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SIGMA, 2012, Volume 8, 039, 17 pages (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

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.

DOI: https://doi.org/10.3842/SIGMA.2012.039

Full text: PDF file (450 kB)
Full text: http://emis.mi.ras.ru/.../039
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Bibliographic databases:

ArXiv: 1204.0254
MSC: 33D15; 33D45
Received: April 5, 2012; in final form June 18, 2012; Published online June 27, 2012
Language:

Citation: Jasper V. Stokman, “Some remarks on very-well-poised $ _8\phi_7$ series”, SIGMA, 8 (2012), 039, 17 pp.

Citation in format AMSBIB
\Bibitem{Sto12}
\by Jasper V. Stokman
\paper Some remarks on very-well-poised ${}_8\phi_7$ series
\jour SIGMA
\yr 2012
\vol 8
\papernumber 039
\totalpages 17
\mathnet{http://mi.mathnet.ru/sigma716}
\crossref{https://doi.org/10.3842/SIGMA.2012.039}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2946861}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000305677000001}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84864532874}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Chalykh O., Etingof P., “Orthogonality Relations and Cherednik Identities for Multivariable Baker-Akhiezer Functions”, Adv. Math., 238 (2013), 246–289  crossref  mathscinet  zmath  isi  elib  scopus
    2. Stokman J.V., “Connection Coefficients for Basic Harish-Chandra Series”, Adv. Math., 250 (2014), 351–386  crossref  mathscinet  zmath  isi  elib  scopus
    3. Stokman J.V., “The C-Function Expansion of a Basic Hypergeometric Function Associated to Root Systems”, Ann. Math., 179:1 (2014), 253–299  crossref  mathscinet  zmath  isi  scopus
    4. Stokman J.V., “Connection Problems For Quantum Affine Kz Equations and Integrable Lattice Models”, Commun. Math. Phys., 338:3 (2015), 1363–1409  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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