Polynomials generated by a three-term recurrence relation with asymptotically periodic complex coefficients

In a previous paper of the authors the location of zeros of polynomials generated by a three-term recurrence relation with complex coefficients satisfying rather general conditions was studied. In particular, it was proved there that when these coefficients have limits in the complex plane, there are asymptotics of the ratio as in the Nevai–Blumenthal class of orthogonal polynomials. In this paper the case of asymptotically periodic recurrence coefficients is studied and the results known for the case of real recurrence coefficients are extended. Applications to rational approximation and continued fractions are presented.