Download or read book Lectures on Divergent Series written by Emile Borel and published by . This book was released on 1975 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Ramanujan Summation of Divergent Series written by Bernard Candelpergher and published by Springer. This book was released on 2017-09-12 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this monograph is to give a detailed exposition of the summation method that Ramanujan uses in Chapter VI of his second Notebook. This method, presented by Ramanujan as an application of the Euler-MacLaurin formula, is here extended using a difference equation in a space of analytic functions. This provides simple proofs of theorems on the summation of some divergent series. Several examples and applications are given. For numerical evaluation, a formula in terms of convergent series is provided by the use of Newton interpolation. The relation with other summation processes such as those of Borel and Euler is also studied. Finally, in the last chapter, a purely algebraic theory is developed that unifies all these summation processes. This monograph is aimed at graduate students and researchers who have a basic knowledge of analytic function theory.
Download or read book Introduction to the Theory of Divergent Series written by Otto Szász and published by . This book was released on 1952 with total page 81 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Divergent Series written by Otto Szász and published by . This book was released on 1936 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lectures on Divergent Series written by Emile Borel and published by . This book was released on 1975 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Divergent Series Summability and Resurgence I written by Claude Mitschi and published by Springer. This book was released on 2016-08-27 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Introduction to the Theory of Divergent Series written by Otto Szász and published by . This book was released on 1944 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book From Divergent Power Series to Analytic Functions written by Werner Balser and published by Springer. This book was released on 2006-11-15 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Introduction to the Theory of Divergent Series Lectures by O Sz sz Written by Joshua Barlaz written by Otto SZÁSZ and published by . This book was released on 1946 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Divergent Series written by Godfrey H. Hardy and published by American Mathematical Society. This book was released on 2024-06-14 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Divergent Series Summability and Resurgence III written by Eric Delabaere and published by Springer. This book was released on 2016-06-28 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this volume is two-fold. First, to show how the resurgent methods introduced in volume 1 can be applied efficiently in a non-linear setting; to this end further properties of the resurgence theory must be developed. Second, to analyze the fundamental example of the First Painlevé equation. The resurgent analysis of singularities is pushed all the way up to the so-called “bridge equation”, which concentrates all information about the non-linear Stokes phenomenon at infinity of the First Painlevé equation. The third in a series of three, entitled Divergent Series, Summability and Resurgence, this volume is aimed at graduate students, mathematicians and theoretical physicists who are interested in divergent power series and related problems, such as the Stokes phenomenon. The prerequisites are a working knowledge of complex analysis at the first-year graduate level and of the theory of resurgence, as presented in volume 1.
Download or read book The History and Development of the Theory of Divergent Series and Integrals written by L. S. Bosanquet and published by . This book was released on 1965 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Studies on Divergent Series and Summability written by Walter Burton Ford and published by Wentworth Press. This book was released on 2019-02-24 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Download or read book We Can Be Mended written by Veronica Roth and published by HarperCollins. This book was released on 2018-01-09 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: Globally bestselling author Veronica Roth returns to the world of Divergent in this revealing short-story epilogue that takes place five years after the stunning events of Allegiant. As Tobias struggles to understand and move past his fears, the world he once knew has changed beyond recognition. Fringe-dwellers, ex-faction members, Bureau dropouts, and migrants now coexist in the rebuilt streets of Chicago. It’s a new, better world—one where he isn't sure how to belong. As everyone else seems to move forward, Tobias is still haunted by those who couldn’t. But new connections from old friends help him begin to heal—and mend. And don't miss The Fates Divide, Veronica Roth's powerful sequel to the bestselling Carve the Mark!
Download or read book Colloquium Lectures written by and published by . This book was released on 1905 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Studies on Divergent Series and Summability written by Walter Ford and published by . This book was released on 2016-10-30 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: A publication of the University of Michigan's Science Series, Studies on Divergent Series and Summability is based on lectures and courses given by Walter Burton Ford at the University of Michigan about infinite series and divergent series. According to Ford, the study of divergent series can be divided into two parts, the first regarding asymptotic series and the second regarding the theory of summability, both of which are discussed within this volume.
Download or read book Studies on Divergent Series and Summability written by Walter Burton Ford and published by Forgotten Books. This book was released on 2015-06-17 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Studies on Divergent Series and Summability, Vol. 2 During the academic year1908-9 the author was privileged to give as a part of his work at the University of Michigan a course of lectures on infinite series with especial reference in the second semester to divergent series - a subject which, despite the uncertain value so long attached to it, seemed clearly to be coming into increasing prominence and importance in mathematical analysis. Little was accomplished, however, as regards divergent series beyond the merest beginning; yet this was sufficient to awaken a desire to continue farther and this in turn resulted in a course being given throughout the whole of the following year devoted entirely to divergent series and the related topic of summability. But this year also closed with much less ground satisfactorily covered than had been expected, unforeseen difficulties having arisen from time to time, some due to the inherent complexities of the subject in hand and others to the somewhat hastily conceived and hence unsatisfactory state in which much of the related literature was found to be. Thus the course still seemed altogether incomplete. It was therefore decided to continue it once more throughout the following year, 1910-11, and indeed for a like reason it was finally continued throughout 1911-12. As the lectures and class-room discussions progressed, permanent notes were kept in the hope that the whole might possibly pass through the press at some future time and appear in book form a hope which, after various delays during which the original notes have been considerably supplemented, now reaches its realization in the appearance of the present volume. In its final form it certainly presents a large mass of detail and is doubtless open to criticism in many respects, but it does not seem advisable to attempt any further defence for it than is contained in the remaining sections of this preface wherein, after certain generalities, the content and motive of the various chapters are discussed in some detail. Speaking roughly, the study of divergent series, at least as the author has come to conceive of it, may be divided into two parts, the one concerning the so-called asymptotic series and the other the theory of summability. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
