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Author : Glenn James
Publisher :
ISBN 13 :
Total Pages : 40 pages
Book Rating : 4.:/5 (5 download)
Download or read book Some Theorems on the Summation of Divergent Series written by Glenn James and published by . This book was released on 1917 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Frank Joseph McMackin
Publisher :
ISBN 13 :
Total Pages : 32 pages
Book Rating : 4.3/5 (91 download)
Download or read book Some Theorems in the Theory of Summable Divergent Series written by Frank Joseph McMackin and published by . This book was released on 1916 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Bernard Candelpergher
Publisher : Springer
ISBN 13 : 3319636308
Total Pages : 211 pages
Book Rating : 4.3/5 (196 download)
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.
Author : Godfrey H. Hardy
Publisher : American Mathematical Society
ISBN 13 : 1470477858
Total Pages : 416 pages
Book Rating : 4.4/5 (74 download)
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
Author : Lloyd Leroy Smail
Publisher :
ISBN 13 :
Total Pages : 192 pages
Book Rating : 4.F/5 ( download)
Download or read book History and Synopsis of the Theory of Summable Infinite Processes written by Lloyd Leroy Smail and published by . This book was released on 1925 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ovidiu Costin
Publisher : CRC Press
ISBN 13 : 1420070320
Total Pages : 266 pages
Book Rating : 4.4/5 (2 download)
Download or read book Asymptotics and Borel Summability written by Ovidiu Costin and published by CRC Press. This book was released on 2008-12-04 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Incorporating substantial developments from the last thirty years into one resource, Asymptotics and Borel Summability provides a self-contained introduction to asymptotic analysis with special emphasis on topics not covered in traditional asymptotics books. The author explains basic ideas, concepts, and methods of generalized Borel summability, tr
Author : Charles Napoleon Moore
Publisher : American Mathematical Soc.
ISBN 13 : 0821846205
Total Pages : 114 pages
Book Rating : 4.8/5 (218 download)
Download or read book Summable Series and Convergence Factors written by Charles Napoleon Moore and published by American Mathematical Soc.. This book was released on 1938-12-31 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fairly early in the development of the theory of summability of divergent series, the concept of convergence factors was recognized as of fundamental importance in the subject. One of the pioneers in this field was C. N. Moore, the author of the book under review.... Moore classifies convergence factors into two types. In type I he places the factors which have only the property that they preserve convergence for a convergent series or produce convergence for a summable series. In type II he places the factors which not only maintain or produce convergence but have the additional property that they may be used to obtain the sum or generalized sum of the series. This book gives a generalized systematic treatment of the theory of convergence factors of both types, for simply infinite series and for multiple series, convergent and summable.... --Bulletin of the American Mathematical Society
Author : University of Oregon
Publisher :
ISBN 13 :
Total Pages : 876 pages
Book Rating : 4.1/5 (36 download)
Download or read book University of Oregon Publication written by University of Oregon and published by . This book was released on 1923 with total page 876 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : University of Oregon
Publisher :
ISBN 13 :
Total Pages : 876 pages
Book Rating : 4.3/5 (91 download)
Download or read book Publications written by University of Oregon and published by . This book was released on 1923 with total page 876 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jacob Korevaar
Publisher : Springer Science & Business Media
ISBN 13 : 3662102250
Total Pages : 497 pages
Book Rating : 4.6/5 (621 download)
Download or read book Tauberian Theory written by Jacob Korevaar and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tauberian theory compares summability methods for series and integrals, helps to decide when there is convergence, and provides asymptotic and remainder estimates. The author shows the development of the theory from the beginning and his expert commentary evokes the excitement surrounding the early results. He shows the fascination of the difficult Hardy-Littlewood theorems and of an unexpected simple proof, and extolls Wiener's breakthrough based on Fourier theory. There are the spectacular "high-indices" theorems and Karamata's "regular variation", which permeates probability theory. The author presents Gelfand's elegant algebraic treatment of Wiener theory and his own distributional approach. There is also a new unified theory for Borel and "circle" methods. The text describes many Tauberian ways to the prime number theorem. A large bibliography and a substantial index round out the book.
Author : E. H. McAlister
Publisher :
ISBN 13 :
Total Pages : 910 pages
Book Rating : 4.:/5 (89 download)
Download or read book Damped Vibrations written by E. H. McAlister and published by . This book was released on 1926 with total page 910 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ibrahim M. Alabdulmohsin
Publisher : Springer
ISBN 13 : 3319746480
Total Pages : 168 pages
Book Rating : 4.3/5 (197 download)
Download or read book Summability Calculus written by Ibrahim M. Alabdulmohsin and published by Springer. This book was released on 2018-03-07 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops the foundations of "summability calculus", which is a comprehensive theory of fractional finite sums. It fills an important gap in the literature by unifying and extending disparate historical results. It also presents new material that has not been published before. Importantly, it shows how the study of fractional finite sums benefits from and contributes to many areas of mathematics, such as divergent series, numerical integration, approximation theory, asymptotic methods, special functions, series acceleration, Fourier analysis, the calculus of finite differences, and information theory. As such, it appeals to a wide audience of mathematicians whose interests include the study of special functions, summability theory, analytic number theory, series and sequences, approximation theory, asymptotic expansions, or numerical methods. Richly illustrated, it features chapter summaries, and includes numerous examples and exercises. The content is mostly developed from scratch using only undergraduate mathematics, such as calculus and linear algebra.
Author : American Mathematical Society
Publisher :
ISBN 13 :
Total Pages : 876 pages
Book Rating : 4.F/5 ( download)
Download or read book Bulletin of the American Mathematical Society written by American Mathematical Society and published by . This book was released on 1913 with total page 876 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Daniel D. Bonar
Publisher : American Mathematical Soc.
ISBN 13 : 1470447827
Total Pages : 278 pages
Book Rating : 4.4/5 (74 download)
Download or read book Real Infinite Series written by Daniel D. Bonar and published by American Mathematical Soc.. This book was released on 2018-12-12 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a widely accessible introductory treatment of infinite series of real numbers, bringing the reader from basic definitions and tests to advanced results. An up-to-date presentation is given, making infinite series accessible, interesting, and useful to a wide audience, including students, teachers, and researchers. Included are elementary and advanced tests for convergence or divergence, the harmonic series, the alternating harmonic series, and closely related results. One chapter offers 107 concise, crisp, surprising results about infinite series. Another gives problems on infinite series, and solutions, which have appeared on the annual William Lowell Putnam Mathematical Competition. The lighter side of infinite series is treated in the concluding chapter where three puzzles, eighteen visuals, and several fallacious proofs are made available. Three appendices provide a listing of true or false statements, answers to why the harmonic series is so named, and an extensive list of published works on infinite series.
Author : Emile Borel
Publisher :
ISBN 13 :
Total Pages : 132 pages
Book Rating : 4.3/5 (91 download)
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:
Author : Edwin Herman
Publisher :
ISBN 13 : 9781947172838
Total Pages : 0 pages
Book Rating : 4.1/5 (728 download)
Download or read book Calculus Volume 3 written by Edwin Herman and published by . This book was released on 2016-03-30 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 3 covers parametric equations and polar coordinates, vectors, functions of several variables, multiple integration, and second-order differential equations.
Author : V. S. Varadarajan
Publisher : American Mathematical Soc.
ISBN 13 : 0821835807
Total Pages : 312 pages
Book Rating : 4.8/5 (218 download)
Download or read book Euler Through Time written by V. S. Varadarajan and published by American Mathematical Soc.. This book was released on 2006 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Euler is one of the greatest and most prolific mathematicians of all time. He wrote the first accessible books on calculus, created the theory of circular functions, and discovered new areas of research such as elliptic integrals, the calculus of variations, graph theory, divergent series, and so on. It took hundreds of years for his successors to develop in full the theories he began, and some of his themes are still at the center of today's mathematics. It is of great interesttherefore to examine his work and its relation to current mathematics. This book attempts to do that. In number theory the discoveries he made empirically would require for their eventual understanding such sophisticated developments as the reciprocity laws and class field theory. His pioneering work onelliptic integrals is the precursor of the modern theory of abelian functions and abelian integrals. His evaluation of zeta and multizeta values is not only a fantastic and exciting story but very relevant to us, because they are at the confluence of much research in algebraic geometry and number theory today (Chapters 2 and 3 of the book). Anticipating his successors by more than a century, Euler created a theory of summation of series that do not converge in the traditional manner. Chapter 5of the book treats the progression of ideas regarding divergent series from Euler to many parts of modern analysis and quantum physics. The last chapter contains a brief treatment of Euler products. Euler discovered the product formula over the primes for the zeta function as well as for a smallnumber of what are now called Dirichlet $L$-functions. Here the book goes into the development of the theory of such Euler products and the role they play in number theory, thus offering the reader a glimpse of current developments (the Langlands program).
