Elementary proofs of some identities of Ramanujan for the Rogers-Ramanujan functions (Q662085)

Ramanujan stated forty identities for Rogers-Ramanujan functions \(G(q)\) and \(H(q)\), but he did not give proofs for these identities. Except for one identity all the others were proved by Rogers, Watson, Bressoud and Biagioli. In this paper the author gives the proof for the solitary unproved identity in (1.5) of Entry 1.1. He also provides simple proofs for two proved identities given in Entry 1.2 and Entry 1.3. and also proves analogous identities. For proving these identities the author uses some of his results obtained in [J. Number Theory 129, No. 6, 1256--1271 (2009; Zbl 1219.11063)] after specializing the parameters.