Howard.Cohl

Affiliation: National Institute of Standards and Technology

Title Of Talk: Connection formulas for Askey-Wilson polynomials and related expansions

URLS:
https://arxiv.org/abs/2602.15824

Abstract: We derive and study expansions of and over the Askey--Wilson polynomials. We study these expansions and examine some limits to the continuous dual $q$-Hahn, Al-Salam--Chihara, continuous big $q$-Hermite and continuous $q$-Hermite polynomials and their $q^{-1}$-analogues. The Poisson kernel for the infinite discrete orthogonality relation for the $q^{-1}$-Al-Salam--Chihara polynomials is derived which in a special case reduces to the Gupta--Masson biorthogonal rational ${}_4\phi_3$-functions. This Poisson kernel implies new infinite series connection relations for the Askey--Wilson polynomials involving these rational ${}_4\phi_3$-functions. We also consider various interesting limits.

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