the last section of this paper, Section 7, we state several new identities involving
the Rogers-Ramanujan functions; proofs may be found in .
In conclusion, we think that modular equations were central in many of Ra-
manujan's proofs, and we also think that Ramanujan may have discovered some
of his identities by examining the asymptotics of theta functions and the Rogers-
Ramanujan functions. Although some of our proofs may be those found by Ra-
manujan, it is clear that all of us, including the aforementioned authors and the
present authors, have not unveiled some of Ramanujan's principal ideas, which
remain hidden by an impenetrable fog.