FORTY IDENTITIES 13
3.26, and 3.27 are provided. Rogers's proofs of Entries 3.9-3.11 are given. Entries
3.28 (second part), 3.29, 3.30, 3.31, and 3.35 are those we are unable to prove. (We
remark that in the sequel we prove that Entries 3.31 and 3.32 are equivalent, and so
it suffices to prove just one of these identities.) In Section 6, we employ asymptotic
formulas for G(q) and H(q) to demonstrate the probable truth of these five entries.