| 書目名稱 | The Rise and Development of the Theory of Series up to the Early 1820s | | 編輯 | Giovanni Ferraro | | 視頻video | http://file.papertrans.cn/919/918679/918679.mp4 | | 概述 | Carefully researched, accompanied by detailed bibliography.Provides a coherent and detailed account of the theory of series in the 18th and early 19th centuries.Includes a comprehensive account of man | | 叢書名稱 | Sources and Studies in the History of Mathematics and Physical Sciences | | 圖書封面 |  | | 描述 | The theory of series in the 17th and 18th centuries poses several interesting problems to historians. Indeed, mathematicians of the time derived num- ous results that range from the binomial theorem to the Taylor formula, from the power series expansions of elementary functions to trigonometric series, from Stirling’s series to series solution of di?erential equations, from theEuler–MaclaurinsummationformulatotheLagrangeinversiontheorem, from Laplace’s theory of generating functions to the calculus of operations, etc. Most of these results were, however, derived using methods that would be found unacceptable today, thus, if we look back to the theory of series priortoCauchywithoutreconstructinginternalmotivationsandtheconc- tual background, it appears as a corpus of manipulative techniques lacking in rigor whose results seem to be the puzzling fruit of the mind of a - gician or diviner rather than the penetrating and complex work of great mathematicians. For this reason, in this monograph, not only do I describe the entire complex of 17th- and 18th-century procedures and results concerning series, but also I reconstruct the implicit and explicit principles upon which they are based | | 出版日期 | Book 2008 | | 關(guān)鍵詞 | Fourier series; Taylor series; calculus; differential equation; number theory | | 版次 | 1 | | doi | https://doi.org/10.1007/978-0-387-73468-2 | | isbn_softcover | 978-1-4419-2520-6 | | isbn_ebook | 978-0-387-73468-2Series ISSN 2196-8810 Series E-ISSN 2196-8829 | | issn_series | 2196-8810 | | copyright | Springer-Verlag New York 2008 |
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