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Some Remarks on Very-Well-Poised ₈∅₇ Series
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2012, том 8
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| dc.contributor.author | Stokman, J.V. | |
| dc.date.accessioned | 2019-02-18T12:38:03Z | |
| dc.date.available | 2019-02-18T12:38:03Z | |
| dc.date.issued | 2012 | |
| dc.identifier.citation | 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. | uk_UA |
| dc.identifier.issn | 1815-0659 | |
| dc.identifier.other | 2010 Mathematics Subject Classification: 33D15; 33D45 | |
| dc.identifier.other | DOI: http://dx.doi.org/10.3842/SIGMA.2012.039 | |
| dc.identifier.uri | http://dspace.nbuv.gov.ua/handle/123456789/148446 | |
| dc.description.abstract | 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. | uk_UA |
| dc.description.sponsorship | 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)). | uk_UA |
| dc.language.iso | en | uk_UA |
| dc.publisher | Інститут математики НАН України | uk_UA |
| dc.relation.ispartof | Symmetry, Integrability and Geometry: Methods and Applications | |
| dc.title | Some Remarks on Very-Well-Poised ₈∅₇ Series | uk_UA |
| dc.type | Article | uk_UA |
| dc.status | published earlier | uk_UA |
