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| 100 |
1 |
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|a Chan, Hei-Chi.
|0 http://id.loc.gov/authorities/names/no2011134072
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| 245 |
1 |
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|a An invitation to q-series :
|b from Jacobi's triple product identity to Ramanujan's "most beautiful identity" /
|c Hei-Chi Chan.
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| 260 |
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|a Singapore :
|b World Scientific Pub Co.,
|c ©2011.
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| 300 |
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|a 1 online resource (ix, 226 pages) :
|b illustrations
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| 336 |
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|a text
|b txt
|2 rdacontent
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|a computer
|b c
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|a Includes appendices, bibliographical references (pages 213-223), and index.
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|a 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.
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| 520 |
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|a 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.
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| 588 |
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|a Print version record.
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| 650 |
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|a q-series.
|0 http://id.loc.gov/authorities/subjects/sh86003971
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| 650 |
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|a Jacobi identity.
|0 http://id.loc.gov/authorities/subjects/sh93005729
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| 650 |
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|a Rogers-Ramanujan identities.
|0 http://id.loc.gov/authorities/subjects/sh2010011513
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| 650 |
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7 |
|a MATHEMATICS
|x Infinity.
|2 bisacsh
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| 650 |
|
7 |
|a Jacobi identity.
|2 fast
|0 (OCoLC)fst00981026
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| 650 |
|
7 |
|a q-series.
|2 fast
|0 (OCoLC)fst01185036
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| 650 |
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7 |
|a Rogers-Ramanujan identities.
|2 fast
|0 (OCoLC)fst01763050
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| 655 |
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|a Electronic books.
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| 655 |
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4 |
|a Electronic books.
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| 776 |
0 |
8 |
|i Print version:
|a Chan, Hei-Chi.
|t Invitation to q-series.
|d Singapore : World Scientific Pub Co., ©2011
|z 9789814343848
|w (DLC) 2011292543
|w (OCoLC)707965406
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|t Library of Congress classification
|a QA295 .C48 2011eb
|l Online
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|u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=e000xna&AN=389638
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