Ramanujans Notebooks : Part II

During the years 1903-1914, Ramanujan recorded many of his mathematical discoveries in notebooks without providing proofs. Although many of his results were already in the literature, more were not. Almost a decade after Ramanujans death in 1920, G.N. Watson and B.M. Wilson began to edit his notebooks but never completed the task. A photostat edition, with no editing, was published by the Tata Institute of Fundamental Research in Bombay in 1957. This book is the second of four volumes devoted to the editing of <b>Ramanujans</b> <b>Notebooks</b>. Part I, published in 1985, contains an account of Chapters 1-9 in the second notebook as well as a description of Ramanujans quarterly reports. In this volume, we examine Chapters 10-15 in Ramanujans second notebook. If a result is known, we provide references in the literature where proofs may be found; if a result is not known, we attempt to prove it. Not only are the results fascinating, but, for the most part, Ramanujans methods remaina mystery. Much work still needs to be done. We hope readers will strive to discover Ramanujans thoughts and further develop his beautiful ideas.