1.

Record Nr.

UNINA9910826357403321

Autore

Mattes Armin

Titolo

Citizens of a common intellectual homeland : the transatlantic origins of American democracy and nationhood / / Armin Mattes

Pubbl/distr/stampa

Charlottesville, [Virginia] ; ; London, [England] : , : University of Virginia Press, , 2015

©2015

Descrizione fisica

1 online resource (280 pages)

Collana

Jeffersonian America

Disciplina

320.973

Soggetti

Democracy - United States - History

Democracy - Europe - History

Political science - United States - Philosophy

Political science - Europe - History

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

"Preparation of this volume has been supported by the Thomas Jefferson Foundation"--T.p. verso.

Nota di bibliografia

Includes bibliographical references and index.



2.

Record Nr.

UNINA9910257378903321

Autore

Candelpergher Bernard

Titolo

Ramanujan summation of divergent series / / by Bernard Candelpergher

Pubbl/distr/stampa

Cham : , : Springer International Publishing, AG, 2017

ISBN

9783319636306

3-319-63630-8

Edizione

[1st ed. 2017.]

Descrizione fisica

1 online resource (XXIII, 195 p. 7 illus.)

Collana

Lecture Notes in Mathematics, , 0075-8434 ; ; 2185

Disciplina

517.21

Soggetti

Sequences (Mathematics)

Functions of complex variables

Number theory

Successions (Matemàtica)

Nombres, Teoria de

Funcions de variables complexes

Sequences, Series, Summability

Functions of a Complex Variable

Number Theory

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Nota di contenuto

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.

Sommario/riassunto

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.