Ramanujan summation of divergent series /

Ramanujan summation of divergent series /

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Bibliographic Details
Author / Creator:	Candelpergher, Bernard, author.
Imprint:	Cham : Springer, 2017.
Description:	1 online resource (xxiii, 195 pages) : illustrations
Language:	English
Series:	Lecture notes in mathematics, 0075-8434 ; 2185 Lecture notes in mathematics (Springer-Verlag) ; 2185.
Subject:	Divergent series. Divergent series. Electronic books.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11361559

Hidden Bibliographic Details
ISBN:	9783319636306 3319636308 3319636294 9783319636290 9783319636290
Digital file characteristics:	text file PDF
Notes:	Online resource; title from PDF title page (SpringerLink, viewed September 25, 2017).
Summary:	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.
Other form:	Printed edition: 9783319636290
Standard no.:	10.1007/978-3-319-63630-6

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.