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Ramanujan summation of divergent series

Candelpergher, Bernard.

Ramanujan summation of divergent series

Record Type:	Electronic resources : Monograph/item
Title/Author:	Ramanujan summation of divergent seriesby Bernard Candelpergher.
Author:	Candelpergher, Bernard.
Published:	Cham :Springer International Publishing :2017.
Description:	xxiii, 195 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Divergent series.
Online resource:	http://dx.doi.org/10.1007/978-3-319-63630-6
ISBN:	9783319636306$q(electronic bk.)

Ramanujan summation of divergent series
Candelpergher, Bernard.

Ramanujan summation of divergent series[electronic resource] /by Bernard Candelpergher. - Cham :Springer International Publishing :2017. - xxiii, 195 p. :ill., digital ;24 cm. - Lecture notes in mathematics,21850075-8434 ;. - Lecture notes in mathematics ;2035..

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.

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.

ISBN: 9783319636306$q(electronic bk.)

Standard No.: 10.1007/978-3-319-63630-6doiSubjects--Topical Terms:

243698
Divergent series.

LC Class. No.: QA295

Dewey Class. No.: 515.243

Ramanujan summation of divergent series
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245 1 0 $a Ramanujan summation of divergent series $h [electronic resource] / $c by Bernard Candelpergher.
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490 1 $a Lecture notes in mathematics, $x 0075-8434 ; $v 2185
505 0 $a 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.
520 $a 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.
650 0 $a Divergent series. $3 243698
650 1 4 $a Mathematics. $3 184409
650 2 4 $a Sequences, Series, Summability. $3 275704
650 2 4 $a Functions of a Complex Variable. $3 275780
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950 $a Mathematics and Statistics (Springer-11649)