Asymptotics and Mellin-Barnes Integrals - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Asymptotics and Mellin-Barnes Integrals write by R. B. Paris. This book was released on 2001-09-24. Asymptotics and Mellin-Barnes Integrals available 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.
Asymptotics and Mellin-Barnes Integrals
Asymptotics and Mellin-Barnes Integrals - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Asymptotics and Mellin-Barnes Integrals write by R. B. Paris. This book was released on 2001. Asymptotics and Mellin-Barnes Integrals available 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.
The Stokes Phenomenon, Borel Summation and Mellin-Barnes Regularisation
The Stokes Phenomenon, Borel Summation and Mellin-Barnes Regularisation - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Stokes Phenomenon, Borel Summation and Mellin-Barnes Regularisation write by Victor Kowalenko. This book was released on 2009. The Stokes Phenomenon, Borel Summation and Mellin-Barnes Regularisation available 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
Mellin-Barnes Integrals
Mellin-Barnes Integrals - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Mellin-Barnes Integrals write by Ievgen Dubovyk. This book was released on 2022-12-15. Mellin-Barnes Integrals available 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.
Asymptotic Methods For Integrals
Asymptotic Methods For Integrals - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Asymptotic Methods For Integrals write by Nico M Temme. This book was released on 2014-10-31. Asymptotic Methods For Integrals available 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.
