The q-Pollaczek polynomials F ,(x) depend on four parameters u,v, ∆, q and are given by the recurrence relation (1- qn+1 )F n+1 (x) = 2[(1-u∆q n )x+vq n ]F n (x)- (1-∆ 2 q n-1 )F n-1 (x), n ≥ 1, and the initial cond i t i ons F o (x)=1 F 1 (x) = 2 [(1-u∆)x+v]/1-q. The measure with respect to which the F n (x)'s are orthogonal is determined when the parameters are subject to the constraints O ±v, 0 < q < 1. This measure turns out to be absolutelv continuous with respect to Lebesgue's measure.
