書目名稱 | Infinite Families of Exact Sums of Squares Formulas, Jacobi Elliptic Functions, Continued Fractions, | 編輯 | Stephen C. Milne | 視頻video | http://file.papertrans.cn/465/464630/464630.mp4 | 叢書名稱 | Developments in Mathematics | 圖書封面 |  | 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 | doi | https://doi.org/10.1007/978-1-4757-5462-9 | isbn_softcover | 978-1-4419-5213-4 | isbn_ebook | 978-1-4757-5462-9Series ISSN 1389-2177 Series E-ISSN 2197-795X | issn_series | 1389-2177 | copyright | Springer 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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