Multivariable Askey-Wilson function and bispectrality (Q539125)

The paper presents the construction of a meromorphic extension of the multivariable Askey-Wilson polynomials introduced by \textit{G. Gasper} and \textit{M. Rahman} [in: M. E. H. Ismail (ed.) et al., Theory and applications of special functions. A volume dedicated to Mizan Rahman. New York, NY: Springer. Developments in Mathematics 13, 209--219 (2005; Zbl 1219.33027)] and proves its bispectral properties. First the analytic extension is used to obtain the one dimensional Askey-Wilson function. Then there is presented the construction in arbitrary dimensions. Finally there are explicitly written the bispectral equations for the Askey-Wilson function.