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Ramanujan’s Notebooks

Part IV

  • Book
  • © 1994

Overview

Authors:
  1. Bruce C. Berndt

    1. Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, USA

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xii
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  2. Introduction

    • Bruce C. Berndt
    Pages 1-6

  3. Elementary Results

    • Bruce C. Berndt
    Pages 7-50

  4. Number Theory

    • Bruce C. Berndt
    Pages 51-110

  5. Ramanujan’s Theory of Prime Numbers

    • Bruce C. Berndt
    Pages 111-137

  6. Theta-Functions and Modular Equations

    • Bruce C. Berndt
    Pages 138-244

  7. Inversion Formulas for the Lemniscate and Allied Functions

    • Bruce C. Berndt
    Pages 245-260

  8. q-Series

    • Bruce C. Berndt
    Pages 261-286

  9. Integrals

    • Bruce C. Berndt
    Pages 287-333

  10. Special Functions

    • Bruce C. Berndt
    Pages 334-354

  11. Partial Fraction Expansions

    • Bruce C. Berndt
    Pages 355-381

  12. Elementary and Miscellaneous Analysis

    • Bruce C. Berndt
    Pages 382-400

  13. Back Matter

    Pages 401-451
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Keywords

About this book

During the years 1903-1914, Ramanujan worked in almost complete isolation in India. During this time, he recorded most of his mathematical discoveries without proofs in notebooks. Although many of his results were already found in the literature, most were not. Almost a decade after Ramanujan's death in 1920, G.N. Watson and B.M. Wilson began to edit Ramanujan's notebooks, but they 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 fourth of five volumes devoted to the editing of Ramanujan's notebooks. Parts I, II, and III, published in 1985, 1989, and 1991, contain accounts of Chapters 1-21 in Ramanujan's second notebook as well as a description of his quarterly reports. This is the first of two volumes devoted to proving the results found in the unorganized portions of the second notebook and in the third notebook. The author also proves those results in the first notebook that are not found in the second or third notebooks. For those results that are known, references in the literature are provided. Otherwise, complete proofs are given. Over 1/2 of the results in the notebooks are new. Many of them are so startling and different that there are no results akin to them in the literature.

Authors and Affiliations

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

    Bruce C. Berndt

Bibliographic Information

  • Book Title: Ramanujan’s Notebooks

  • Book Subtitle: Part IV

  • Authors: Bruce C. Berndt

  • DOI: https://doi.org/10.1007/978-1-4612-0879-2

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media, LLC, part of Springer Nature 1994

  • Hardcover ISBN: 978-0-387-94109-7Published: 17 December 1993

  • Softcover ISBN: 978-1-4612-6932-8Published: 30 September 2012

  • eBook ISBN: 978-1-4612-0879-2Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: XII, 451

  • Topics: Mathematics, general

  • Industry Sectors: Engineering, IT & Software

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