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Titlebook: Linear Differential Equations and Group Theory from Riemann to Poincare; Jeremy J. Gray Textbook 2008Latest edition Birkhäuser Boston 2008

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书目名称Linear Differential Equations and Group Theory from Riemann to Poincare
编辑Jeremy J. Gray
视频video
概述Chronicles important events not covered anywhere else.Discusses the history and development of ideas, not just mathematicians
丛书名称Modern Birkhäuser Classics
图书封面Titlebook: Linear Differential Equations and Group Theory from Riemann to Poincare;  Jeremy J. Gray Textbook 2008Latest edition Birkhäuser Boston 2008
描述.This book is a study of how a particular vision of the unity of mathematics, often called geometric function theory, was created in the 19th century. The central focus is on the convergence of three mathematical topics: the hypergeometric and related linear differential equations, group theory, and on-Euclidean geometry...The text for this second edition has been greatly expanded and revised, and the existing appendices enriched with historical accounts of the Riemann–Hilbert problem, the uniformization theorem, Picard–Vessiot theory, and the hypergeometric equation in higher dimensions. The exercises have been retained, making it possible to use the book as a companion to mathematics courses at the graduate level..
出版日期Textbook 2008Latest edition
关键词Algebra; Equations; Felix Klein; Group theory; History; History of Mathematics; Lazarus Fuchs; Poincaré; Rie
版次2
doihttps://doi.org/10.1007/978-0-8176-4773-5
isbn_softcover978-0-8176-4772-8
isbn_ebook978-0-8176-4773-5Series ISSN 2197-1803 Series E-ISSN 2197-1811
issn_series 2197-1803
copyrightBirkhäuser Boston 2008
The information of publication is updating

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Hypergeometric Equations,dication of its immediate antecedents and consequences. It therefore looks very briefly at some of the work of Gauss, Legendre, Abel and Jacobi on elliptic functions, in particular at their work on modular functions and modular transformations. It concludes with a description of the general theory o
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Lazarus Fuchs,ichen Coefficienten” (“On the theory of linear differential equations with variable coefficients”). These will be surveyed in this chapter. In them he characterised the class of linear differential equations in a complex variable ., all of whose solutions have only finite poles and possibly logarith
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Modular Equations,f considering groups of motions of the sphere, and, in particular, finite groups. Klein connected this study with that of the quintic equation, and so with the theory of transformations of elliptic functions and modular equations as considered by Hermite, Brioschi, and Kronecker around 1858. Klein’s
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