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Symmetry, Integrability and Geometry: Methods and Applications, 2012, Volume 8, 039, 17 pp.
DOI: https://doi.org/10.3842/SIGMA.2012.039
(Mi sigma716)
 

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
Full-text PDF (450 kB) Citations (4)
References:
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
Bibliographic databases:
Document Type: Article
MSC: 33D15; 33D45
Language: English
Citation: Jasper V. Stokman, “Some remarks on very-well-poised ${}_8\phi_7$ series”, SIGMA, 8 (2012), 039, 17 pp.
Citation in format AMSBIB
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\by Jasper V. Stokman
\paper Some remarks on very-well-poised ${}_8\phi_7$ series
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\vol 8
\papernumber 039
\totalpages 17
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  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Symmetry, Integrability and Geometry: Methods and Applications
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