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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| Дата: | 2012 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2012
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/148446 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1484462019-02-19T01:23:16Z 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. 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 http://dspace.nbuv.gov.ua/handle/123456789/148446 en Symmetry, Integrability and Geometry: Methods and Applications 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 |
http://dspace.nbuv.gov.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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT stokmanjv someremarksonverywellpoised87series |
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2023-05-20T17:30:42Z |
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2023-05-20T17:30:42Z |
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1796153458357698560 |