A Proof of Askey’s Conjectured <i>q</i>-Analogue of Selberg’s Integral and a Conjecture of Morris

Abstract

Aomoto has recently given an extension of Selberg’s integral. We extend his proof to the q-case and establish a conjecture of Askey. Our result is equivalent to a constant term identity for the root system $A_n $. This extends a conjecture of Morris.