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 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:
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.
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 Some Methods of Summation of Divergent Series written by Charles Hill Wallace Sedgewick and published by . This book was released on 1930 with total page 55 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book CK 12 Calculus written by CK-12 Foundation and published by CK-12 Foundation. This book was released on 2010-08-15 with total page 603 pages. Available in PDF, EPUB and Kindle. Book excerpt: CK-12 Foundation's Single Variable Calculus FlexBook introduces high school students to the topics covered in the Calculus AB course. Topics include: Limits, Derivatives, and Integration.
Download or read book Summation of Divergent Series written by Hanna Cohen 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 Summation of Divergent Series written by Nora Mutin and published by . This book was released on 1949 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
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
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:
Download or read book A General Method of Summation of Divergent Series written by Lloyd Leroy Smail and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Summation of Divergent Series written by Isidore Cooper and published by . This book was released on 1931 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Summation of Divergent Series and Sequences written by Bertram Fine and published by . This book was released on 1929 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
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:
Download or read book The Summation of Divergent Series written by Harry Nelson Carter and published by . This book was released on 1950 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Methods of Summation of Divergent Series written by Robert Dean Engle and published by . This book was released on 1961 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt:
