Resumen de Ruijsenaars¿ hypergeometric function and the modular double of

Fokko J. van de Bult

• Simultaneous 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 . These eigenfunctions are shown to be equal to Ruijsenaars¿ hypergeometric function under a proper parameter correspondence.