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This article is cited in 4 scientific papers (total in 4 papers)
Some remarks on very-well-poised ${}_8\phi_7$ series
Jasper V. Stokman Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
Abstract:
Nonpolynomial basic hypergeometric eigenfunctions of the Askey–Wilson second order difference operator
are known to be expressible as very-well-poised ${}_8\phi_7$ 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 ${}_8\phi_7$ series. We also provide a link to
Chalykh's theory on (rank one, BC type) Baker–Akhiezer functions.
Keywords:
very-well-poised basic hypergeometric series, Askey–Wilson functions, quadratic transformation formulas, theta functions.
Received: April 5, 2012; in final form June 18, 2012; Published online June 27, 2012
Citation:
Jasper V. Stokman, “Some remarks on very-well-poised ${}_8\phi_7$ series”, SIGMA, 8 (2012), 039, 17 pp.
Linking options:
https://www.mathnet.ru/eng/sigma716 https://www.mathnet.ru/eng/sigma/v8/p39
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Abstract page: | 161 | Full-text PDF : | 41 | References: | 55 |
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