| 书目名称 | Infinite Families of Exact Sums of Squares Formulas, Jacobi Elliptic Functions, Continued Fractions, | | 编辑 | Stephen C. Milne | | 视频video | | | 丛书名称 | Developments in Mathematics | | 图书封面 |  | | 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 | | 关键词 | 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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书目名称Infinite Families of Exact Sums of Squares Formulas, Jacobi Elliptic Functions, Continued Fractions,影响因子(影响力)
书目名称Infinite Families of Exact Sums of Squares Formulas, Jacobi Elliptic Functions, Continued Fractions,影响因子(影响力)学科排名
书目名称Infinite Families of Exact Sums of Squares Formulas, Jacobi Elliptic Functions, Continued Fractions,网络公开度
书目名称Infinite Families of Exact Sums of Squares Formulas, Jacobi Elliptic Functions, Continued Fractions,网络公开度学科排名
书目名称Infinite Families of Exact Sums of Squares Formulas, Jacobi Elliptic Functions, Continued Fractions,被引频次
书目名称Infinite Families of Exact Sums of Squares Formulas, Jacobi Elliptic Functions, Continued Fractions,被引频次学科排名
书目名称Infinite Families of Exact Sums of Squares Formulas, Jacobi Elliptic Functions, Continued Fractions,年度引用
书目名称Infinite Families of Exact Sums of Squares Formulas, Jacobi Elliptic Functions, Continued Fractions,年度引用学科排名
书目名称Infinite Families of Exact Sums of Squares Formulas, Jacobi Elliptic Functions, Continued Fractions,读者反馈
书目名称Infinite Families of Exact Sums of Squares Formulas, Jacobi Elliptic Functions, Continued Fractions,读者反馈学科排名
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发表于 2025-3-21 17:33:51
