A generalized hypergeometric function satisfying four analytic difference equations of Askey-Wilson type

The hypergeometric function F-2(1) can be written in terms of a contour int egral involving gamma functions. We generalize this (Barnes) representation by using a certain generalized gamma function as a building block. In this way we obtain a new F-2(1)-generalization R(a(+), a(-), c(0), c(1), c(2), c(3); upsilon, <(upsilon)over cap>) with various symmetry features. We dete rmine the analyticity properties of the R-function in all of its eight argu ments, and show that it is a joint eigenfunction of four distinct Askey-Wil son type difference operators, two acting on upsilon and two on <(upsilon)o ver cap>. The Askey-Wilson polynomials can be obtained by a suitable discre tization of upsilon or <(upsilon)over cap>.