Elliptic Well-Poised Bailey Transforms and Lemmas on Root Systems

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dc.contributor.authorBhatnagar, G.
dc.contributor.authorSchlosser, M.J.
dc.date.accessioned2025-11-21T18:52:47Z
dc.date.issued2018
dc.description.abstractWe list An, Cn, and Dn extensions of the elliptic WP Bailey transform and lemma, given for n=1 by Andrews and Spiridonov. Our work requires multiple series extensions of Frenkel and Turaev's terminating, balanced, and very-well-poised ₁₀V₉ elliptic hypergeometric summation formula due to Rosengren and Rosengren and Schlosser. In our study, we discover two new An ₁₂V₁₁ transformation formulas that reduce to two new An extensions of Bailey's 10ϕ9 transformation formulas when the nome p is 0, and two multiple series extensions of Frenkel and Turaev's sum.
dc.description.sponsorshipThe first author thanks Hjalmar Rosengren and the organizers of OPSF-S6 for the series of lectures [32] on this subject. We thank Ole Warnaar for showing his notes [48] and much encouragement, Slava Spiridonov for some comments, and Zhizheng Zhang and Junli Huang for sending us their preprint [51]. We thank the anonymous referees for many insightful suggestions. We thank the Erwin Schrödinger Institute for its workshop on Elliptic hypergeometric functions in combinatorics, integrable systems, and physics held in Vienna in March 2017, where we benefited from discussions with other participants. Finally, the research of both authors was supported by a grant of the Austrian Science Fund (FWF): F 50-N15.
dc.identifier.citationElliptic Well-Poised Bailey Transforms and Lemmas on Root Systems / G. Bhatnagar, M.J. Schlosser // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 52 назв. — англ.
dc.identifier.doihttps://doi.org/10.3842/SIGMA.2018.025
dc.identifier.issn1815-0659
dc.identifier.other2010 Mathematics Subject Classification: 33D67
dc.identifier.otherarXiv: 1704.00020
dc.identifier.urihttps://nasplib.isofts.kiev.ua/handle/123456789/209439
dc.language.isoen
dc.publisherІнститут математики НАН України
dc.relation.ispartofSymmetry, Integrability and Geometry: Methods and Applications
dc.statuspublished earlier
dc.titleElliptic Well-Poised Bailey Transforms and Lemmas on Root Systems
dc.typeArticle

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Symmetry, Integrability and Geometry: Methods and Applications, 2018, том 14, випуск за цей рік