LOCATION OF ZEROS AND ASYMPTOTICS OF POLYNOMIALS SATISFYING 3-TERM RECURRENCE RELATIONS WITH COMPLEX COEFFICIENTS

Under very general conditions on the complex coefficients of a three-term recurrence relation, it is proved that ''almost all'' zeros of the polynomials generated by these relations ''accumulate'' on a certain segment in the complex plane. From this result follow the convergence of diagonal Pade approximants and a generalization of Van Vleck's theorem on the convergence of S-fractions. Another interesting application is an extension of the so-called Nevai-Blumenthal class of polynomials M(a, 2b) to the case when a, b is an element of C.