Ramanujan’s Notebooks

1. Front Matter

   Pages i-xiii

   PDF

2. Introduction

   • Bruce C. Berndt

   Pages 1-7

3. Continued Fractions

   • Bruce C. Berndt

   Pages 9-88

4. Ramanujan’s Theories of Elliptic Functions to Alternative Bases

   • Bruce C. Berndt

   Pages 89-181

5. Class Invariants and Singular Moduli

   • Bruce C. Berndt

   Pages 183-322

6. Values of Theta—Functions

   • Bruce C. Berndt

   Pages 323-351

7. Modular Equations and Theta—Function Identities in Notebook 1

   • Bruce C. Berndt

   Pages 353-407

8. Infinite Series

   • Bruce C. Berndt

   Pages 409-502

9. Approximations and Asymptotic Expansions

   • Bruce C. Berndt

   Pages 503-564

10. Miscellaneous Results in the First Notebook

    • Bruce C. Berndt

    Pages 565-578

11. Back Matter

    Pages 579-624

    PDF

During the years 1903-1914, Ramanujan recorded most of his mathematical dis­ coveries without proofs in notebooks. Although many of his results had already been published by others, most had not. Almost a decade after Ramanujan's death in 1920, G. N. Watson and B. M. Wilson began to edit Ramanujan's notebooks, but, despite devoting over ten years to this project, they never completed their task. An unedited photostat edition of the notebooks was published by the Tata Institute of Fundamental Research in Bombay in 1957. This book is the fifth and final volume devoted to the editing of Ramanujan's notebooks. Parts I-III, published, respectively, in 1985, 1989, and 1991, contain accounts of Chapters 1-21 in the second notebook, a revised enlarged edition of the first. Part IV, published in 1994, contains results from the 100 unorganized pages in the second notebook and the 33 unorganized pages comprising the third notebook. Also examined in Part IV are the 16 organized chapters in the first notebook, which contain very little that is not found in the second notebook. In this fifth volume, we examine the remaining contents from the 133 unorganized pages in the second and third notebooks, and the claims in the 198 unorganized pages of the first notebook that cannot be found in the succeeding notebooks.

• Finite
• Identity
• Invariant
• Ramanujan
• average
• continued fraction
• equation
• function
• theorem

• Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, USA

  Bruce C. Berndt

Policies and ethics