拉马努金笔记(第一卷)

拉马努金笔记(第一卷)
作 者: 布鲁斯 伯恩特
出版社: 哈尔滨工业大学出版社
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作者简介

暂缺《拉马努金笔记(第一卷)》作者简介

内容简介

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, fo...

图书目录

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