Some Remarks on Very-Well-Poised ₈∅₇ Series

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...

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Bibliographic Details
Date:2012
Main Author: Stokman, J.V.
Format: Article
Language:English
Published: Інститут математики НАН України 2012
Series:Symmetry, Integrability and Geometry: Methods and Applications
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/148446
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this: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.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Summary: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.