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Ramanujan's Lost Notebook Part III

"In the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge, to examine the papers of the late G.N. Watson. Among these papers, Andrews discovered a sheaf of 138 pages in the handwriting of Srinivasa Ramanujan. This manuscript was soon designated, 'Ramanujan's lost notebook'. Its discovery has frequently been deemed the mathematical equivalent of finding Beethoven's tenth symphony. The 'lost notebook' contains considerable material on mock theta functions and so undoubtedly emanates from the last year of Ramanujan's life. It should be emphasized that the material on mock theta functions is perhaps Ramanujan's deepest work. Mathematicians are probably several decades away from a complete understanding of those functions. More than half of the material in the book is on q-series, including mock theta functions; the remaining part deals with theta function identities, modular equations, incomplete elliptic integrals of the first kind and other integrals of theta functions, Eisenstein series, particular values of theta functions, the Rogers-Ramanujan continued fraction, other q-continued fractions, other integrals, and parts of Hecke's theory of modular forms."--Publisher's description.

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  • ""In the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge, to examine the papers of the late G.N. Watson. Among these papers, Andrews discovered a sheaf of 138 pages in the handwriting of Srinivasa Ramanujan. This manuscript was soon designated, 'Ramanujan's lost notebook'. Its discovery has frequently been deemed the mathematical equivalent of finding Beethoven's tenth symphony. The 'lost notebook' contains considerable material on mock theta functions and so undoubtedly emanates from the last year of Ramanujan's life. It should be emphasized that the material on mock theta functions is perhaps Ramanujan's deepest work. Mathematicians are probably several decades away from a complete understanding of those functions. More than half of the material in the book is on q-series, including mock theta functions; the remaining part deals with theta function identities, modular equations, incomplete elliptic integrals of the first kind and other integrals of theta functions, Eisenstein series, particular values of theta functions, the Rogers-Ramanujan continued fraction, other q-continued fractions, other integrals, and parts of Hecke's theory of modular forms."--Publisher's description."@en
  • "Part of the four volumes on Ramanujan's lost notebook, this book addresses topics such as q-series, Eisenstein series, and theta functions."@en
  • "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."
  • "In the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge to examine the papers of the late G.N. Watson.  Among these papers, Andrews discovered a sheaf of 138 pages in the handwriting of Srinivasa Ramanujan. This manuscript was soon designated, 'Ramanujan's lost notebook.' Its discovery has frequently been deemed the mathematical equivalent of finding Beethoven's tenth symphony. This volume is the third of five volumes that the authors plan to write on Ramanujanâs lost notebook and other manuscripts and fragments found in The Lost Notebook and Other Unpublished Papers, published by Narosa in 1988. The ordinary partition function p(n) is the focus of this third volume. In particular, ranks, cranks, and congruences for p(n) are in the spotlight. Other topics include the Ramanujan tau-function, the Rogersâ"Ramanujan functions, highly composite numbers, and sums of powers of theta functions. Review from the second volume:'Fans of Ramanujan's mathematics are sure to be delighted by this book. While some of the content is taken directly from published papers, most chapters contain new material and some previously published proofs have been improved. Many entries are just begging for further study and will undoubtedly be inspiring research for decades to come. The next installment in this series is eagerly awaited.' - MathSciNetReview from the first volume:'Andrews and Berndt are to be congratulated on the job they are doing. This is the first step ... on the way to an understanding of the work of the genius Ramanujan. It should act as an inspiration to future generations of mathematicians to tackle a job that will never be complete.' - Gazette of the Australian Mathematical Society."@en
  • "This volume is the second of approximately four volumes that the authors plan to write on Ramanujan's lost notebook, which is broadly interpreted to include all material published in The Lost Notebook and Other Unpublished Papers in 1988. The primary topics addressed in the authors' second volume on the lost notebook are q-series, Eisenstein series, and theta functions. Most of the entries on q-series are located in the heart of the original lost notebook, while the entries on Eisenstein series are either scattered in the lost notebook or are found in letters that Ramanujan wrote to G.H. Hardy from nursing homes. About Ramanujan's Lost Notebook, Volume I: "Andrews and Berndt are to be congratulated on the job they are doing. This is the first step...on the way to an understanding of the work of the genius Ramanujan. It should act as an inspiration to future generations of mathematicians to tackle a job that will never be complete." - Gazette of the Australian Mathematical Society "...the results are organized topically with cross-references to the identities as they appear in the original Ramanujan manuscript. Particularly helpful are the extensive references, indicating where in the literature these results have been proven or independently discovered as well as where and how they have been used." - Bulletin of the American Mathematical Society "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 chaotically written mathematical thoughts of Ramanujan during the last year of his life. Some 85 years after his death, beautiful "new" and useful results of Ramanujan continue to be brought to light." - Mathematical Reviews"@en
  • "In the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge, to examine the papers of the late G.N. Watson. Among these papers, Andrews discovered a sheaf of 138 pages in the handwriting of Srinivasa Ramanujan. This manuscript was soon designated, "Ramanujan's lost notebook." Its discovery has frequently been deemed the mathematical equivalent of finding Beethoven's tenth symphony. The "lost notebook" contains considerable material on mock theta functions and so undoubtedly emanates from the last year of Ramanujan's life. It should be emphasized that the material on mock theta functions is perhaps Ramanujan's deepest work. Mathematicians are probably several decades away from a complete understanding of those functions.; More than half of the material in the book is on q-series, including mock theta functions; the remaining part deals with theta function identities, modular equations, incomplete elliptic integrals of the first kind and other integrals of theta functions, Eisenstein series, particular values of theta functions, the Rogers-Ramanujan continued fraction, other q-continued fractions, other integrals, and parts of Hecke's theory of modular forms."@en

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  • "Electronic books"
  • "Electronic books"@en
  • "Biography"
  • "Biography"@en
  • "Llibres electrònics"

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  • "Ramanujan's lost notebook. 1"
  • "Ramanujan's lost notebook. Part 1"
  • "Ramanujan's lost notebook / Part"
  • "Ramanujan's Lost Notebook Part III"@en
  • "Ramanujan's lost notebook / 1"
  • "Ramanujan's lost notebook"
  • "Ramanujan's lost notebook"@en
  • "Ramanujan's Lost Notebook Part I"
  • "Ramanujan's Lost Notebook/ 2, Part II"
  • "Ramanujan's Lost notebook"
  • "Ramanujan's lost notebook Part II"
  • "Ramanujan's lost notebook : part i"@en
  • "Ramanujan's lost notebook: Part 2"
  • "Ramanujan's Lost Notebook Part II"
  • "Ramanujan's lost notebook Pt. I"@en
  • "Ramanujan's Lost Notebook : Part III"
  • "Ramanujan's Lost Notebook/ 3, Part III"
  • "Ramanujan's Lost Notebook : Part I"
  • "Ramanujan's Lost Notebook"
  • "Ramanujan's Lost Notebook"@en
  • "Ramanujan's Lost Notebook : Part II"
  • "Ramanujan's lost notebook. Part I"@en
  • "Ramanujan's lost notebook. Part I"

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