$q$-Difference Equations and Identities of the Rogers--Ramanujan--Bailey Type
Classical Analysis and ODEs
2018-12-12 v1
Abstract
In a recent paper, I defined the "standard multiparameter Bailey pair" (SMPBP) and demonstrated that all of the classical Bailey pairs considered by W.N. Bailey in his famous paper (\textit{Proc. London Math. Soc. (2)}, \textbf{50} (1948), 1--10) arose as special cases of the SMPBP. Additionally, I was able to find a number of new Rogers-Ramanujan type identities. From a given Bailey pair, normally only one or two Rogers-Ramanujan type identities follow immediately. In this present work, I present the set of -difference equations associated with the SMPBP, and use these -difference equations to deduce the complete families of Rogers-Ramanujan type identities.
Cite
@article{arxiv.1812.04467,
title = {$q$-Difference Equations and Identities of the Rogers--Ramanujan--Bailey Type},
author = {Andrew V. Sills},
journal= {arXiv preprint arXiv:1812.04467},
year = {2018}
}
Comments
14 pages