary phase and steepest descents. Also includes Mellin transform method and less elementary aspects of the method of steepest descents. Abundant exercises. 1975 edition.
Asymptotic Expansions And Analytic Continuations For A Class Of Barnes Integrals
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Author : Boele Lieuwe Jan Braaksma
language : en
Publisher:
Release Date : 1963
Asymptotic Expansions And Analytic Continuations For A Class Of Barnes Integrals written by Boele Lieuwe Jan Braaksma and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with Asymptotic expansions categories.
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.
Asymptotic Approximations Of Integrals
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Author : R. Wong
language : en
Publisher: SIAM
Release Date : 2001-01-01
Asymptotic Approximations Of Integrals written by R. Wong and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-01 with Mathematics categories.
Asymptotic methods are frequently used in many branches of both pure and applied mathematics, and this classic text remains the most up-to-date book dealing with one important aspect of this area, namely, asymptotic approximations of integrals. In Asymptotic Approximations of Integrals, all results are proved rigorously, and many of the approximation formulas are accompanied by error bounds. A thorough discussion on multidimensional integrals is given, and references are provided. The book contains the "distributional method," which is not available elsewhere. Most of the examples in this text come from concrete applications. Since its publication twelve years ago, significant developments have occurred in the general theory of asymptotic expansions, including smoothing of the Stokes phenomenon, uniform exponentially improved asymptotic expansions, and hyperasymptotics. These new concepts belong to the area now known as "exponential asymptotics." Expositions of these new theories are available in papers published in various journals, but not yet in book form. Audience: this book can be used either as a text for graduate students in mathematics, physics, and engineering or as a reference for research workers in these fields.
Asymptotic Methods For Integrals
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Author : Nico M Temme
language : en
Publisher: World Scientific
Release Date : 2014-10-31
Asymptotic Methods For Integrals written by Nico M Temme and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-31 with Mathematics categories.
This book gives introductory chapters on the classical basic and standard methods for asymptotic analysis, such as Watson's lemma, Laplace's method, the saddle point and steepest descent methods, stationary phase and Darboux's method. The methods, explained in great detail, will obtain asymptotic approximations of the well-known special functions of mathematical physics and probability theory. After these introductory chapters, the methods of uniform asymptotic analysis are described in which several parameters have influence on typical phenomena: turning points and transition points, coinciding saddle and singularities. In all these examples, the special functions are indicated that describe the peculiar behavior of the integrals. The text extensively covers the classical methods with an emphasis on how to obtain expansions, and how to use the results for numerical methods, in particular for approximating special functions. In this way, we work with a computational mind: how can we use certain expansions in numerical analysis and in computer programs, how can we compute coefficients, and so on. Contents:Basic Methods for IntegralsBasic Methods: Examples for Special FunctionsOther Methods for IntegralsUniform Methods for IntegralsUniform Methods for Laplace-Type IntegralsUniform Examples for Special FunctionsA Class of Cumulative Distribution Functions Readership: Researchers in applied mathematics, engineering, physics, mathematical statistics, probability theory and biology. The introductory parts and examples will be useful for post-graduate students in mathematics. Key Features:The book gives a complete overview of the classical asymptotic methods for integralsThe many examples give insight in the behavior of the well-known special functionsThe detailed explanations on how to obtain the coefficients in the expansions make the results useful for numerical applications, in particular, for computing special functionsThe many results on asymptotic representations of special functions supplement and extend those in the NIST Handbook of Mathematical FunctionsKeywords:Asymptotic Analysis;Approximation of Integrals;Asymptotic Approximations;Asymptotic Expansions;Steepest Descent Methods;Saddle Point Methods;Stationary Phase Method;Special Functions;Numerical Approximation of Special Functions;Cumulative Distribution FunctionsReviews: “The book is a useful contribution to the literature. It contains many asymptotic formulas that can be used by practitioners.” Zentralblatt MATH