Ramanujan’s Notebooks

Part II

  • Bruce C. Berndt

Table of contents

  1. Front Matter
    Pages i-xi
  2. Bruce C. Berndt
    Pages 1-6
  3. Bruce C. Berndt
    Pages 7-47
  4. Bruce C. Berndt
    Pages 48-102
  5. Bruce C. Berndt
    Pages 103-184
  6. Bruce C. Berndt
    Pages 185-239
  7. Bruce C. Berndt
    Pages 240-299
  8. Bruce C. Berndt
    Pages 300-338
  9. Back Matter
    Pages 339-359

About this book

Introduction

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. 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.

Keywords

Finite Mathematica Modular form integral proof

Authors and affiliations

  • Bruce C. Berndt
    • 1
  1. 1.Department of MathematicsUniversity of IllinoisUrbanaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-4530-8
  • Copyright Information Springer-Verlag New York 1989
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-8865-7
  • Online ISBN 978-1-4612-4530-8
  • About this book