SOME VALUES FOR THE ROGERS-RAMANUJAN CONTINUED-FRACTION

In his first and lost notebooks, Ramanujan recorded several values for the Rogers-Ramanujan continued fraction. Some of these results have b een proved by K. G. Ramanathan, using mostly ideas with which Ramanuja n was unfamiliar. In this paper, eight of Ramanujan's values are estab lished; four are proved for the first time, while the remaining four h ad been previously proved by Ramanathan by entirely different methods. Our proofs employ some of Ramanujan's beautiful eta-function identiti es, which have not been heretofore used for evaluating continued fract ions.