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国外很好数学著作原版系列拉马努金笔记(第5卷) 内容简介
拉马努金数学笔记第5卷
国外很好数学著作原版系列拉马努金笔记(第5卷) 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 Ramanuian's Theories of Elliptic Functions to Alternative
Bases
Introduction Ramanujans 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 9)n
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-Functions
Introduction Elementary values Nonelementary Values of p(e-n)
3 A Remarkable Product of Theta-Functions
36 Modular Equations and Theta-Function 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 Expa
39 Miscellaneous Results in the First Notebook
Location of Entries in the Unorganized Portions of Ramanujan's
First Notebook
References
lIndex
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
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