Ramanujan Summation Of Divergent Series
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Ramanujan Summation Of Divergent Series
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Author : Bernard Candelpergher
language : en
Publisher: Springer
Release Date : 2017-09-12
Ramanujan Summation Of Divergent Series written by Bernard Candelpergher and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-12 with Mathematics categories.
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.
Ramanujan S Notebooks
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Author : Srinivasa Ramanujan Aiyangar
language : en
Publisher:
Release Date : 1985
Ramanujan S Notebooks written by Srinivasa Ramanujan Aiyangar and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Mathematics categories.
Proceedings Of First International Conference On Mathematical Modeling And Computational Science
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Author : Sheng-Lung Peng
language : en
Publisher: Springer Nature
Release Date : 2021-05-04
Proceedings Of First International Conference On Mathematical Modeling And Computational Science written by Sheng-Lung Peng and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-04 with Technology & Engineering categories.
This book presents the most recent scientific and technological advances in the fields of engineering mathematics and computational science, to strengthen the links in the scientific community. It is a collection of high-quality, peer-reviewed research papers presented at the First International Conference on Mathematical Modeling and Computational Science (ICMMCS 2020), held in Pattaya, Thailand, during 14–15 August 2020. The topics covered in the book are mathematical logic and foundations, numerical analysis, neural networks, fuzzy set theory, coding theory, higher algebra, number theory, graph theory and combinatory, computation in complex networks, calculus, differential educations and integration, application of soft computing, knowledge engineering, machine learning, artificial intelligence, big data and data analytics, high-performance computing, network and device security, and Internet of things (IoT).
Summability Calculus
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Author : Ibrahim M. Alabdulmohsin
language : en
Publisher: Springer
Release Date : 2018-03-15
Summability Calculus written by Ibrahim M. Alabdulmohsin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-15 with Mathematics categories.
This book develops the foundations of "summability calculus", which is a comprehensive theory of fractional finite sums. It fills an important gap in the literature by unifying and extending disparate historical results. It also presents new material that has not been published before. Importantly, it shows how the study of fractional finite sums benefits from and contributes to many areas of mathematics, such as divergent series, numerical integration, approximation theory, asymptotic methods, special functions, series acceleration, Fourier analysis, the calculus of finite differences, and information theory. As such, it appeals to a wide audience of mathematicians whose interests include the study of special functions, summability theory, analytic number theory, series and sequences, approximation theory, asymptotic expansions, or numerical methods. Richly illustrated, it features chapter summaries, and includes numerous examples and exercises. The content is mostly developed from scratch using only undergraduate mathematics, such as calculus and linear algebra.
Arithmetic Of Infinity
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Author : Yaroslav D. Sergeyev
language : en
Publisher: Yaroslav D. Sergeyev
Release Date : 2016-05-13
Arithmetic Of Infinity written by Yaroslav D. Sergeyev and has been published by Yaroslav D. Sergeyev this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-13 with Science categories.
The first chapter of the book gives a brief description of the modern viewpoint on real numbers and presents the famous results of Georg Cantor regarding infinity. The second chapter has a preparative character and links the first and the third parts of the book. On the one hand, it shows that the commonly accepted point of view on numbers and infinity is not so clear as it seems at first sight (for example, it leads to numerous paradoxes). On the other hand, the chapter contains preliminary observations that will be used in the constructive introduction of a new arithmetic of infinity, given in the third chapter. This last part of the book contains the main results. It introduces notions of infinite and infinitesimal numbers, extended natural and real numbers, and operations with them. Surprisingly, the introduced arithmetical operations result in being very simple and are obtained as immediate extensions of the usual addition, multiplication, and division of finite numbers to infinite ones. This simplicity is a consequence of a newly developed positional numeral system used to express infinite numbers. Finally, the chapter contains solutions to a number of paradoxes regarding infinity (we can say that the new approach allows us to avoid paradoxes) and some examples of applications. In order to broaden the audience, the book was written as a popular one. The interested reader can find a number of technical articles of several researches that use the approach introduced here for solving a variety of research problems at the web page of the author. The author Yaroslav D. Sergeyev is Distinguished Professor and Head of Numerical Calculus Laboratory at the University of Calabria, Italy. He is also Professor (part-time contract) at Lobachevsky Nizhni Novgorod State University, Russia. His research interests include numerical analysis, global optimization, infinity computing, set theory, number theory, fractals, and parallel computing. He has been awarded several national and international prizes (Pythagoras International Prize in Mathematics, Italy; Lagrange Lecture, Turin University, Italy; MAIK Prize for the best scientific monograph published in Russian, Moscow, etc.). His list of scientific publications contains more than 200 items. He is a member of editorial boards of 5 international journals and has given more than 50 plenary and keynote lectures at prestigious international congresses.
My Search For Ramanujan
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Author : Ken Ono
language : en
Publisher: Springer
Release Date : 2016-04-20
My Search For Ramanujan written by Ken Ono and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-20 with Mathematics categories.
"The son of a prominent Japanese mathematician who came to the United States after World War II, Ken Ono was raised on a diet of high expectations and little praise. Rebelling against his pressure-cooker of a life, Ken determined to drop out of high school to follow his own path. To obtain his father’s approval, he invoked the biography of the famous Indian mathematical prodigy Srinivasa Ramanujan, whom his father revered, who had twice flunked out of college because of his single-minded devotion to mathematics. Ono describes his rocky path through college and graduate school, interweaving Ramanujan’s story with his own and telling how at key moments, he was inspired by Ramanujan and guided by mentors who encouraged him to pursue his interest in exploring Ramanujan’s mathematical legacy. Picking up where others left off, beginning with the great English mathematician G.H. Hardy, who brought Ramanujan to Cambridge in 1914, Ono has devoted his mathematical career to understanding how in his short life, Ramanujan was able to discover so many deep mathematical truths, which Ramanujan believed had been sent to him as visions from a Hindu goddess. And it was Ramanujan who was ultimately the source of reconciliation between Ono and his parents. Ono’s search for Ramanujan ranges over three continents and crosses paths with mathematicians whose lives span the globe and the entire twentieth century and beyond. Along the way, Ken made many fascinating discoveries. The most important and surprising one of all was his own humanity."
Ramanujan S Theta Functions
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Author : Shaun Cooper
language : en
Publisher: Springer
Release Date : 2017-06-12
Ramanujan S Theta Functions written by Shaun Cooper and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-12 with Mathematics categories.
Theta functions were studied extensively by Ramanujan. This book provides a systematic development of Ramanujan’s results and extends them to a general theory. The author’s treatment of the subject is comprehensive, providing a detailed study of theta functions and modular forms for levels up to 12. Aimed at advanced undergraduates, graduate students, and researchers, the organization, user-friendly presentation, and rich source of examples, lends this book to serve as a useful reference, a pedagogical tool, and a stimulus for further research. Topics, especially those discussed in the second half of the book, have been the subject of much recent research; many of which are appearing in book form for the first time. Further results are summarized in the numerous exercises at the end of each chapter.
Ramanujan S Lost Notebook
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Author : George E. Andrews
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-04-05
Ramanujan S Lost Notebook written by George E. Andrews and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-05 with Mathematics categories.
In the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge, to examine the papers of the late G.N. Watson. Among these papers, Andrews discovered a sheaf of 138 pages in the handwriting of Srinivasa Ramanujan. This manuscript was soon designated "Ramanujan's lost notebook." The "lost notebook" contains considerable material on mock theta functions and so undoubtedly emanates from the last year of Ramanujan's life. It should be emphasized that the material on mock theta functions is perhaps Ramanujan's deepest work.
Infinite Sequences And Series
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Author : Konrad Knopp
language : en
Publisher: Courier Corporation
Release Date : 2012-09-14
Infinite Sequences And Series written by Konrad Knopp and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-14 with Mathematics categories.
Careful presentation of fundamentals of the theory by one of the finest modern expositors of higher mathematics. Covers functions of real and complex variables, arbitrary and null sequences, convergence and divergence, Cauchy's limit theorem, more.
Collected Papers Of Srinivasa Ramanujan
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Author : Srinivasa Ramanujan
language : en
Publisher: Cambridge University Press
Release Date : 2015-12-03
Collected Papers Of Srinivasa Ramanujan written by Srinivasa Ramanujan and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-03 with Mathematics categories.
Originally published in 1927, this book presents the collected papers of the renowned Indian mathematician Srinivasa Ramanujan (1887-1920), with editorial contributions from G. H. Hardy (1877-1947). Detailed notes are incorporated throughout and appendices are also included. This book will be of value to anyone with an interest in the works of Ramanujan and the history of mathematics.