2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/101041Simultaneous eigenfunctions of two Askey-Wilson second order difference operators are constructed as formal matrix coefficients of the principal series representation of the modular double of the quantized universal enveloping algebra U_q(sl(2,C)). These eigenfunctions are shown to be equal to Ruijsenaars' hypergeometric function under a proper parameter correspondence.Replaced to synchronize formula numbers with the published version. 25 pagesQuantum AlgebraRepresentation Theory33D80text