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Synopsis
Excerpt from Jacobian Elliptic Functions
The design of this treatise will now be intelligible. There are three divisions of the subject, first the direct theory of functions with simple poles derived from a Weierstrassian function whose periods are arbi trary, then the theory of the inverted integral and the solution of the problem of inversion, and lastly the fertile theory of the classical system. To the writer the order of exposition is almost inevitable, but the reader impatient to make the acquaintance of J acobi's functions can pass to Chapter X from Chapter IV or even from Chapter III, and he can return at any time to read Chapter VI, on the connexion between integration and periodicity, as an independent chapter and not necessarily as a stage in the inversion argument.
Far from being new to analysis, the three 'primitive' functions defined in Chapter I have often been studied. Jordan in his Cows d'analyse and Tannery and Molk in their Fonctions Elliptiques allow a few pages to them and define the classical functions in terms of them; in papers on Poncelet's poristic polygons, Chaundy and Baker* use the same three functions, instead of relying explicitly, as does Halphen in the account of this problem in the second volume of his treatise, on the Weierstrassian functions (oz, The point to be emphasized is the deliberate construction of the functions as functions with simple poles. As algebraic functions of gm, important in the development of the theory of @z itself, the functions go back to Weierstrass.
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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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- PublisherForgotten Books
- Publication date2018
- ISBN 10 1527839745
- ISBN 13 9781527839748
- BindingPaperback
- LanguageEnglish
- Number of pages356
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Jacobian Elliptic Functions (Classic Reprint)
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Paperback. Condition: New. Print on Demand. This book delves into the intricate world of elliptic functions, mathematical constructs with fascinating properties and applications. It challenges the traditional approach to the subject, advocating for a revitalization of Jacobian functions within the elementary curriculum. The author's approach presents these functions as constructs built upon lattices, offering a fresh perspective on their inherent double periodicity and connections to Weierstrassian functions. The text delves into the intricacies of the inversion problem, exploring the relationship between elliptic functions and elliptic integrals. It examines the existence theorem and addresses the fundamental question of whether the inverse of every elliptic integral is indeed an elliptic function. Moving beyond theory, the book delves into the practical applications of Jacobian functions, including their role in integration and conformal representation. The author introduces a novel notation system designed to reflect the structure and interrelationships of these functions, offering a more streamlined and efficient approach to understanding their complexities. By illuminating the beauty and utility of Jacobian functions and their integration, this book provides a valuable resource for mathematicians and students seeking a deeper understanding of this captivating area of mathematics. 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 # 9781527839748_0
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Jacobian Elliptic Functions Classic Reprint
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Paperback. Condition: Brand New. 358 pages. 9.02x5.98x0.74 inches. This item is printed on demand. Seller Inventory # zk1527839745
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