A Q-BETA INTEGRAL ON THE UNIT-CIRCLE AND SOME BIORTHOGONAL RATIONAL FUNCTIONS

In this paper we first consider a pair of polynomial sets which are bi orthogonal on the unit circle with respect to a complex weight functio n. We then show how the biorthogonality of this pair of polynomial set s implies a q-beta integral which in turn leads to a pair of biorthogo nal rational functions. Finally we show that the asymptotics for these pairs of rational functions exhibit qualitative properties reminiscen t of the Szego theory for orthogonal polynomials.