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拉马努金笔记(第5卷)(英文)/国外优秀数学著作原版系列

  • 定价: ¥165
  • ISBN:9787560381411
  • 开 本:16开 平装
  • 作者:编者:(美)布鲁斯...
  • 立即节省:
  • 2019-06-01 第1版
  • 2019-06-01 第1次印刷
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导语

  

内容提要

  

    印度神奇数学家拉马努金有着深邃的数学直觉和洞察力,这套丛书给出了拉马努金很多漂亮的数学结果,共分为5卷。本书为第5卷,主要介绍了数论、素数的拉马努金理论、模方程的函数、双纽线与联合方程的逆公式等内容。本书适合高年级本科生、研究生,以及数学爱好者参考阅读。

目录

Preface
Introduction
32 Continued Fractions
  1 The Rogers-Ramanujan Continued Fraction
  2 Other q-Continued Fractions
  3 Continued Fractions Arising from Products of Gamma Functions
  4 Other Continued Fractions
  5 General Theorems
33 Ramanujan's Theories of Elliptic Functions to Alternative Bases
  1 Introduction
  2 Ramanujan's Cubic Transformation, the Borweins' Cubic Theta-Function Identity, and the Inversion Formula
  3 The Principles of Triplication and Trimidiation
  4 The Eisenstein Series L, M, and N
  5 A Hypergeometric Transformation and Associated Transfer Principle
  6 More Higher Order Transformations for Hypergeometric Series
  7 Modular Equations in the Theory of Signature 3
  8 The Inversion of an Analogue of K (k) in Signature 3
  9 The Theory for Signature 4
  10 Modular Equations in the Theory of Signature 4
  11 The Theory for Signature 6
  12 An Identity from the First Notebook and Further Hypergeometric Transformations
  13 Some Enigmatic Formulas Near the End of the Third Notebook
  14 Concluding Remarks
34 Class Invariants and Singular Moduli
  1 Introduction
  2 Table of Class Invariants
  3 Computation of Gn and gn when 9In
  4 Kronecker's Limit Formula and General Formulas for Class Invariants
  5 Class Invariants Via Kronecker's Limit Formula
  6 Class Invariants Via Modular Equations
  7 Class Invariants Via Class Field Theory
  8 Miscellaneous Results
  9 Singular Moduli
  10 A Certain Rational Function of Singular Moduli
  11 The Modular j-invariant
35 Values of Theta-Funetions
  0 Introduction
  1 Elementary Values
  2 Nonelementary Values of φo(e-nπ)
  3 A Remarkable Product of Theta-Functions
36 Modular Equations and Theta-Funetion Identities in Notebook 1
  1 Modular Equations of Degree 3 and Related Theta-Function Identities
  2 Modular Equations of Degree 5 and Related Theta-Function Identities
  3 Other Modular Equations and Related Theta-Function Identities
  4 Identities Involving Lambert Series
  5 Identities Involving Eisenstein Series
  6 Modular Equations in the Form of Schlafli
  7 Modular Equations in the Form of Russell
  8 Modular Equations in the Form of Weber
  9 Series Transformations Associated with Theta-Functions
  10 Miscellaneous Results
37 Infinite Series
38 Approximations and Asymptotic Expansions
39 Misceilaneous Resuits in the First Notebook
  Location of Entries in the Unorganized Portions of Ramanujan’s First Notebook
References
Index
附录I
拉马努金的中国知音:数学家刘治国的“西天取经”之旅
附录II
刘治国教授访谈
编辑手记