| 书目名称 | Ramanujan Summation of Divergent Series |
| 编辑 | Bernard Candelpergher |
| 视频video | |
| 概述 | Provides a clear and rigorous exposition of Ramanujan‘s theory of divergent series.A special chapter is devoted to an algebraic formalism unifying the most important summation processes.Only little ba |
| 丛书名称 | Lecture Notes in Mathematics |
| 图书封面 |  |
| 描述 | 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. |
| 出版日期 | Book 2017 |
| 关键词 | Ramanujan; Divergent; Series; Summation; Euler-MacLaurin formula; Borel Summation; Euler Summation |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-3-319-63630-6 |
| isbn_softcover | 978-3-319-63629-0 |
| isbn_ebook | 978-3-319-63630-6Series ISSN 0075-8434 Series E-ISSN 1617-9692 |
| issn_series | 0075-8434 |
| copyright | Springer International Publishing AG 2017 |
发表于 2025-3-21 18:54:48
