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Titlebook: Infinite Families of Exact Sums of Squares Formulas, Jacobi Elliptic Functions, Continued Fractions,; Stephen C. Milne Book 2002 Springer

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發(fā)表于 2025-3-21 17:33:51 | 只看該作者 |倒序瀏覽 |閱讀模式
書目名稱Infinite Families of Exact Sums of Squares Formulas, Jacobi Elliptic Functions, Continued Fractions,
編輯Stephen C. Milne
視頻videohttp://file.papertrans.cn/465/464630/464630.mp4
叢書名稱Developments in Mathematics
圖書封面Titlebook: Infinite Families of Exact Sums of Squares Formulas, Jacobi Elliptic Functions, Continued Fractions,;  Stephen C. Milne Book 2002 Springer
描述.The problem of representing an integer as a sum of squares of integers is one of the oldest and most significant in mathematics. It goes back at least 2000 years to Diophantus, and continues more recently with the works of Fermat, Euler, Lagrange, Jacobi, Glaisher, Ramanujan, Hardy, Mordell, Andrews, and others. Jacobi‘s elliptic function approach dates from his epic .Fundamenta Nova. of 1829. Here, the author employs his combinatorial/elliptic function methods to derive many infinite families of explicit exact formulas involving either squares or triangular numbers, two of which generalize Jacobi‘s (1829) 4 and 8 squares identities to 4.n.2. or 4.n.(.n.+1) squares, respectively, without using cusp forms such as those of Glaisher or Ramanujan for 16 and 24 squares. These results depend upon new expansions for powers of various products of classical theta functions. This is the first time that infinite families of non-trivial exact explicit formulas for sums of squares have been found. ..The author derives his formulas by utilizing combinatorics to combine a variety of methods and observations from the theory of Jacobi elliptic functions, continued fractions, Hankel or Turanian det
出版日期Book 2002
關(guān)鍵詞Combinatorics; approximation theory; mathematical physics; number theory
版次1
doihttps://doi.org/10.1007/978-1-4757-5462-9
isbn_softcover978-1-4419-5213-4
isbn_ebook978-1-4757-5462-9Series ISSN 1389-2177 Series E-ISSN 2197-795X
issn_series 1389-2177
copyrightSpringer Science+Business Media New York 2002
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書目名稱Infinite Families of Exact Sums of Squares Formulas, Jacobi Elliptic Functions, Continued Fractions,影響因子(影響力)




書目名稱Infinite Families of Exact Sums of Squares Formulas, Jacobi Elliptic Functions, Continued Fractions,影響因子(影響力)學(xué)科排名




書目名稱Infinite Families of Exact Sums of Squares Formulas, Jacobi Elliptic Functions, Continued Fractions,網(wǎng)絡(luò)公開度




書目名稱Infinite Families of Exact Sums of Squares Formulas, Jacobi Elliptic Functions, Continued Fractions,網(wǎng)絡(luò)公開度學(xué)科排名




書目名稱Infinite Families of Exact Sums of Squares Formulas, Jacobi Elliptic Functions, Continued Fractions,被引頻次




書目名稱Infinite Families of Exact Sums of Squares Formulas, Jacobi Elliptic Functions, Continued Fractions,被引頻次學(xué)科排名




書目名稱Infinite Families of Exact Sums of Squares Formulas, Jacobi Elliptic Functions, Continued Fractions,年度引用




書目名稱Infinite Families of Exact Sums of Squares Formulas, Jacobi Elliptic Functions, Continued Fractions,年度引用學(xué)科排名




書目名稱Infinite Families of Exact Sums of Squares Formulas, Jacobi Elliptic Functions, Continued Fractions,讀者反饋




書目名稱Infinite Families of Exact Sums of Squares Formulas, Jacobi Elliptic Functions, Continued Fractions,讀者反饋學(xué)科排名




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發(fā)表于 2025-3-21 21:47:51 | 只看該作者
1389-2177 ck at least 2000 years to Diophantus, and continues more recently with the works of Fermat, Euler, Lagrange, Jacobi, Glaisher, Ramanujan, Hardy, Mordell, Andrews, and others. Jacobi‘s elliptic function approach dates from his epic .Fundamenta Nova. of 1829. Here, the author employs his combinatorial
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發(fā)表于 2025-3-22 04:36:19 | 只看該作者
Developments in Mathematicshttp://image.papertrans.cn/i/image/464630.jpg
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978-1-4419-5213-4Springer Science+Business Media New York 2002
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發(fā)表于 2025-3-22 19:06:50 | 只看該作者
Infinite Families of Exact Sums of Squares Formulas, Jacobi Elliptic Functions, Continued Fractionsr Turánian determinants, Fourier series, Lambert series, inclusion/exclusion, Laplace expansion formula for determinants, and Schur functions. The Schur function form of these infinite families of identities are analogous to the .-function identities of Macdonald. Moreover, the powers 4.(. 1), 2. .
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發(fā)表于 2025-3-23 00:37:31 | 只看該作者
Stephen C. Milneption of the opportunities and challenges faced by organizations in exploiting Web 2.0 capabilities. Part II looks at the technologies, and also some methodologies, developed in ACTIVE. Part III describes how these technologies have been evaluated in three case studies within the project. Part IV st
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發(fā)表于 2025-3-23 02:54:37 | 只看該作者
1389-2177 ilizing combinatorics to combine a variety of methods and observations from the theory of Jacobi elliptic functions, continued fractions, Hankel or Turanian det978-1-4419-5213-4978-1-4757-5462-9Series ISSN 1389-2177 Series E-ISSN 2197-795X
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發(fā)表于 2025-3-23 08:26:48 | 只看該作者
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