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Basic hypergeometric transformations from symmetric and q-inverse sub-families of the Askey-Wilson polynomials in the q-Askey scheme


Basic hypergeometric transformations from symmetric and q-inverse sub-families of the Askey-Wilson polynomials in the q-Askey scheme

Date: 2020..01..31
Event: Seminario IEMath-GR
Venue: Universidad de Granada

Abstract

By starting with known basic hypergeometric representations of the Askey-Wilson polynomials, we derive basic hypergeometric representations for the q-inverse Askey-Wilson polynomials and a set of sub-families for both of these these polynomials.

These sub-families are obtained by repeatedly setting one of the free parameters (not q) equal to zero until no parameters are left. These subfamilies, are the continuous dual q-Hahn, Al-Salam-Chihara, continuous big q-Hermite, the continuous q-Hermite polynomials, and their q-inverse analogues.

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