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Author : Louis Lazarus Silverman
Publisher :
ISBN 13 :
Total Pages : 116 pages
Book Rating : 4.84/5 ( download)
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:
Author : Louis Lazarus Silverman
Publisher :
ISBN 13 : 9781332768400
Total Pages : 116 pages
Book Rating : 4.07/5 ( download)
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.
Author :
Publisher :
ISBN 13 :
Total Pages : 100 pages
Book Rating : 4.41/5 ( download)
Download or read book On the Definition of the Sum of a Divergent Series written by and published by . This book was released on 1913 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : HardPress
Publisher : Hardpress Publishing
ISBN 13 : 9781314604740
Total Pages : 120 pages
Book Rating : 4.40/5 ( download)
Download or read book On the Definition of the Sum of a Divergent Series written by HardPress and published by Hardpress Publishing. This book was released on 2013-01 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unlike some other reproductions of classic texts (1) We have not used OCR(Optical Character Recognition), as this leads to bad quality books with introduced typos. (2) In books where there are images such as portraits, maps, sketches etc We have endeavoured to keep the quality of these images, so they represent accurately the original artefact. Although occasionally there may be certain imperfections with these old texts, we feel they deserve to be made available for future generations to enjoy.
Author : Lloyd Leroy Smail
Publisher :
ISBN 13 : 9781332770106
Total Pages : 60 pages
Book Rating : 4.0X/5 ( download)
Download or read book Some Generalizations in the Theory of Summable Divergent Series (Classic Reprint) written by Lloyd Leroy Smail and published by . This book was released on 2016-06-26 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Some Generalizations in the Theory of Summable Divergent Series Our problem of divergent series is then to associate with such a series a number, which we call the Sum* of the series, which should be defined in such a way that the resulting laws of calculation agree as far as possible with those of convergent series. If the series has variable terms, we wish to associate with it, not a number, but a function, which shall satisfy the above condition. Any definite method by which we can associate with a given series a Sum is called a method of summation. 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.
Author : Louis Lazarus Silverman
Publisher : Wentworth Press
ISBN 13 : 9780530086712
Total Pages : 106 pages
Book Rating : 4.19/5 ( download)
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.
Author : Louis Lazarus Silverman
Publisher :
ISBN 13 :
Total Pages : 178 pages
Book Rating : 4.79/5 ( download)
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:
Author : Glenn James
Publisher : Forgotten Books
ISBN 13 : 9780265441107
Total Pages : 28 pages
Book Rating : 4.02/5 ( download)
Download or read book Some Theorems on the Summation of Divergent Series written by Glenn James and published by Forgotten Books. This book was released on 2017-10-17 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Some Theorems on the Summation of Divergent Series: Dissertation In general it seems desirable to seek methods of summing divergent series which make the sum bear the closest possible analogy to the ordinary sum of convergent series. However, in this paper we shall be concerned only with the above restrictions, which are indeed most essential. 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.
Author : Louis Lazarus Silverman
Publisher : Createspace Independent Publishing Platform
ISBN 13 : 9781534890336
Total Pages : 102 pages
Book Rating : 4.35/5 ( download)
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....
Author : Walter Burton Ford
Publisher : Forgotten Books
ISBN 13 : 9781528151856
Total Pages : 220 pages
Book Rating : 4.52/5 ( download)
Download or read book Studies on Divergent Series and Summability, Vol. 2 (Classic Reprint) written by Walter Burton Ford and published by Forgotten Books. This book was released on 2017-09-12 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Studies on Divergent Series and Summability, Vol. 2 The theory of summability, or second general aspect of divergent series mentioned above, is essentially concerned with the question as to whether in any proper sense a sum may be assigned to the series, assumed divergent. 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.
