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Ramanujan Summation of Divergent Series

Name: Ramanujan Summation of Divergent Series
Brand: Springer International Publishing AG
SKU: 16499372
Price: 27.76 EUR
Availability: InStock
Author: Bernard Candelpergher
ISBN: 9783319636290

Bernard Candelpergher

Jezik

Angleščina

Knjiga Mehka

Koda Libristo: 16499372

Založba Springer International Publishing AG, september 2017

The aim of this monograph is to give a detailed exposition of the summation method that Ramanujan us... Celoten opis

Koda Libristo: 16499372

68 b

27.76 €

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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.