Download or read book On the Definition of the Sum of a Divergent Series written by Louis Lazarus Silverman and published by . This book was released on 1913 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On the Definition of the Sum of a Divergent Series written by Louis Lazarus Silverman and published by . This book was released on 1991 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On the Definition of the Sum of a Divergent Series written by Louis Lazarus Silverman and published by Createspace Independent Publishing Platform. This book was released on 2016-06-24 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents. § 1. Introduction § 2. Historical Resumé § 3. Averageable Sequences § 4. Product Definitions § 5. On Certain Possible Definitions Of Summability § 6. Definitions Of Evaluability § 7. Applications § 8. Tests For Cesaro-Summability § 9. Theorems On Limits §10. Conclusion * * * * * An excerpt from: § 2. Historical Resumé. The earliest interest in divergent series centers about the series 1 - 1 + 1 - 1 + ... If we assume that this series has a generalized sum s, then the series, obtained by dropping the first term, - 1 + 1 - 1 + 1... must, by the third fundamental requirement of page 2, also have a generalized sum which is obviously -s. We have then, s - 1 = -s or s = 1/2. Thus, if the series is to have any value at all, that value must be 1/2. And this is precisely the value which Leibniz was led to attach to the series, by different considerations. The sum of n terms of the series is 0 or 1 according as n is even or odd; and since this sum is just as often equal to 1 as it is to 0, its probable value is the arithmetic mean, 1/2. This same value was later attached to the series by Euler, in a more satisfactory, though not entirely rigorous manner. "Let us say that the sum of any infinite series is the finite expression, by the expansion of which the series is generated. In this sense, the sum of the infinite series 1 - x + x2 - x3... will be 1/(1 + x), because the series arises from the expansion of the fraction, whatever number is put in place of x." In particular, 1/2 = 1 - 1 + 1 - 1 + ... It is true, as has already been intimated, that none of the methods given above, to prove that the series should have the value 1/2, is satisfactory from a theoretical point of view. But objections have been raised to the result for practical reasons also....
Download or read book ON THE DEFINITION OF THE SUM OF A DIVERGENT SERIES written by LOUIS LAZARUS. SILVERMAN and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On the Definition of the Sum of a Divergent Series Classic Reprint written by Louis Lazarus Silverman and published by . This book was released on 2016-06-26 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from On the Definition of the Sum of a Divergent Series This paper was accepted as a dissertation by the Graduate Faculty Of the University Of Missouri in May, 1910, in partial fulfillment Of the require ments for the degree of Doctor Of Philosophy. 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.
Download or read book Mathematics Series on the Definition of the Sum of a Divergent Series written by Louis Lazarus Silverman and published by Wentworth Press. This book was released on 2019-03-05 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Download or read book On Various Definitions of the Sum of a Divergent Series written by Louis Lazarus Silverman and published by . This book was released on 1910 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Studies on Divergent Series and Summability and The Asymptotic Developments of Functions Defined by Maclaurin Series written by Walter B. Ford and published by American Mathematical Soc.. This book was released on 1960-01-30 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers 2 main topics: asymptotic series and the theory of summability. This book provides a discussion of nowhere convergent asymptotic series that includes the so-called MacLaurent summation formula, determining asymptotic expansions of various classes of functions, and the study of asymptotic solutions of linear ordinary differential equations.
Download or read book Some Theorems on the Summation of Divergent Series written by Glenn James and published by . This book was released on 1917 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Some Theorems on the Summation of Divergent Series written by Glenn James and published by . This book was released on 1917 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical and Algorithmic Puzzles written by Pramod Ganapathi and published by . This book was released on 2024-05-29 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents serious mathematical and algorithmic puzzles that are mostly counterintuitive. The presented puzzles are simultaneously entertaining, challenging, intriguing, and haunting. This book introduces its readers to counterintuitive mathematical ideas and revolutionary algorithmic insights from a wide variety of topics. The presented solutions that are discovered by many mathematicians and computer scientists are highly counterintuitive and show supreme mathematical beauty. These counterintuitive solutions are intriguing to the degree that they shatter our preconceived notions, shake our long-held belief systems, debunk our fundamental intuitions, and finally rob us of sleep and haunt us for a lifetime. Multiple ways of attacking the same puzzle are presented which teach the application of elegant problem-solving strategies.
Download or read book Studies on Divergent Series and Summability written by Walter Burton Ford and published by . This book was released on 1916 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Some Theorems in the Theory of Summable Divergent Series written by Frank Joseph McMackin and published by . This book was released on 1916 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Summability Calculus written by Ibrahim M. Alabdulmohsin and published by Springer. This book was released on 2018-03-07 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book CK 12 Calculus written by CK-12 Foundation and published by CK-12 Foundation. This book was released on 2010-08-15 with total page 603 pages. Available in PDF, EPUB and Kindle. Book excerpt: CK-12 Foundation's Single Variable Calculus FlexBook introduces high school students to the topics covered in the Calculus AB course. Topics include: Limits, Derivatives, and Integration.
Download or read book Introduction to Mathematical Physics written by Chun Wa Wong and published by Oxford University Press, USA. This book was released on 2013-01-24 with total page 731 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Mathematical Physics explains why and how mathematics is needed in describing physical events in space. It helps physics undergraduates master the mathematical tools needed in physics core courses. It contains advanced topics for graduate students, short tutorials on basic mathematics, and an appendix on Mathematica.
Download or read book Active Calculus 2018 written by Matthew Boelkins and published by Createspace Independent Publishing Platform. This book was released on 2018-08-13 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: Active Calculus - single variable is a free, open-source calculus text that is designed to support an active learning approach in the standard first two semesters of calculus, including approximately 200 activities and 500 exercises. In the HTML version, more than 250 of the exercises are available as interactive WeBWorK exercises; students will love that the online version even looks great on a smart phone. Each section of Active Calculus has at least 4 in-class activities to engage students in active learning. Normally, each section has a brief introduction together with a preview activity, followed by a mix of exposition and several more activities. Each section concludes with a short summary and exercises; the non-WeBWorK exercises are typically involved and challenging. More information on the goals and structure of the text can be found in the preface.
