描述
开 本: 16开纸 张: 胶版纸包 装: 平装-胶订是否套装: 否国际标准书号ISBN: 9787560381312
Ramanujan’s notebooks were compiled approximately in the years 1903-1914， prior to his departure for England. After Ramanujan’s death in 1920， many mathematicians， including G. H. Hardy， strongly urged that Ramanujan’s notebooks be edited and published. In fact， original plans called for the publislung of the notebooks along with Ramanujan’s Collected Papers in 1927， but financial considerations prevented this. In 1929， G. N. Watson and B. M. Wilson began the editing of the notebooks， but the task was never completed. Finally， in 1957 an unedited photostat edition of Ramanujan’s notebooks was published.
This volume is the first of three volumes devoted to the editing of Ramanujan’s notebooks. Many of the results found herein are very well known， but many are new. Some results are rather easy to prove， but others are established only with great difficulty. A glance at the contents indicates a wide diversity of topics examined by Ramanujan. Our goal has been to prove each of Ramanujan’s theorems. However， for results that are lcnown， we generally refer to the literature where proofs may be found.
We hope that this volume and succeeding volumes will further enhance the reputation of Srinivasa Ramanujan， one of the truly great figures in the history of mathematics. In particular， Ramanujan’s notebooks contain new， interesting， and profound theorems that deserve the attention of the mathematical public.
Introduction
CHAPTER 1
Magic Squares
CHAPTER 2
Sums Related to the Harmonic Series or the Inverse Tangent Function
CHAPTER 3
Combinatorial Analysis and Series Inversions
CHAPTER 4
Iterates of the Exponential Function and an Ingenious
Formal Technique
CHAPTER 5
Eulerian Polynomials and Numbers， Bernoulli Numbers， and the Riemann Zeta-Function
CHAPTER 6
Ramanujan’s Theory of Divergent Series
CHAPTER 7
Sums of Powers， Bernoulli Numbers， and the Gamma Function
CHAPTER 8
Analogues of the Gamma Function
CHAPTER 9
Infinite Series Identities， Transformations， and Evaluations
Ramanujan’s Quarterly Reports
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
评论
还没有评论。