拉马努金笔记（第二卷）

During the years 1903-1914， Ramanujan recorded many of his mathematical discoveries in notebooks without providing proofs. Although many of his results were already in the literature， more were not. Almost a decade after Ramanujan’s death in 1920， G. N. Watson and B. M. Wilson began to edit his notebooks， but never completed the task. A photostat edition， with no editing， was published by the Tata Institute of Fundamental Research in Bombay in 1957.
　　This book is the second of four volumes devoted to the editing of Ramanujan’s notebooks. Part I， published in 1985， contains an account of Chapters 1-9 in the second notebook as well as a description of Ramanujan’s quarterly reports. In this volume， we examine Chapters 10-15 in Ramanujan’s second notebook. If a result is known， we provide references in the literature where proofs may be found； if a result is not known， we attempt to prove it. Except in a few instances when Ramanujan’s intent is not clear， we have been able to establish each result in these six chapters.
　　Chapters 10-15 are among the most interesting chapters in the notebooks. Not only are the results fascinating， but for the most part， Ramanujan’s methods remain a mystery. Much work still needs to be done. We hope readers will strive to discover Ramanujan’s thoughts and further develop his beautiful ideas.

Preface
Introduction

CHAPTER 10
Hypergcometric Series， I

CHAPTER 11
Hypergeometric Series， II

CHAPTER 12
Continued Fractions

CHAPTER 13
Integrals and Asymptotic Expansions

CHAPTER 14
Infinite Series

CHAPTER 15
Asymptotic Expansions and Modular Forms

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