| 国外很好数学著作原版系列拉马努金遗失笔记(第1卷) |
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2020-07-02 00:00:00 |
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国外很好数学著作原版系列拉马努金遗失笔记(第1卷) 内容简介
拉马努金数学遗失笔记,包括了S. Ramanujan在1988年由Narosa出版的《Lost Notebook and Other Unpublished Papers》和其他未发表的论文中提出的所有主张。这本书包含了“遗失的笔记”，它是1976年春天由作者在剑桥三一学院图书馆发现的。其中还包含其他部分手稿、碎片和拉马努金1917年-1919年在疗养院写给G.H.哈迪的信件。这是五卷中的卷。
国外很好数学著作原版系列拉马努金遗失笔记(第1卷) 目录
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) 13
1.3 Hybrids of(11.10)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)R(q2)
1.9 Other Representations of Theta Functions Involving R(q)..39
1.10 Explicit Formulas Arising from(1.1.11)….……,44
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-2mVn) and S(e-TVn).66
2.4 Page 210 of Ramanujan's Lost Notebook
2.5 Some Theta-Function Identities
2.6 Ramanujans General Explicit Formulas for the
Rogers-Ramanujan Continued Fraction 79
3 A Fragment on the Rogers-Ramanujan and Cubic
Continued fractions
3.1 Introduction
3.23 The RogersTheory-RamanujofanujaContinuedsCubicFractionContinued Fraction,...86
3.4 Explicit Evaluations of G(a)
4 Rogers-Ramanujan Continued Fraction- Partitions,
Lambert series
4.1 Introduction.....,,,,.,...........
4.2 Connections with Partitions
4.3 Further Identities Involving the Power Series Coefficients of
C(q)and1/C(q)……
4.4 Generalized Lambert Series
4.5 Further g-Series Representations for C(a)
5 Finite Rogers-Ramanujan Continued Fractions......125 5.1 Introduction......... 5.2 Finite Rogers-Ramanujan Continued Fractions......126
53 A generalization of Entry5.2.1..………∵
5.4 Class invariant
5.5 A Finite Generalized Rogers-Ramanujan Continued Fraction 140
6 Other q-continued fractions
6.1 Introduction
6.2The Main Theore 6.3A Second General Continued Fraction 6.4 A Third General Continued Fraction...........1596.5 A Transformation Formula 6.6 Zeros................,165
6.7 Two Entries on Page 200 of Ramanujan's Lost Notebook.. 169
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
Ramanujans Lost Notebook
7.4 An Asymptotic Formula for R(a, q)
8 Ramanujan,s Continued Fraction for(q
8.1 Introduction
8.2 A Proof of Ramanujan's Formula(8.1.2)
3 The Special Case a= w of(8.1.2)8.4 Two Continued Fractions Related to(q; q)oo/(q; oo... 213
8.5 An Asymptotic Expansion
9 The Rogers-Fine Identity
1 Introduction........ 9.2Series Transformations 9.3The Seriesnan(n 1)/2 n=09n(3n 1)/2 9. 4 The Series 9.5 The Seriesn=o gun 2n
10 An Empirical Study of the Rogers-Ramanujan Identities. 241
10.1 Introduction.......,,,,,∴,.241
10.2 The First Argument
10.3 The Second Argument
10.4 The Third Argument
10.5 The Fourth Argument
11 Rogers-Ramanujan-Slater-Type Identities........ 251 11.1 Introduction. 11.2 Identities Associated with Modulus 5.,.................. 252 11.3 Identities Associated with the Moduli 3. 6. and 12.........253 11.4 Identities Associated with the Modulus 7 11.5 False Theta Functions 12 Partial fractions..,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,..261 12.1 Introduction.,,,,,,,,,,,,,,,,,,,,,,,....261 12.2 The Basic Partial Fractions 12.3 Applications of the Partial Fraction Decompositions 12.4 Partial Fractions Plus 12.5 Related Identities ......................................279 12.6 Remarks on the Partial Fraction Method 13.2 Stieltjes-Wigert Polynomial............285 13 Hadamard Products for Two q-Series 13.1 Introduction 13.3 The Hadamard Factorization..............288 13. 4 Some Theta series
13.5 a Formal Power Series..,,,,,,,,,,,,,,,...,291
136 The Zeros of K。(2x)
13.7 Small Zeros of Koo(z)
13.8 A New Polynomial Sequence
13.9 The Zeros of pn(a)
13.10 A Theta Function Expansion
13.11 Ramanujan's Product for poo(a)
14 Integrals of Theta Functions
1 Introduction 309
14.2 Preliminary Results
14.3 The Identities on Page 207
14.4 Integral Representations of the Rogers-Ramanujan Continued fraction
15 Incomplete Elliptic Integrals
15.1 Introduction....................,.327 15.2 Preliminary Result 15.3 Two Simpler Integrals ...............:..................33015.4 Elliptic Integrals of Order 51) 15.5 Elliptic Integrals of Order 5(II) 15.6 Elliptic Integrals of Order 5(III)............34215.7 Elliptic Integrals of Order 15.............................349
15.8 Elliptic Integrals of Order 14
15.9 An Elliptic Integral of Order 35
15.10 Constructions of New Incomplete Elliptic Integral Identities.365
16 Infinite Integrals of q-Products
16.1 Introduction
16.2 Proofs
17 Modular Equations in Ramanujan's Lost Notebook....37317..13IntroductionSummaryof Modular Equations of Six Kind
172Eta- Function Identities.…………………375
4 A Fragment on Page 349
18 Fragments on Lambert Series...............395
18.1 Introduction...................... 395
18.2 Entries from the Two Fragments.............396
Location guide
Provenance....
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.438
附录II刘治国教授访谈
编辑手记
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