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arxiv: 1812.05563 · v1 · pith:XSAXX53Vnew · submitted 2018-12-13 · 🧮 math.NT

Identities of the Rogers--Ramanujan--Slater Type

classification 🧮 math.NT
keywords identitiesrogers-ramanujantypeslateralongassociatedbaileybonus
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It is shown that (two-variable generalizations of) more than half of Slater's list of 130 Rogers-Ramanujan identities (L. J. Slater, Further identities of the Rogers-Ramanujan type, \emph{Proc. London Math Soc. (2)} \textbf{54} (1952), 147--167) can be easily derived using just three multiparameter Bailey pairs and their associated $q$-difference equations. As a bonus, new Rogers-Ramanujan type identities are found along with natural combinatorial interpretations for many of these identities.

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