Asymptotics And Mellin Barnes Integrals

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

DOWNLOAD NOW!

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)

DOWNLOAD NOW!

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 : R. Wong
Publisher : Academic Press
ISBN 13 : 1483220710
Total Pages : 561 pages
Book Rating : 4.10/5 ( download)

DOWNLOAD NOW!

Download or read book Asymptotic Approximations of Integrals written by R. Wong and published by Academic Press. This book was released on 2014-05-10 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Victor Kowalenko
Publisher : Bentham Science Publishers
ISBN 13 : 1608050106
Total Pages : 262 pages
Book Rating : 4.09/5 ( download)

DOWNLOAD NOW!

Download or read book The Stokes Phenomenon, Borel Summation and Mellin-Barnes Regularisation written by Victor Kowalenko and published by Bentham Science Publishers. This book was released on 2009 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
ISBN 13 : 3031142721
Total Pages : 296 pages
Book Rating : 4.27/5 ( download)

DOWNLOAD NOW!

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 : R. B. Paris
Publisher : Longman
ISBN 13 :
Total Pages : 360 pages
Book Rating : 4.99/5 ( download)

DOWNLOAD NOW!

Download or read book Asymptotics of High Order Differential Equations written by R. B. Paris and published by Longman. This book was released on 1986 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Thanh Hai Nguyen
Publisher : World Scientific
ISBN 13 : 9789810206901
Total Pages : 318 pages
Book Rating : 4.09/5 ( download)

DOWNLOAD NOW!

Download or read book The Double Mellin-Barnes Type Integrals and Their Applications to Convolution Theory written by Thanh Hai Nguyen and published by World Scientific. This book was released on 1992 with total page 318 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.

Author : Norman Bleistein
Publisher : Ardent Media
ISBN 13 : 9780030835964
Total Pages : 456 pages
Book Rating : 4.68/5 ( download)

DOWNLOAD NOW!

Download or read book Asymptotic Expansions of Integrals written by Norman Bleistein and published by Ardent Media. This book was released on 1975 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Nico M. Temme
Publisher : World Scientific Publishing Company
ISBN 13 : 9789814612159
Total Pages : 0 pages
Book Rating : 4.54/5 ( download)

DOWNLOAD NOW!

Download or read book Asymptotic Methods for Integrals written by Nico M. Temme and published by World Scientific Publishing Company. This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Boele Lieuwe Jan Braaksma
Publisher :
ISBN 13 :
Total Pages : 116 pages
Book Rating : 4.02/5 ( download)

DOWNLOAD NOW!

Download or read book Asymptotic Expansions and Analytic Continuations for a Class of Barnes-integrals written by Boele Lieuwe Jan Braaksma and published by . This book was released on 1963 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: