Ramanujan Summation of Divergent Series: 2185 (Lecture Notes in Mathematics) - Softcover

Candelpergher, Bernard

Softcover

ISBN 10: 3319636294 ISBN 13: 9783319636290

Verlag: Springer, 2017

Inhaltsangabe

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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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.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2017
• Sprache: Englisch
• ISBN 10: 3319636294
• ISBN 13: 9783319636290
• Einband: Tapa blanda
• Auflage: 1
• Anzahl der Seiten: 220
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: CMN Printpool Inh. Mathis Neumann; https://www.also.com/ec/cms5/en_6000/6000/index.jsp; ; Friedrich-Karl-Str. 9; Hamburg; Deutschland