INVITATION TO Q-SERIES, AN: 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.

The aim of this 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.