Invitation To Q-series, An: From Jacobi's Triple Product Identity To Ramanujan's &quote;Most Beautiful Identity&quote; e-bog

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 "e;mathematician of the highest class"e;, and (2) what G. H. Hardy called Ramanujan's "e;Most Beautiful Identity"e;. 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.