Year: 2026
Type: preprint
Abstract: We present a determinantal evaluation formula for the very-well-poised ${}_8Φ_7$ basic hypergeometric Askey-Wilson function in terms of elementary functions. The formula in question is valid for discrete values of the four permutation-symmetric Askey-Wilson parameters; specifically, these consist of all quadruples of parameter values that are given, up to a sign, by powers $q^k$ with $k$ a positive integer or half-integer, in such a way that each of the four types (positive/negative sign, integer/half-integer power) occurs exactly once. The proof hinges on a product formula for an associated Cauchy-type determinant, which is of independent interest and is established here by elementary means using Krattenthaler's `identification of factors' method for determinant evaluations.
Source: arXiv (Cornell University)
Authors: van Diejen, J. F., Kirillov, A. N.
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214992521