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1. |
Record Nr. |
UNINA9910826357403321 |
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Autore |
Mattes Armin |
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Titolo |
Citizens of a common intellectual homeland : the transatlantic origins of American democracy and nationhood / / Armin Mattes |
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Pubbl/distr/stampa |
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Charlottesville, [Virginia] ; ; London, [England] : , : University of Virginia Press, , 2015 |
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©2015 |
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Descrizione fisica |
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1 online resource (280 pages) |
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Collana |
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Disciplina |
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Soggetti |
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Democracy - United States - History |
Democracy - Europe - History |
Political science - United States - Philosophy |
Political science - Europe - History |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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"Preparation of this volume has been supported by the Thomas Jefferson Foundation"--T.p. verso. |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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2. |
Record Nr. |
UNINA9910257378903321 |
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Autore |
Candelpergher Bernard |
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Titolo |
Ramanujan summation of divergent series / / by Bernard Candelpergher |
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Pubbl/distr/stampa |
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Cham : , : Springer International Publishing, AG, 2017 |
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ISBN |
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9783319636306 |
3-319-63630-8 |
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Edizione |
[1st ed. 2017.] |
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Descrizione fisica |
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1 online resource (XXIII, 195 p. 7 illus.) |
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Collana |
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Lecture Notes in Mathematics, , 0075-8434 ; ; 2185 |
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Disciplina |
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Soggetti |
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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 |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di contenuto |
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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. |
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Sommario/riassunto |
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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 |
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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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