Ramanujan's lost notebook / George E. Andrews, Bruce C. Berndt.
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 public...
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| Main Authors: | , |
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| Format: | Ebook |
| Language: | English |
| Published: |
New York ; London :
Springer,
2005-2018.
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| Subjects: | |
| Online Access: | Table of contents Publisher description Springer eBooks: Vol. 1 Springer eBooks: Vol. 2 Springer eBooks: Vol. 3 Springer eBooks: Vol. 4 |
| Summary: | 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 In addition to the lost notebook, this publication contains copies of unpublished manuscripts in the Oxford library, in particular, his famous unpublished manuscript on the partition and tau-functions; fragments of both published and unpublished papers; miscellaneous sheets; and Ramanujan's letters to G.H. Hardy, written from nursing homes during Ramanujan's final two years in England.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. |
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| Physical Description: | 1 online resource (5 volumes) : portraits |
| Bibliography: | Includes bibliographical references and index. |
| ISBN: | 038725529X 038728124X 0387777660 1280308346 1461438101 1461440815 331977834X 9780387255293 9780387281247 9780387777665 9781280308345 9781461438106 9781461440819 9783319778341 |