Asymptotics And Mellin Barnes Integrals PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Asymptotics And Mellin Barnes Integrals PDF full book. Access full book title Asymptotics And Mellin Barnes Integrals.
Author | : R. B. Paris |
Publisher | : Cambridge University Press |
Total Pages | : 452 |
Release | : 2001-09-24 |
Genre | : Mathematics |
ISBN | : 9781139430128 |
Download Asymptotics and Mellin-Barnes Integrals Book in PDF, ePub and Kindle
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 | : |
Total Pages | : 422 |
Release | : 2001 |
Genre | : Asymptotic expansions |
ISBN | : 9780511069192 |
Download Asymptotics and Mellin-Barnes Integrals Book in PDF, ePub and Kindle
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 | : Boele Lieuwe Jan Braaksma |
Publisher | : |
Total Pages | : 103 |
Release | : 1963 |
Genre | : Asymptotic expansions |
ISBN | : |
Download Asymptotic Expansions and Analytic Continuations for a Class of Barnes-integrals Book in PDF, ePub and Kindle
Author | : Victor Kowalenko |
Publisher | : Bentham Science Publishers |
Total Pages | : 262 |
Release | : 2009 |
Genre | : Mathematics |
ISBN | : 1608050106 |
Download The Stokes Phenomenon, Borel Summation and Mellin-Barnes Regularisation Book in PDF, ePub and Kindle
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
Author | : Ievgen Dubovyk |
Publisher | : Springer Nature |
Total Pages | : 296 |
Release | : 2022-12-15 |
Genre | : Science |
ISBN | : 3031142721 |
Download Mellin-Barnes Integrals Book in PDF, ePub and Kindle
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 | : R. Wong |
Publisher | : Academic Press |
Total Pages | : 561 |
Release | : 2014-05-10 |
Genre | : Mathematics |
ISBN | : 1483220710 |
Download Asymptotic Approximations of Integrals Book in PDF, ePub and Kindle
Asymptotic Approximations of Integrals deals with the methods used in the asymptotic approximation of integrals. Topics covered range from logarithmic singularities and the summability method to the distributional approach and the Mellin transform technique for multiple integrals. Uniform asymptotic expansions via a rational transformation are also discussed, along with double integrals with a curve of stationary points. For completeness, classical methods are examined as well. Comprised of nine chapters, this volume begins with an introduction to the fundamental concepts of asymptotics, followed by a discussion on classical techniques used in the asymptotic evaluation of integrals, including Laplace's method, Mellin transform techniques, and the summability method. Subsequent chapters focus on the elementary theory of distributions; the distributional approach; uniform asymptotic expansions; and integrals which depend on auxiliary parameters in addition to the asymptotic variable. The book concludes by considering double integrals and higher-dimensional integrals. This monograph is intended for graduate students and research workers in mathematics, physics, and engineering.
Author | : Thanh Hai Nguyen |
Publisher | : World Scientific |
Total Pages | : 318 |
Release | : 1992 |
Genre | : Mathematics |
ISBN | : 9789810206901 |
Download The Double Mellin-Barnes Type Integrals and Their Applications to Convolution Theory Book in PDF, ePub and Kindle
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.
Author | : R. B. Paris |
Publisher | : Longman |
Total Pages | : 360 |
Release | : 1986 |
Genre | : Mathematics |
ISBN | : |
Download Asymptotics of High Order Differential Equations Book in PDF, ePub and Kindle
Author | : Norman Bleistein |
Publisher | : Courier Corporation |
Total Pages | : 453 |
Release | : 1986-01-01 |
Genre | : Mathematics |
ISBN | : 0486650820 |
Download Asymptotic Expansions of Integrals Book in PDF, ePub and Kindle
Excellent introductory text, written by two experts, presents a coherent and systematic view of principles and methods. Topics include integration by parts, Watson's lemma, LaPlace's method, stationary phase, and steepest descents. Additional subjects include the Mellin transform method and less elementary aspects of the method of steepest descents. 1975 edition.
Author | : Nico M. Temme |
Publisher | : World Scientific Publishing Company |
Total Pages | : 0 |
Release | : 2015 |
Genre | : Differential equations |
ISBN | : 9789814612159 |
Download Asymptotic Methods for Integrals Book in PDF, ePub and Kindle
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.