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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2012 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2012
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148446 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862540805759041536 |
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| author | Stokman, J.V. |
| author_facet | Stokman, J.V. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-11-24T16:26:16Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-148446 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-24T16:26:16Z |
| publishDate | 2012 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Stokman, J.V. 2019-02-18T12:38:03Z 2019-02-18T12:38:03Z 2012 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 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)). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Some Remarks on Very-Well-Poised ₈∅₇ Series Article published earlier |
| spellingShingle | Some Remarks on Very-Well-Poised ₈∅₇ Series Stokman, J.V. |
| title | 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_short | Some Remarks on Very-Well-Poised ₈∅₇ Series |
| title_sort | some remarks on very-well-poised ₈∅₇ series |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148446 |
| work_keys_str_mv | AT stokmanjv someremarksonverywellpoised87series |