拉馬努金遺失筆記（第一卷）

《拉馬努金遺失筆記（第一卷）》哈爾濱工業大學出版社2019年6月出版的書籍，作者是(美)喬治·E.安德魯斯。

基本介紹

• 中文名：拉馬努金遺失筆記（第一卷）
• 作者：(美)喬治·E.安德魯斯
• 出版時間：2019年6月
• 出版社：哈爾濱工業大學出版社
• ISBN：9787560381299

內容簡介

Readers will learn in the introduction to this volume that mathematicians owe a huge debt to R.A. Rankin and J.M. Whittaker for their efforts in preserving Ramanujan's "Lost Notebook." If it were not for them， Ramanujan's lost notebook likely would have been permanently lost. Rankin was born in Garlieston， Scotland， in October 1915 and died in Glasgow in January 2001. For several years he was professor of Mathematics at the University of Glasgow. An account of his life and work has been given by B.C. Berndt， W. Kohnen， and K. Ono in [79]. Whittaker was born in March 1905 in Cambridge and died in Sheffield in January 1984. At his retirement， he was vicechancellor of Sheffield University. A description of Whittaker's life and work has been written by W.K， Hayman.

圖書目錄

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 and S

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 Rogers-Ramanujan Continued Fraction - Partitions,Lambert Series

4.1 Introduction

4.2 Connections with Partitions

4.3 Fhrther 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

5.4 Class Invariants

5.5 A Finite Generalized Rogers-Ramanujan Continued Fraction

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; q3)/(q; q3)

8.1 Introduction

8.2 A Proof of Ramanujan's Formula (8.1 :2)

8.3 The Special Case a = w of (8.1.2 )

8.4 Two Continued Fractions Related to (q2; q3)/(q; q3)

8.5 An Asymptotic Expansion