Ramanujan's Lost Notebook: Part I / Edition 1

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Overview

In the library at Trinity College, Cambridge in 1976, George Andrews of Pennsylvania State University discovered a sheaf of pages in the handwriting of Srinivasa Ramanujan. Soon designated as "Ramanujan’s Lost Notebook," it contains considerable material on mock theta functions and undoubtedly dates from the last year of Ramanujan’s life. In this book, the notebook is presented with additional material and expert commentary.

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Editorial Reviews

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"The ‘lost notebook’ was in fact a 138-page manuscript found in materials from the estate of G.N. Watson. The manuscript, written in ‘Ramanujan’s distinctive handwriting’, contained over 600 formulas. The authors have taken these results, provided proofs, placed them in the context of contemporary mathematics, and organized them accordingly … This book is for the true fans of ... Ramanujan (Ramanuphiles?). If you enjoyed the original Ramanujan’s Notebook series, then it’s hard to pass this up." (Donald L. Vestal, MathDL-online, October 2006)

"The present work is the first of an estimated four volumes devoted to all of the claims made by Ramanujan … . The mathematics community owes a huge debt of gratitude to Andrews and Berndt for undertaking the monumental task of producing a coherent presentation along with complete proofs of the … mathematical thoughts of Ramanujan during the last year of his life. … Practitioners of q-series and other mathematicians interested in the work of Ramanujan, will delight in studying this book … ." (Andrew V. Sills, Mathematical Reviews, Issue 2005 m)

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Product Details

  • ISBN-13: 9780387255293
  • Publisher: Springer New York
  • Publication date: 5/6/2005
  • Edition description: 2005
  • Edition number: 1
  • Pages: 438
  • Product dimensions: 9.21 (w) x 6.14 (h) x 1.00 (d)

Table of Contents

Preface.- Introduction.- The Rogers–Ramanujan Continued Fraction and Its Modular Properties.- Explicit Evaluations of the Rogers–Ramanujan Continued Fraction.- A Fragment on the Rogers–Ramanujan and Cubic Continued Fractions.- The Rogers–Ramanujan Continued Fraction and Its Connections with Partitions and Lambert Series.- Finite Rogers–Ramanujan Continued Fractions.- Other q-continued Fractions.- Asymptotic Formulas for Continued Fractions.- Ramanujan’s Continued Fraction for (q2; q3)8/(q; q3)8.- The Rogers–Fine Identity.- An Empirical Study of the Rogers–Ramanujan Identities.- Rogers–Ramanujan–Slater Type Identities.- Partial Fractions.- Hadamard Products for Two q-Series.- Integrals of Theta-functions.- Incomplete Elliptic Integrals.- Infinite Integrals of q-Products.- Modular Equations in Ramanujan’s Lost Notebook.- Fragments on Lambert Series.- Location Guide.- Provenance.- References.- Index.

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