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Author Chan, Hei-Chi.

Title An invitation to q-series : from Jacobi's triple product identity to Ramanujan's "most beautiful identity" / Hei-Chi Chan
Published Singapore : World Scientific Pub Co., ©2011
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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.
Jacobi identity.
Rogers-Ramanujan identities.
MATHEMATICS -- Infinity.
Jacobi identity
q-series
Rogers-Ramanujan identities
Form Electronic book
LC no. 2011292543
ISBN 9789814343855
9814343854
1283235056
9781283235051