An Invitation to Q-series From Jacobi's Triple Product Identity to Ramanujan's "most Beautiful Identity"

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.