An invitation to q-series : from Jacobi's triple product identity to Ramanujan's "most beautiful identity" /

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Bibliographic Details
Author / Creator:	Chan, Hei-Chi.
Imprint:	Singapore : World Scientific Pub Co., ©2011.
Description:	1 online resource (ix, 226 pages) : illustrations
Language:	English
Subject:	q-series. Jacobi identity. Rogers-Ramanujan identities. Jacobi identity. q-series. Rogers-Ramanujan identities. Electronic books.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11279816

Hidden Bibliographic Details
ISBN:	9789814343855 9814343854 1283235056 9781283235051 9789814343848 9814343846
Notes:	Includes appendices, bibliographical references (pages 213-223), and index. Print version record.
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.
Other form:	Print version: Chan, Hei-Chi. Invitation to q-series. Singapore : World Scientific Pub Co., ©2011 9789814343848

Table of 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.

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