A Proof of some identities of Ramanujan using modular forms

Source abstract

In 1974 B. J. Birch [ 1 ] published a description of some manuscripts of Ramanujan which contained, among other things, a list of forty identities involving the Rogers-Ramanujan functions At that time nine of these had been proven, and since then twenty-two more of them have been proven, fifteen of them by David Bressoud in his thesis [ 2 ]. Bressoud gives a synopsis of the extant proofs, where he attributes proofs to H. B. C. Darling [ 3 ], L. J. Rogers [ 4 ], L. J. Mordell [ 5 ], and G. N. Watson [ 6 ].