Some Remarks on Very-Well-Poised ₈∅₇ Series
Nonpolynomial basic hypergeometric eigenfunctions of the Askey-Wilson second order difference operator are known to be expressible as very-well-poised ₈∅₇ series. In this paper we use this fact to derive various basic hypergeometric and theta function identities. We relate most of them to identities...
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Інститут математики НАН України
2012
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| Schriftenreihe: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/148446 |
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| Zitieren: | Some Remarks on Very-Well-Poised ₈∅₇ Series / J.V. Stokman // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 26 назв. — англ. |
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nasplib_isofts_kiev_ua-123456789-1484462025-02-23T19:35:39Z Some Remarks on Very-Well-Poised ₈∅₇ Series Stokman, J.V. Nonpolynomial basic hypergeometric eigenfunctions of the Askey-Wilson second order difference operator are known to be expressible as very-well-poised ₈∅₇ series. In this paper we use this fact to derive various basic hypergeometric and theta function identities. We relate most of them to identities from the existing literature on basic hypergeometric series. This leads for example to a new derivation of a known quadratic transformation formula for very-well-poised ₈∅₇ series. We also provide a link to Chalykh's theory on (rank one, BC type) Baker-Akhiezer functions. I thank Tom Koornwinder for drawing my attention to the quadratic transformation formula for continuous q-Jacobi polynomials. I thank Mizan Rahman for pointing out to me how the quadratic transformations (5.2) and (5.3) for very-well-poised ₈∅₇ series are related to the known quadratic transformation formula [6, (3.5.10)] (see Reamark 5.3(i)). 2012 Article Some Remarks on Very-Well-Poised ₈∅₇ Series / J.V. Stokman // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 26 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 33D15; 33D45 DOI: http://dx.doi.org/10.3842/SIGMA.2012.039 https://nasplib.isofts.kiev.ua/handle/123456789/148446 en Symmetry, Integrability and Geometry: Methods and Applications application/pdf Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
Nonpolynomial basic hypergeometric eigenfunctions of the Askey-Wilson second order difference operator are known to be expressible as very-well-poised ₈∅₇ series. In this paper we use this fact to derive various basic hypergeometric and theta function identities. We relate most of them to identities from the existing literature on basic hypergeometric series. This leads for example to a new derivation of a known quadratic transformation formula for very-well-poised ₈∅₇ series. We also provide a link to Chalykh's theory on (rank one, BC type) Baker-Akhiezer functions. |
| format |
Article |
| author |
Stokman, J.V. |
| spellingShingle |
Stokman, J.V. Some Remarks on Very-Well-Poised ₈∅₇ Series Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Stokman, J.V. |
| author_sort |
Stokman, J.V. |
| title |
Some Remarks on Very-Well-Poised ₈∅₇ Series |
| title_short |
Some Remarks on Very-Well-Poised ₈∅₇ Series |
| title_full |
Some Remarks on Very-Well-Poised ₈∅₇ Series |
| title_fullStr |
Some Remarks on Very-Well-Poised ₈∅₇ Series |
| title_full_unstemmed |
Some Remarks on Very-Well-Poised ₈∅₇ Series |
| title_sort |
some remarks on very-well-poised ₈∅₇ series |
| publisher |
Інститут математики НАН України |
| publishDate |
2012 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/148446 |
| citation_txt |
Some Remarks on Very-Well-Poised ₈∅₇ Series / J.V. Stokman // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 26 назв. — англ. |
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Symmetry, Integrability and Geometry: Methods and Applications |
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AT stokmanjv someremarksonverywellpoised87series |
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2025-11-24T16:26:16Z |
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2025-11-24T16:26:16Z |
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