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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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Excerpt from An Introduction to the Theory of Infinite Series
This book is based on courses of lectures on Elementary Analysis given at Queen's College, Galway, during each of the sessions 1902-1907. But additions have naturally been made in preparing the manuscript for press: in particular the whole of Chapter XI. and the greater part of the Appendices have been added. In selecting the subject-matter, I have attempted to include proofs of all theorems stated in Pringsheim's article, Irrationalzahlen und Konvergenz unendlicher Prozesse, with the exception of theorems relating to continued fractions.
In Chapter I. a preliminary account is given of the notions of a limit and of convergence. I have not in this chapter attempted to supply arithmetic proofs of the fundamental theorems concerning the existence of limits, but have allowed their truth to rest on an appeal to the reader's intuition, in the hope that the discussion may thus be made more attractive to beginners. An arithmetic treatment will be found in Appendix I., where Dedekind's definition of irrational numbers is adopted as fundamental; this method leads at once to the monotonic principle of convergence (Art. 149), from which the existence of extreme limits is deduced (Arts. 5, 150);it is then easy to establish the general principle of convergence (Art. 151).
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
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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- VerlagForgotten Books
- Erscheinungsdatum2018
- ISBN 10 1330230639
- ISBN 13 9781330230633
- EinbandTapa blanda
- SpracheEnglisch
- Anzahl der Seiten532
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An Introduction to the Theory of Infinite Series (Classic Reprint)
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Paperback. Zustand: 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. Bestandsnummer des Verkäufers 9781330230633_0
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An Introduction to the Theory of Infinite Series (Classic Reprint)
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An Introduction to the Theory of Infinite Series Classic Reprint
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PAP. Zustand: New. New Book. Shipped from UK. Established seller since 2000. Bestandsnummer des Verkäufers LW-9781330230633
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