Elliptic Well-Poised Bailey Transforms and Lemmas on Root Systems
We 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 Roseng...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2018 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2018
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/209439 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Elliptic 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862718008374329344 |
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| author | Bhatnagar, G. Schlosser, M.J. |
| author_facet | Bhatnagar, G. Schlosser, M.J. |
| citation_txt | Elliptic 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We 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.
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| first_indexed | 2025-12-07T18:12:50Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-209439 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T18:12:50Z |
| publishDate | 2018 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Bhatnagar, G. Schlosser, M.J. 2025-11-21T18:52:47Z 2018 Elliptic 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. 1815-0659 2010 Mathematics Subject Classification: 33D67 arXiv: 1704.00020 https://nasplib.isofts.kiev.ua/handle/123456789/209439 https://doi.org/10.3842/SIGMA.2018.025 We 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. The 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Elliptic Well-Poised Bailey Transforms and Lemmas on Root Systems Article published earlier |
| spellingShingle | Elliptic Well-Poised Bailey Transforms and Lemmas on Root Systems Bhatnagar, G. Schlosser, M.J. |
| title | Elliptic Well-Poised Bailey Transforms and Lemmas on Root Systems |
| title_full | Elliptic Well-Poised Bailey Transforms and Lemmas on Root Systems |
| title_fullStr | Elliptic Well-Poised Bailey Transforms and Lemmas on Root Systems |
| title_full_unstemmed | Elliptic Well-Poised Bailey Transforms and Lemmas on Root Systems |
| title_short | Elliptic Well-Poised Bailey Transforms and Lemmas on Root Systems |
| title_sort | elliptic well-poised bailey transforms and lemmas on root systems |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/209439 |
| work_keys_str_mv | AT bhatnagarg ellipticwellpoisedbaileytransformsandlemmasonrootsystems AT schlossermj ellipticwellpoisedbaileytransformsandlemmasonrootsystems |