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Author : John Edward Weidlich
Publisher :
ISBN 13 :
Total Pages : 144 pages
Book Rating : 4.68/5 ( download)
Download or read book Summability Methods for Divergent Series written by John Edward Weidlich and published by . This book was released on 1950 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Bernard Candelpergher
Publisher : Springer
ISBN 13 : 3319636308
Total Pages : 195 pages
Book Rating : 4.06/5 ( 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 195 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 : Claude Mitschi
Publisher : Springer
ISBN 13 : 3319287362
Total Pages : 298 pages
Book Rating : 4.62/5 ( download)
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 298 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.
Author : Eric Delabaere
Publisher : Springer
ISBN 13 : 3319290002
Total Pages : 230 pages
Book Rating : 4.03/5 ( download)
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 230 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.
Author : Kauzo Ishiguro
Publisher :
ISBN 13 :
Total Pages : 1054 pages
Book Rating : 4.31/5 ( download)
Download or read book On the Summability Methods of Divergent Series written by Kauzo Ishiguro and published by . This book was released on 1965 with total page 1054 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ibrahim M. Alabdulmohsin
Publisher : Springer
ISBN 13 : 3319746480
Total Pages : 165 pages
Book Rating : 4.87/5 ( 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 165 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 : Glenn James
Publisher :
ISBN 13 :
Total Pages : 32 pages
Book Rating : 4.04/5 ( 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 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : John Edward Weidlich
Publisher :
ISBN 13 :
Total Pages : 152 pages
Book Rating : 4.46/5 ( download)
Download or read book Summability Methods for Divergent Series written by John Edward Weidlich and published by . This book was released on 1950 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ovidiu Costin
Publisher : CRC Press
ISBN 13 : 1420070320
Total Pages : 266 pages
Book Rating : 4.23/5 ( 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 : Louis Lazarus Silverman
Publisher :
ISBN 13 :
Total Pages : 116 pages
Book Rating : 4.84/5 ( download)
Download or read book On the Definition of the Sum of a Divergent Series written by Louis Lazarus Silverman and published by . This book was released on 1913 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:
