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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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Some Remarks on Very-Well-Poised ₈∅₇ Series
Інший ID:
2010 Mathematics Subject Classification: 33D15; 33D45
DOI: http://dx.doi.org/10.3842/SIGMA.2012.039
DOI: http://dx.doi.org/10.3842/SIGMA.2012.039
Посилання:
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.
Підтримка:
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)).
Дата:
2012
Переглядів:
492
Завантажень:
246
Анотація:
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.
