Contents: Introduction - Hypergeometric Series, I - Hypergeometric Series, II - Continued Fractions - Integrals and Asymptotic Expansions - Infinite Series - Asymptotic Expansions and Modular Forms - References - Index.
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, many 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 second of four 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. This volume examines chapters 10-15 in Ramanujan's second notebook. If a result is known, then references are provided in the literature where proofs may be found; if a result is not known, then attempts are made to prove it. Not only are the results of interest, but, for the most part, Ramanujan's methods remain a mystery. Much work still needs to be done.
Hypergeometric series, I; hypergeometric series, II; continued fractions; integrals and asymptotic expansions; infinite series; asymptotic expansions and modular forms.