Some more identities of the Rogers-Ramanujan type

Abstract

In this we paper we prove several new identities of the Rogers-RamanujanSlater type. These identities were found as the result of computer searches. The proofs involve a variety of techniques, including series-series identities, Bailey pairs, a theorem of Watson on basic hypergeometric series, generating functions and miscellaneous methods.

Higher order SPT functions for overpartitions, overpartitions with smallest part even, and partitions with smallest part even and without repeated odd parts

“…This Bailey pair is also given as Lemma 2.3 in [9]. Applying Theorem 2.2 to this Bailey pair gives the identity.…”

Ramanujan–Slater type identities related to the moduli 18 and 24

“…We included identity (1.5) in our joint paper with D. Bowman [13,Eq. (3.35)], as it also occurs as part of a different family of four identities.…”

Rogers-Ramanujan-Slater Type Identities

“…This identity is also equivalent to a result found in Andrews [3], where Andrews attributes it to Cauchy. Proofs of (6.1.6), (6.1.7), (6.1.8) and (6.1.9) can be found in [24], and alternative proofs can be found in [16]. Identities (6.1.7), (6.1.8) and (6.1.9) were also stated by Ramanujan in the lost notebook (see Entries 1.5.1 and 1.5.2 in [10]).…”

“…We now exhibit two identities of Rogers-Ramanujan type which are related via (6.3.1). The first appears in [16]:…”