Ramanujan's Notebooks, Vol. 2 Book

During the years 1903-1914, Ramanujan worked in almost complete isolation in India. During this time, he recorded most of his mathematical discoveries without proofs in notebooks. Although many of his results were already found in the literature, most were not. Almost a decade after Ramanujan's death in 1920, G.N. Watson and B.M. Wilson began to edit Ramanujan's notebooks, but they 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 fourth of five volumes devoted to the editing of Ramanujan's notebooks. Parts I, II, and III, published in 1985, 1989, and 1991, contain accounts of Chapters 1-21 in Ramanujan's second notebook as well as a description of his quarterly reports. This is the first of two volumes devoted to proving the results found in the unorganized portions of the second notebook and in the third notebook. The author also proves those results in the first notebook that are not found in the second or third notebooks. For those results that are known, references in the literature are provided. Otherwise, complete proofs are given. Over 1/2 of the results in the notebooks are new. Many of them are so startling and different that there are no results akin to them in the literature.

Booknews

"Ramanujan studies" have recently--and happily--become something of an industry; several mathematicians are presently devoting their professional energy to the explication of inspired insight and unearthly beauty long buried in Ramanujan's notebooks (themselves recently published, in photo-facsimile, for the first time). The present volume represents the continuation of a projected four-part series, by a mathematician associated with the University of Illinois. In six chapters it treats notebook entries pertaining to hypergeometric series, continued fractions, integrals and asymptotic expansions, infinite series, asymptotic expansions and modular forms. Chapters begin with an introductory essay, followed by notebook entries, proofs, corollaries and remarks, an overall objective being to detect and expose the pattern of Ramanujan's argument (at this point still frequently elusive). (NW) Annotation c. Book News, Inc., Portland, OR (booknews.com)