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Lecture Notes in Mathematics

Ramanujan Summation of Divergent Series

Authors: Candelpergher, Bernard

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  • 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 basic knowledge in analysis is required to read this monograph
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eBook 37,44 €
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  • ISBN 978-3-319-63630-6
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Softcover 46,79 €
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About this book

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 (5 chapters)

Table of contents (5 chapters)

Buy this book

eBook 37,44 €
price for Spain (gross)
  • ISBN 978-3-319-63630-6
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 46,79 €
price for Spain (gross)
  • ISBN 978-3-319-63629-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Ramanujan Summation of Divergent Series
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2185
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-63630-6
DOI
10.1007/978-3-319-63630-6
Softcover ISBN
978-3-319-63629-0
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XXIII, 195
Number of Illustrations
7 b/w illustrations
Topics