On the orthogonality measure of the q-pollaczek polynomials (1987)
The q-Pollaczek polynomials F ,(x) depend on four parameters u,v, ∆, q and are given by the recurrence relation (1-qn+1)Fn+1(x) = 2[(1-u∆qn)x+vqn]Fn(x)- (1-∆2qn-1)Fn-1 (x), n ≥ 1, and the initial cond i t i ons Fo(x)=1 F1(x) = 2 [(1-u∆)x+v]/1-q. The measure with respect to which the Fn(x)'s are orthogonal is determined when the parameters are subject to the constraints O and lt;u and lt;∆ and lt; 1, ∆(1-u) and gt;±v, 0 and lt; q and lt; 1. This measure turns out to be absolutelv continuous with respect to Lebesgue's measure.