Description |
1 online resource (ix, 226 pages) : illustrations |
Contents |
Introduction -- Part I: Jacobi's triple product identity ; First proof (via functional equation) -- Second proof (via Gaussian polynomials and the q-binomial theorem) -- Some applications -- The Boson-Fermion correspondence -- Macdonald's identities -- Part II: The Rogers-Ramanujan identitites ; First proof (via functional equation) -- Second proof (involving Gaussian polynomials and difference equations) -- Third proof (via Bailey's lemma) -- Excursus : mock theta functions -- Part III: The Rogers-Ramanujan continued fraction ; A list of theorems to be proven -- The evaluation of the Rogers-Ramanujan continued fraction -- A "difficult and deep" identity -- A remarkable identity from the Lost Notebook and cranks -- A differential equation for the Rogers-Ramanujan continued fraction -- Part IV: From the "most beautiful identity" to Ramanujan's congruences ; Proofs of the "most beautiful identity" -- Ramanujan's congruences I : analytical methods -- Ramanujan's congruences II : an introduction to t -cores -- Ramanujan's congruences III : more congruences -- Excursus : modular forms and more congruences for the partition function |
Summary |
The aim of these lecture notes is to provide a self-contained exposition of several fascinating formulas discovered by Srinivasa Ramanujan. Two central results in these notes are: (1) the evaluation of the Rogers-Ramanujan continued fraction -- a result that convinced G H Hardy that Ramanujan was a "mathematician of the highest class", and (2) what G.H. Hardy called Ramanujan's "Most Beautiful Identity". This book covers a range of related results, such as several proofs of the famous Rogers-Ramanujan identities and a detailed account of Ramanujan's congruences. It also covers a range of techniques in q-series |
Bibliography |
Includes appendices, bibliographical references (pages 213-223), and index |
Notes |
Print version record |
Subject |
q-series.
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Jacobi identity.
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Rogers-Ramanujan identities.
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MATHEMATICS -- Infinity.
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Jacobi identity
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q-series
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Rogers-Ramanujan identities
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Form |
Electronic book
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LC no. |
2011292543 |
ISBN |
9789814343855 |
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9814343854 |
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1283235056 |
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9781283235051 |
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