Abstract
We study the recurrence relations of rational functions that are orthonormal on the unit circle and have all their poles in a given sequence of points outside the unit disk. These relations enable us to find the recurrence relations and the ratio asymptotic behaviors for the orthonormal polynomials with respect to varying weights dμ n and dμ n+1 . At the end of this paper, we also consider the convergence theorem for multipoint Padé approximations of Markov type functions.
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