Ramanujan Summation of Divergent Series, Bernard Candelpergher

Автор: Bruce C. Berndt
Название: Ramanujan`s Notebooks
ISBN: 1461288657 ISBN-13(EAN): 9781461288657
Издательство: Springer
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Цена: 153720.00 T
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Описание: During the years 1903-1914, Ramanujan recorded many of his mathematical discoveries in notebooks without providing proofs. Part I, published in 1985, contains an account of Chapters 1-9 in the second notebook as well as a description of Ramanujan`s quarterly reports. In this volume, we examine Chapters 10-15 in Ramanujan`s second notebook.

Автор: Bruce C. Berndt
Название: Ramanujan`s Notebooks
ISBN: 1461272211 ISBN-13(EAN): 9781461272212
Издательство: Springer
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Цена: 232910.00 T
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Описание: The fifth and final volume to establish the results claimed by the great Indian mathematician Srinivasa Ramanujan in his "Notebooks" first published in 1957. Although each of the five volumes contains many deep results, the average depth in this volume is possibly greater than in the first four.

Автор: Cooper Shaun Et Al
Название: Development Of Elliptic Functions According To Ramanujan
ISBN: 9814366455 ISBN-13(EAN): 9789814366458
Издательство: World Scientific Publishing
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Цена: 74970.00 T
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Описание: Provides an efficient approach to elliptic functions, based on the ideas of the great Indian mathematician Srinivasa Ramanujan. This book is suitable for graduate students and researchers in Number Theory and Classical Analysis, as well for scholars and aficionados of Ramanujan`s work.

Автор: M. Ram Murty; V. Kumar Murty
Название: The Mathematical Legacy of Srinivasa Ramanujan
ISBN: 8132217438 ISBN-13(EAN): 9788132217435
Издательство: Springer
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Цена: 107130.00 T
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Описание: Focusing on a subset of Ramanujan`s significant papers, this book gives an informal account of major developments that emanated from his work in the 20th and 21st centuries. The essays presented here show how Ramanujan shaped the course of modern mathematics.

Автор: Bruce C. Berndt
Название: Ramanujan`s Notebooks
ISBN: 1461270073 ISBN-13(EAN): 9781461270072
Издательство: Springer
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Цена: 186330.00 T
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Описание: Srinivasa Ramanujan is, arguably, the greatest mathematicianthat India has produced. He died very young, at the age of 32,leaving behind three notebooks containing almost 3000theorems, virtually all without proof. Hardy andothers strongly urged that notebooks be edited andpublished, and the result is this series of books.

Автор: Loday-Richaud
Название: Divergent Series, Summability and Resurgence II
ISBN: 3319290746 ISBN-13(EAN): 9783319290744
Издательство: Springer
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Цена: 41920.00 T
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Описание: Addressing the question how to “sum” a power series in one variable when it diverges, that is, how to attach to it analytic functions, the volume gives answers by presenting and comparing the various theories of k-summability and multisummability. These theories apply in particular to all solutions of ordinary differential equations.The volume includes applications, examples and revisits, from a cohomological point of view, the group of tangent-to-identity germs of diffeomorphisms of C studied in volume 1. With a view to applying the theories to solutions of differential equations, a detailed survey of linear ordinary differential equations is provided, which includes Gevrey asymptotic expansions, Newton polygons, index theorems and Sibuya’s proof of the meromorphic classification theorem that characterizes the Stokes phenomenon for linear differential equations.This volume is the second in a series of three, entitled Divergent Series, Summability and Resurgence. It is aimed at graduate students and researchers in mathematics and theoretical physics who are interested in divergent series, Although closely related to the other two volumes, it can be read independently.

Автор: Delabaere
Название: Divergent Series, Summability and Resurgence III
ISBN: 3319289993 ISBN-13(EAN): 9783319289991
Издательство: Springer
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Цена: 41920.00 T
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Описание: The aim of this volume is two-fold. First, to show howthe resurgent methods introduced in volume 1 can be applied efficiently in anon-linear setting; to this end further properties of the resurgence theorymust be developed. Second, to analyze the fundamental example of the FirstPainlev? equation. The resurgent analysis of singularities is pushed all theway up to the so-called “bridge equation”, which concentrates allinformation about the non-linear Stokes phenomenon at infinity of the First Painlev?equation. The third in a series of three, entitled Divergent Series, Summability andResurgence, this volume is aimed at graduate students, mathematicians andtheoretical physicists who are interested in divergent power series and relatedproblems, such as the Stokes phenomenon. The prerequisites are a workingknowledge of complex analysis at the first-year graduate level and of thetheory of resurgence, as presented in volume 1.

Автор: Bruce C. Berndt
Название: Ramanujan`s Notebooks
ISBN: 1461269326 ISBN-13(EAN): 9781461269328
Издательство: Springer
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Цена: 167700.00 T
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Описание: This is the first of two volumes devoted to proving the results found in the unorganized portions of the second notebook and in the third notebook. The author also proves those results in the first notebook that are not found in the second or third notebooks.

Автор: Davidoff
Название: Elementary Number Theory, Group Theory and Ramanujan Graphs
ISBN: 0521824265 ISBN-13(EAN): 9780521824262
Издательство: Cambridge Academ
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Цена: 160510.00 T
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Описание: This text is a self contained treatment of expander graphs and in particular their explicit construction. Expander graphs are both highly connected but sparse, and besides their interest within combinatorics and graph theory, they also find various applications in computer science and engineering.

Автор: Bruce C. Berndt
Название: Ramanujan`s Notebooks
ISBN: 1461269636 ISBN-13(EAN): 9781461269632
Издательство: Springer
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Цена: 232910.00 T
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Описание: In 1957, the Tata Institute of Fundamental Research in Bombay finally published a photostat edition of the notebooks, but no editing was undertaken. In 1977, Berndt began the task of editing Ramanujans notebooks: proofs are provided to theorems not yet proven in previous literature, and many results are so startling as to be unique.

Автор: Anthony Sofo
Название: Computational Techniques for the Summation of Series
ISBN: 1461349044 ISBN-13(EAN): 9781461349044
Издательство: Springer
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Цена: 93160.00 T
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Описание: "This book collects in one volume the author`s considerable results in the area of the summation of series and their representation in closed form, and details the techniques by which they have been obtained...

Автор: Mitschi
Название: Divergent Series, Summability and Resurgence I
ISBN: 3319287354 ISBN-13(EAN): 9783319287355
Издательство: Springer
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Цена: 41920.00 T
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Описание: Providing an elementary introduction to analytic continuation and monodromy, the first part of this volume applies these notions to the local and global study of complex linear differential equations, their formal solutions at singular points, their monodromy and their differential Galois groups. The Riemann-Hilbert problem is discussed from Bolibrukh’s point of view. The second part expounds 1-summability and Ecalle’s theory of resurgence under fairly general conditions. It contains numerous examples and presents an analysis of the singularities in the Borel plane via “alien calculus”, which provides a full description of the Stokes phenomenon for linear or non-linear differential or difference equations. The first of a series of three, entitled Divergent Series, Summability and Resurgence, this volume is aimed at graduate students, mathematicians and theoretical physicists interested in geometric, algebraic or local analytic properties of dynamical systems. It includes useful exercises with solutions. The prerequisites are a working knowledge of elementary complex analysis and differential algebra.