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An Invitation to Q-Series: From Jacobi's Triple Product Identity to Ramanujan's Most Beautiful Identity

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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.

Author(s): Hei-chi Chan
Edition: 1
Publisher: World Scientific
Year: 2011

Language: English
Pages: 237
Tags: Математика;Теория чисел;