From Divergent Power Series To Analytic Functions PDF Download
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| Author | : Werner Balser |
| Publisher | : Springer |
| Total Pages | : 117 |
| Release | : 2006-11-15 |
| Genre | : Mathematics |
| ISBN | : 3540485945 |
Download From Divergent Power Series to Analytic Functions Book in PDF, ePub and Kindle
Multisummability is a method which, for certain formal power series with radius of convergence equal to zero, produces an analytic function having the formal series as its asymptotic expansion. This book presents the theory of multisummabi- lity, and as an application, contains a proof of the fact that all formal power series solutions of non-linear meromorphic ODE are multisummable. It will be of use to graduate students and researchers in mathematics and theoretical physics, and especially to those who encounter formal power series to (physical) equations with rapidly, but regularly, growing coefficients.
| Author | : Werner Balser |
| Publisher | : |
| Total Pages | : 124 |
| Release | : 2014-01-15 |
| Genre | : |
| ISBN | : 9783662187739 |
Download From Divergent Power Series to Analytic Functions Book in PDF, ePub and Kindle
| Author | : Michèle Loday-Richaud |
| Publisher | : Springer |
| Total Pages | : 286 |
| Release | : 2016-06-28 |
| Genre | : Mathematics |
| ISBN | : 3319290754 |
Download Divergent Series, Summability and Resurgence II Book in PDF, ePub and Kindle
Addressing the question how to “sum” a power series in one variable when it diverges, that is, how to attach to it analytic functions, the volume gives answers by presenting and comparing the various theories of k-summability and multisummability. These theories apply in particular to all solutions of ordinary differential equations. The volume includes applications, examples and revisits, from a cohomological point of view, the group of tangent-to-identity germs of diffeomorphisms of C studied in volume 1. With a view to applying the theories to solutions of differential equations, a detailed survey of linear ordinary differential equations is provided, which includes Gevrey asymptotic expansions, Newton polygons, index theorems and Sibuya’s proof of the meromorphic classification theorem that characterizes the Stokes phenomenon for linear differential equations. This volume is the second in a series of three, entitled Divergent Series, Summability and Resurgence. It is aimed at graduate students and researchers in mathematics and theoretical physics who are interested in divergent series, Although closely related to the other two volumes, it can be read independently.
| Author | : Edmund Taylor Whittaker |
| Publisher | : |
| Total Pages | : 410 |
| Release | : 1902 |
| Genre | : Calculus |
| ISBN | : |
Download A Course of Modern Analysis Book in PDF, ePub and Kindle
| Author | : Emile Borel |
| Publisher | : |
| Total Pages | : 132 |
| Release | : 1975 |
| Genre | : Divergent series |
| ISBN | : |
Download Lectures on Divergent Series Book in PDF, ePub and Kindle
| Author | : Godfrey Harold Hardy |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 418 |
| Release | : 2000 |
| Genre | : Mathematics |
| ISBN | : 0821826492 |
Download Divergent Series Book in PDF, ePub and Kindle
From the Preface by J. E. Littlewood: "All [Hardy's] books gave him some degree of pleasure, but this one, his last, was his favourite. When embarking on it he told me that he believed in its value (as well he might), and also that he looked forward to the task with enthusiasm. He had actually given lectures on the subject at intervals ever since his return to Cambridge in 1931, and he had at one time or another lectured on everything in the book except Chapter XIII [TheEuler-MacLaurin sum formula] ... [I]n the early years of the century the subject [Divergent Series], while in no way mystical or unrigorous, was regarded as sensational, and about the present title, now colourless, there hung an aroma of paradox and audacity."
| Author | : Claude Mitschi |
| Publisher | : Springer |
| Total Pages | : 314 |
| Release | : 2016-08-27 |
| Genre | : Mathematics |
| ISBN | : 3319287362 |
Download Divergent Series, Summability and Resurgence I Book in PDF, ePub and Kindle
Providing an elementary introduction to analytic continuation and monodromy, the first part of this volume applies these notions to the local and global study of complex linear differential equations, their formal solutions at singular points, their monodromy and their differential Galois groups. The Riemann-Hilbert problem is discussed from Bolibrukh’s point of view. The second part expounds 1-summability and Ecalle’s theory of resurgence under fairly general conditions. It contains numerous examples and presents an analysis of the singularities in the Borel plane via “alien calculus”, which provides a full description of the Stokes phenomenon for linear or non-linear differential or difference equations. The first of a series of three, entitled Divergent Series, Summability and Resurgence, this volume is aimed at graduate students, mathematicians and theoretical physicists interested in geometric, algebraic or local analytic properties of dynamical systems. It includes useful exercises with solutions. The prerequisites are a working knowledge of elementary complex analysis and differential algebra.
| Author | : Godfrey H. Hardy |
| Publisher | : American Mathematical Society |
| Total Pages | : 416 |
| Release | : 2024-06-14 |
| Genre | : Mathematics |
| ISBN | : 1470477858 |
Download Divergent Series Book in PDF, ePub and Kindle
Review of the original edition: This is an inspiring textbook for students who know the theory of functions of real and complex variables and wish further knowledge of mathematical analysis. There are no problems displayed and labelled “problems,” but one who follows all of the arguments and calculations of the text will find use for his ingenuity and pencil. The book deals with interesting and important problems and topics in many fields of mathematical analysis, to an extent very much greater than that indicated by the titles of the chapters. It is, of course, an indispensable handbook for those interested in divergent series. It assembles a considerable part of the theory of divergent series, which has previously existed only in periodical literature. Hardy has greatly simplified and improved many theories, theorems and proofs. In addition, numerous acknowledgements show that the book incorporates many previously unpublished results and improvements of old results, communicated to Hardy by his colleagues and by others interested in the book. —Mathematical Reviews
| Author | : James Pierpont |
| Publisher | : |
| Total Pages | : 606 |
| Release | : 1914 |
| Genre | : Mathematics |
| ISBN | : |
Download Functions of a Complex Variable Book in PDF, ePub and Kindle
A thorough treatment of fundamental elements, concepts, and theorems pertaining to the function of a complex variable, this rigorous treatment is suitable for advanced mathematics students, physicists, and engineers. 1914 edition.
| Author | : Galina Filipuk |
| Publisher | : Springer |
| Total Pages | : 274 |
| Release | : 2018-09-24 |
| Genre | : Mathematics |
| ISBN | : 3319991485 |
Download Formal and Analytic Solutions of Diff. Equations Book in PDF, ePub and Kindle
These proceedings provide methods, techniques, different mathematical tools and recent results in the study of formal and analytic solutions to Diff. (differential, partial differential, difference, q-difference, q-difference-differential.... ) Equations. They consist of selected contributions from the conference "Formal and Analytic Solutions of Diff. Equations", held at Alcalá de Henares, Spain during September 4-8, 2017. Their topics include summability and asymptotic study of both ordinary and partial differential equations. The volume is divided into four parts. The first paper is a survey of the elements of nonlinear analysis. It describes the algorithms to obtain asymptotic expansion of solutions of nonlinear algebraic, ordinary differential, partial differential equations, and of systems of such equations. Five works on formal and analytic solutions of PDEs are followed by five papers on the study of solutions of ODEs. The proceedings conclude with five works on related topics, generalizations and applications. All contributions have been peer reviewed by anonymous referees chosen among the experts on the subject. The volume will be of interest to graduate students and researchers in theoretical and applied mathematics, physics and engineering seeking an overview of the recent trends in the theory of formal and analytic solutions of functional (differential, partial differential, difference, q-difference, q-difference-differential) equations in the complex domain.
