Ramanujan’s lost notebook : part i拉玛努贾丢失的笔记本 第1部分

Preface
Introduction
1 The Rogers-Ramanujan Continued Fraction and Its Modular Properties
　1.1　Introduction
　1.2　Two-Variable Generalizations of (1.1.10) and (1.1.11)
　1.3 Hybrids of (1.1.10) and (1.1.11)
　1.4 Factorizations of (1.1.10) and (1.1.11)
　1.5　Modular Equations
　1.6　Theta-Function Identities of Degree 5
　1.7　Refinements of the Previous Identities
　1.8 Identities Involving the Parameter k = R(q)R2(q2)
　1.9　Other Representations of Theta Functions Involving R(q)
　1.10 Explicit Formulas Arising from (1.1.11)
2 Explicit Evaluations of the Rogers-Ramanujan Continued Fraction
　2.1　Introduction
　2.2　Explicit Evaluations Using Eta-Function Identities
　2.3　General Formulas for Evaluating R(e-2~v~) and S(e-~v~)
　2.4　Page 210 of Ramanujan's Lost Notebook
　2.5　Some Theta-Function Identities
　2.6　Ramanujan's General Explicit Formulas for the Rogers-Ramanujan Continued Fraction
3 A Fragment on the Rogers-Ramanujan and Cubic Continued Fractions
　3.1　Introduction
　3.2　The Rogers-Ramanujan Continued Fraction
　3.3　The Theory of Ramanujan's Cubic Continued Fraction
　3.4　Explicit Evaluations of G(q)
4 The Rogers-Ramanujan Continued Fraction and Its Partitions and Lambert Series
　4.1　Introduction
　4.2　Connections with Partitions
　4.3　Further Identities Involving the Power Series Coefficients of C(q) and 1/C(q)
　4.4　Generalized Lambert Series
　4.5　Further q-Series Representations for C(q)
5 Finite Rogers-Ramanujan Continued Fractions
　5.1　Introduction
　5.2　Finite Rogers Ramanujan Continued Fractions
　5.3　A generalization of Entry 5.2.1
　5.4　Class Invariants
　5.5　A Finite Generalized Rogers-Ramanujan Continued Fraction 14(
6 Other q-continued Fractions
　6.1　Introduction
　6.2　The Main Theorem
　6.3　A Second General Continued Fraction
　6.4　A Third General Continued Fraction
　6.5　A Transformation Formula
　6.6　Zeros
　6.7　Two Entries on Page 200 of Ramanujan's Lost Notebook
　6.8　An Elementary Continued Fraction
7 Asymptotic Formulas for Continued Fractions
　7.1　Introduction
　7.2　The Main Theorem
　7.3　Two Asymptotic Formulas Found on Page 45 of Ramanujan's Lost Notebook
　7.4　An Asymptotic Formula for R(a, q)
8 Ramanujan's Continued Fraction for (q2; qa)ov/(q; q3)c~
　8.1　Introduction
　8.2　A Proof of Ramanujan's Formula (8.1.2)
　8.3　The Special Case a = a~ of (8.1.2)
　8.4 Two Continued Fractions Related to (q2; q3)~/(q; q3)~
　8.5　An Asymptotic Expansion
9　The Rogers-Fine Identity
10 An Empirical Study of the Rogers-Ramanujan Identities
11 Rogers-Ramanujan-Slater-Type Identities
12 Partial Fractions
13 Hadamard Products for Two q-Series
14 Integrals of Theta Functions
15 Incomplete Ellitic Integrals
16 Intinite Integrals of q-Products
17 Modular Equations in Rammanujan's Lost Notebook
18 Fragments on Lambert Series
LOcation Guide
Provenance
References
Index