Ramanujan summation of divergent series
Author(s)
Bibliographic Information
Ramanujan summation of divergent series
（Lecture notes in mathematics, 2185）
Springer, c2017
Available at / 38 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
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Note
Includes bibliographical references (p. 191-192) and index
Description and Table of Contents
Description
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.
Table of Contents
Introduction: The Summation of Series.- 1 Ramanujan Summation.- 3 Properties of the Ramanujan Summation.- 3 Dependence on a Parameter.- 4 Transformation Formulas.- 5 An Algebraic View on the Summation of Series.- 6 Appendix.- 7 Bibliography.- 8 Chapter VI of the Second Ramanujan's Notebook.
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