Some Values For The Rogers-Ramanujan Continued Fraction

this paper we establish four values for R(q) stated on page 311 in Ramanujan's first notebook, and four values for S(q) found in the lost notebook [12, pp. 204, 210]. All of our proofs use only theorems and methods known to Ramanujan. In particular, each of our proofs employs an eta--function identity from the unorganized portions of the second notebook [10], [3, Chap. 25]. Ramanathan [6] gave different proofs of Theorems 1, 5, and 6 below; proofs of Theorems 2, 3, and 4 have not been heretofore given. In order to state the first four theorems, we set (0.4) 2c = 1