During the years 1903-1914， Ramanujan recorded most of his mathematical discoveries without proofs in notebooks. Although many of his results were already in the literature， more were not. Almost a decade after Ramanujan's 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 third offive volumes devoted to the editing of Ramanujan's notebooks. Part I， published in 1985， contains an account of Chapters 1-9 in the second notebook as well as a description of Ramanujan's quarterly reports. Part II， published in 1989， comprises accounts of Chapters 10-15 in Ramanujan's second notebook. In this volume， we examine Chapters 16-21 in the second notebook. For many of the results that are known， we provide references in the literature where proofs may be found. Otherwise， we give complete proofs. Most of the theorems in these six chapters have not previously been proved in print. Parts IV and V will contain accounts of the 100 pages of unorganized material at the end of the second notebook， the tlurty-three pages of unorganized results comprising the third notebook， and those results in the first notebook not recorded by Ramanujan in the second or third notebooks. The second notebook is chiefly a much enlarged and somewhat more organized edition of the first notebook.
鄂公网安备 42010302001612号 