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| 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 |
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