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Ramanujan summation of divergent series

Candelpergher, Bernard.

Ramanujan summation of divergent series

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Ramanujan summation of divergent seriesby Bernard Candelpergher.
作者:	Candelpergher, Bernard.
出版者:	Cham :Springer International Publishing :2017.
面頁冊數:	xxiii, 195 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Divergent series.
電子資源:	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

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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.
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