Author: Henry Frederick Baker
Publisher:
ISBN:
Category : Functions
Languages : en
Pages : 360

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Author: Henry Frederick Baker
Publisher:
ISBN:
Category : Functions
Languages : en
Pages : 366

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Author: Henry Frederick Baker
Publisher:
ISBN:
Category :
Languages : en
Pages : 335

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Author: Henry Frederick Baker
Publisher: University of Michigan Library
ISBN: 9781418167035
Category : Science
Languages : en
Pages : 354

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Author: Henry Frederick Baker
Publisher: Palala Press
ISBN: 9781341290824
Category :
Languages : en
Pages : 358

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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: Ganesh Prasad
Publisher:
ISBN:
Category : Elliptic functions
Languages : en
Pages : 122

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Author: Andrew Russell Forsyth
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 308

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Author: H F Baker
Publisher: CreateSpace
ISBN: 9781494778033
Category :
Languages : en
Pages : 352

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An excerpt from the PREFACE: THE present volume consists of two parts; the first of these deals with the theory of hyper-elliptic functions of two variables, the second with the reduction of the theory of general multiply-periodic functions to the theory of algebraic functions; taken together they furnish what is intended to be an elementary and self-contained introduction to many of the leading ideas of the theory of multiply-periodic functions, with the incidental aim of aiding the comprehension of the importance of this theory in analytical geometry. The first part is centred round some remarkable differential equations satisfied by the functions, which appear to be equally illuminative both of the analytical and geometrical aspects of the theory; it was in fact to explain this that the book was originally entered upon. The account has no pretensions to completeness: being anxious to explain the properties of the functions from the beginning, I have been debarred from following Humbert's brilliant monograph, which assumes from the first Poincare's theorem as to the number of zeros common to two theta functions; this theorem is reached in this volume, certainly in a generalised form, only in the last chapter of PartII.: being anxious to render the geometrical portions of the volume quite elementary, I have not been able to utilise the theory of quadratic complexes, which has proved so powerful in this connexion in the hands of Kummer and Klein; and, for both these reasons, the account given here, and that given in the remarkable book from the pen of R. W. H. T. Hudson, will, I believe, only be regarded by readers as complementary. The theory of Kummer's surface, and of the theta functions, has been much studied since the year (1847 or before) in which Gopel first obtained the biquadratic relation connecting four theta functions; and Wirtinger has shown, in his "Untersuchungen uber Thetafunctionen," which has helped me in several ways in the second part of this volume, that the theory is capable of generalisation, in many of its results, to space of "2p-1" dimensions; but even in the case of two variables there is a certain inducement, not to come to too close quarters with the details, in the fact of the existence of sixteen theta functions connected together by many relations, at least in the minds of beginners. I hope therefore that the treatment here followed, which reduces the theory, in a very practical way, to that of one theta function and three periodic functions connected by an algebraic equation, may recommend itself to others, and, in a humble way, serve the purpose of the earlier books on elliptic functions, of encouraging a wider use of the functions in other branches of mathematics. The slightest examination will show that, even for the functions of two variables, many of the problems entered upon demand further study; while, for the hyper-elliptic functions of "p" variables, for which the forms of the corresponding differential equations are known, there exist constructs, of "p" dimensions, in space of "1/2p (p+1) " dimensions, which await similar investigatio

Author: American Mathematical Society
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 560

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Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 532

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