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Ramanujan’s Notebooks

Part I

  • Book
  • © 1985

Overview

Authors:
  1. Bruce C. Berndt

    1. Department of Mathematics, University of Illinois, Urbana, USA

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About this book

Srinivasa Ramanujan is, arguably, the greatest mathematician that India has produced. His story is quite unusual: although he had no formal education inmathematics, he taught himself, and managed to produce many important new results. With the support of the English number theorist G. H. Hardy, Ramanujan received a scholarship to go to England and study mathematics. He died very young, at the age of 32, leaving behind three notebooks containing almost 3000 theorems, virtually all without proof. G. H. Hardy and others strongly urged that notebooks be edited and published, and the result is this series of books. This volume dealswith Chapters 1-9 of Book II; each theorem is either proved, or a reference to a proof is given.

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Table of contents (10 chapters)

  1. Front Matter

    Pages I-X
    Download chapter PDF

  2. Introduction

    • Bruce C. Berndt
    Pages 1-15

  3. Magic Squares

    • Bruce C. Berndt
    Pages 16-24

  4. Sums Related to the Harmonic Series or the Inverse Tangent Function

    • Bruce C. Berndt
    Pages 25-43

  5. Combinatorial Analysis and Series Inversions

    • Bruce C. Berndt
    Pages 44-84

  6. Iterates of the Exponential Function and an Ingenious Formal Technique

    • Bruce C. Berndt
    Pages 85-108

  7. Eulerian Polynomials and Numbers, Bernoulli Numbers, and the Riemann Zeta-Function

    • Bruce C. Berndt
    Pages 109-132

  8. Ramanujan’s Theory of Divergent Series

    • Bruce C. Berndt
    Pages 133-149

  9. Sums of Powers, Bernoulli Numbers, and the Gamma Function

    • Bruce C. Berndt
    Pages 150-180

  10. Analogues of the Gamma Function

    • Bruce C. Berndt
    Pages 181-231

  11. Infinite Series Identities, Transformations, and Evaluations

    • Bruce C. Berndt
    Pages 232-294

  12. Back Matter

    Pages 295-357
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Authors and Affiliations

  • Department of Mathematics, University of Illinois, Urbana, USA

    Bruce C. Berndt

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Bibliographic Information

  • Book Title: Ramanujan’s Notebooks

  • Book Subtitle: Part I

  • Authors: Bruce C. Berndt

  • DOI: https://doi.org/10.1007/978-1-4612-1088-7

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1985

  • Hardcover ISBN: 978-0-387-96110-1Published: 12 March 1985

  • Softcover ISBN: 978-1-4612-7007-2Published: 02 October 2012

  • eBook ISBN: 978-1-4612-1088-7Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: X, 357

  • Topics: Number Theory

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