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Synopsis
Excerpt from An Introduction to the Theory of Infinite Series
The investigations of Chapter XI. Imply an acquaintance with the convergence of infinite integrals, but when the manu script was being prepared for printing no English book was available from which the necessary theorems could be quoted.
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This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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Review
The book is especially good at counterexamples, and includes many of these to warn against pitfalls in reasoning and to show that all the hypotheses of the theorems are really needed. One especially nice feature is the use of Tannery's theorem, on interchanging limit and summation, throughout the book. --MAA Reviews
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- PublisherForgotten Books
- Publication date2018
- ISBN 10 1330230639
- ISBN 13 9781330230633
- BindingPaperback
- LanguageEnglish
- Number of pages531
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An Introduction to the Theory of Infinite Series (Classic Reprint)
Print on DemandSeller: Forgotten Books, London, United Kingdom
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Paperback. Condition: New. Print on Demand. This book delves into the fascinating realm of infinite series, exploring their convergence, divergence, and oscillation. The author guides readers through fundamental concepts such as limits, sequences, and the intricacies of series manipulation. Rooted in the rich history of mathematical analysis, the book builds upon the works of renowned mathematicians like Cauchy, Pringsheim, and Tannery. It presents a comprehensive treatment of single and double series, exploring powerful tools like the integral test, ratio tests, and Cauchy's condensation test. The exploration extends beyond mere convergence, venturing into absolute convergence, uniform convergence, and the intriguing world of power series. Examples and applications illuminate the theoretical concepts, showcasing the practical significance of infinite series in various branches of mathematics. Ultimately, this book provides readers with a profound understanding of infinite series, equipping them with the knowledge to navigate the complexities of these mathematical wonders and appreciate their far-reaching implications in the world of analysis. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Seller Inventory # 9781330230633_0
Quantity: Over 20 available
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An Introduction to the Theory of Infinite Series (Classic Reprint)
Seller: PBShop.store US, Wood Dale, IL, U.S.A.
Seller rating 5 out of 5 stars
PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781330230633
Quantity: 15 available
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An Introduction to the Theory of Infinite Series Classic Reprint
Seller: PBShop.store UK, Fairford, GLOS, United Kingdom
Seller rating 4 out of 5 stars
PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781330230633
Quantity: 15 available