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Mathematics > Classical Analysis and ODEs

arXiv:1812.07542 (math)
[Submitted on 18 Dec 2018]

Title:Ramanujan--Slater type identities related to the moduli $18$ and $24$

Authors:James Mc Laughlin, Andrew V. Sills
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Abstract:We present several new families of Rogers-Ramanujan type identities related to the moduli 18 and 24. A few of the identities were found by either Ramanujan, Slater, or Dyson, but most are believed to be new. For one of these families, we discuss possible connections with Lie algebras. We also present two families of related false theta function identities.
Comments: 20 pages. After publication, it was noticed that (1.3) and (1.4) are actually due to J. H. Loxton, Acta Arith. 43 (1984) 155--166. See pp. 158--9, Eqs. (P12) and (P12 bis)
Subjects: Classical Analysis and ODEs (math.CA)
MSC classes: 11B65, 33D15, 05A10, 17B57, 17B10
Cite as: arXiv:1812.07542 [math.CA]
  (or arXiv:1812.07542v1 [math.CA] for this version)
  https://doi.org/10.48550/arXiv.1812.07542
Journal reference: Journal of Mathematical Analysis and Applications 344 (2008) 765--777
Related DOI: https://doi.org/10.1016/j.jmaa.2008.03.033

Submission history

From: Andrew Sills [view email]
[v1] Tue, 18 Dec 2018 18:19:44 UTC (13 KB)
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