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Ramanujan’s Lost Notebook

Part I

  • George E. Andrews
  • Bruce Berndt
Book

Table of contents

  1. Front Matter
    Pages i-xiv
  2. George E. Andrews, Bruce Berndt
    Pages 1-8
  3. George E. Andrews, Bruce Berndt
    Pages 9-55
  4. George E. Andrews, Bruce Berndt
    Pages 57-84
  5. George E. Andrews, Bruce Berndt
    Pages 85-105
  6. George E. Andrews, Bruce Berndt
    Pages 125-142
  7. George E. Andrews, Bruce Berndt
    Pages 143-177
  8. George E. Andrews, Bruce Berndt
    Pages 179-195
  9. George E. Andrews, Bruce Berndt
    Pages 197-222
  10. George E. Andrews, Bruce Berndt
    Pages 223-239
  11. George E. Andrews, Bruce Berndt
    Pages 241-249
  12. George E. Andrews, Bruce Berndt
    Pages 251-259
  13. George E. Andrews, Bruce Berndt
    Pages 261-284
  14. George E. Andrews, Bruce Berndt
    Pages 285-308
  15. George E. Andrews, Bruce Berndt
    Pages 309-326
  16. George E. Andrews, Bruce Berndt
    Pages 327-366
  17. George E. Andrews, Bruce Berndt
    Pages 367-371
  18. George E. Andrews, Bruce Berndt
    Pages 373-393
  19. George E. Andrews, Bruce Berndt
    Pages 395-408
  20. Back Matter
    Pages 409-437

About this book

Introduction

This volume is the first of approximately four volumes devoted to providing statements, proofs, and discussions of all the claims made by Srinivasa Ramanujan in his lost notebook and all his other manuscripts and letters published with the lost notebook. In addition to the lost notebook, this publication contains copies of unpublished manuscripts in the Oxford library, in particular, his famous unpublished manuscript on the partition and tau-functions; fragments of both published and unpublished papers; miscellaneous sheets; and Ramanujan's letters to G. H. Hardy, written from nursing homes during Ramanujan's final two years in England. This volume contains accounts of 442 entries (counting multiplicities) made by Ramanujan in the aforementioned publication. The present authors have organized these claims into eighteen chapters, containing anywhere from two entries in Chapter 13 to sixty-one entries in Chapter 17.

Most of the results contained in Ramanujan's Lost Notebook fall under the purview of q-series. These include mock theta functions, theta functions, partial theta function expansions, false theta functions, identities connected with the Rogers-Fine identity, several results in the theory of partitions, Eisenstein series, modular equations, the Rogers-Ramanujan continued fraction, other q-continued fractions, asymptotic expansions of q-series and q-continued fractions, integrals of theta functions, integrals of q-products, and incomplete elliptic integrals. Other continued fractions, other integrals, infinite series identities, Dirichlet series, approximations, arithmetic functions, numerical calculations, diophantine equations, and elementary mathematics are some of the further topics examined by Ramanujan in his lost notebook.

Keywords

Finite Identity Modular form equation function

Authors and affiliations

  • George E. Andrews
    • 1
  • Bruce Berndt
    • 2
  1. 1.Department of Mathematics, Eberly College of SciencePennsylvania State UniversityState CollegeUSA
  2. 2.Department of MathematicsUniversity of IllinoisUrbana-Champaign UrbanaUSA

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