An Invitation to Q-Series: From Jacobi's Triple Product Identity to Ramanujan's "Most Beautiful Identity" (repost)
An Invitation to Q-Series: From Jacobi's Triple Product Identity to Ramanujan's "Most Beautiful Identity" by Hei-Chi Chan
English | 2011 | ISBN: 9814343846 | 236 pages | PDF | 1,2 MB
English | 2011 | ISBN: 9814343846 | 236 pages | PDF | 1,2 MB
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: 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 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.