Identities of the Rogers--Ramanujan--Slater Type
Number Theory
2018-12-14 v1
Abstract
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 -difference equations. As a bonus, new Rogers-Ramanujan type identities are found along with natural combinatorial interpretations for many of these identities.
Keywords
Cite
@article{arxiv.1812.05563,
title = {Identities of the Rogers--Ramanujan--Slater Type},
author = {Andrew V. Sills},
journal= {arXiv preprint arXiv:1812.05563},
year = {2018}
}
Comments
28 pages