- 拉马努金遗失笔记(第1卷)(英文)/国外优秀数学著作原版系列
- - 作者：编者:(美)乔治·E.安德鲁斯//布鲁斯·C.伯恩特
  - 出版社：哈尔滨工业大学
  - ISBN：9787560381299
  - 出版日期：2019/06/01
  - 页数：499
- 售价：43.6

内容大纲
印度神奇数学家拉马努金有着深邃的数学直觉和洞察力，这套丛书给出了拉马努金很多漂亮的数学结果，共分为4卷。《拉马努金遗失笔记(第1卷)(英文)/国外优秀数学著作原版系列》为第1卷，主要介绍了级数、积分、特殊函数、部分分式展开等内容。本书适合高年级本科生、研究生，以及数学爱好者参考阅读。
作者介绍
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)
  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
9  The Rogers-Fine Identity
10  An Empirical Study of the Rogers-Ramanujan Identities .
  10.1  Introduction
  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
  11.1  Introduction
  11.2  Identities Associated with Modulus 5
  11.3  Identities Associated with the Moduli 3, 6, and 12
  11.4  Identities Associated with the Modulus 7
  11.5  False Theta Functions
12  Partial Fractions
  12.1  Introduction
  12.2  The Basic Partial Fractions
  12.3  Applications of the Partial Fraction Decompositions
  12.4  Partial Fractions Plus
  12.5  Related Identities
  12.6  Remarks on the Partial Fraction Method
13  Hadamard Products for Two q-Series
  13.1  Introduction
  13.2  Stieltjes-Wigert Polynomials
  13.3  The Hadamard Factorization
  13.4  Some Theta Series
  13.5  A Formal Power Series
  13.6  The Zeros of K~(zx)
  13.7  Small Zeros of K~(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 p~(a)
14  Integrals of Theta Functions
  14.1  Introduction
  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
  15.2  Preliminary Results
  15.3  Two Simpler Integrals
  15.4  Elliptic Integrals of Order 5 (I)
  15.5  Elliptic Integrals of Order 5 (II)
  15.6  Elliptic Integrals of Order 5 (III)
  15.7  Elliptic Integrals of Order 15

  15.8  Elliptic Integrals of Order 14
  15.9  An Elliptic Integral of Order 35
  15.10  Constructions of New Incomplete Elliptic Integral Identities
16  Infinite Integrals of q-Products
  16.1  Introduction
  16.2  Proofs
17  Modular Equations in Ramanujan's Lost Notebook
  17.1  Introduction
  17.2  Eta-Function Identities
  17.3  Summary of Modular Equations of Six Kinds
  17.4  A Fragment on Page 349
18  Fragments on Lambert Series
  18.1  Introduction
  18.2  Entries from the Two Fragments
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
附录II  刘治国教授访谈
编辑手记

内容大纲

作者介绍

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