On Dyson’s q-Series Identities

Before receiving his B.A. from Cambridge University, Freeman Dyson served as referee for a pair of seminal papers by W. N. Bailey on the derivation of identities of Rogers-Ramanujan type. Dyson wound up contributing a number of Rogers-Ramanujan type identities of his own to Bailey\u27s papers, including a set of four identities related to modulus 27 in the same way that the two Rogers-Ramanujan identities are related to the modulus 5. After providing some mathematical and historical background, I will present a set of identities related to the modulus 108, which I discovered experimentally by playing around with variants on Dyson\u27s mod 27 identities