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SIGMA 8 (2012), 039, 17 pages arXiv:1204.0254
https://doi.org/10.3842/SIGMA.2012.039
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
Received April 05, 2012, in final form June 18, 2012; Published online June 27, 2012
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.
Key words:
very-well-poised basic hypergeometric series; Askey-Wilson functions; quadratic transformation formulas; theta functions.
pdf (450 kb)
tex (23 kb)
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