Jacobian Elliptic Functions (Classic Reprint)

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Excerpt from Jacobian Elliptic FunctionsThe 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.About the PublisherForgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.comThis 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.