Finite Rogers--Ramanujan type identities
Abstract
Polynomial generalizations of all 130 of the identities in Slater's list of identities of the Rogers-Ramanujan type are presented. Furthermore, duality relationships among many of the identities are derived. Some of the these polynomial identities were previously known but many are new. The author has implemented much of the finitization process in a Maple package which is available for free download from the author's website.
Keywords
Cite
@article{arxiv.1901.02435,
title = {Finite Rogers--Ramanujan type identities},
author = {Andrew V. Sills},
journal= {arXiv preprint arXiv:1901.02435},
year = {2019}
}
Comments
122 pages. The research contained herein comprises a substantial portion of the author's doctoral dissertation, submitted in partial fulfillment of the requirements for the Ph.D. degree at the University of Kentucky. The doctoral dissertation was completed under the supervision of George E. Andrews, Evan Pugh Professor of Mathematics at the Pennsylvania State University