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arXiv · 1812.04467

$q$-Difference Equations and Identities of the Rogers--Ramanujan--Bailey Type

Andrew V. Sills
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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 $q$-difference equations associated with the SMPBP, and use these $q$-difference equations to deduce the complete families of Rogers-Ramanujan type identities.

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Andrew V. Sills. 2018-12-11. $q$-Difference Equations and Identities of the Rogers--Ramanujan--Bailey Type. https://doi.org/10.1080/10236190412331314169

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