Exceptional zeros of polynomials satisfying a three-term recurrence

Let P-m(z) be a sequence of polynomials satisfying the recurrence relation P-m(z) + B(z)Pm-1 (z) A(z)Pm-2 (z) = 0. Tran showed that with a suitable initial condition, the zeros of P-m(z) lie on a fixed explicit curve C on the complex plane. We study a more general initial condition in which we can count the finite number of zeros lying off C. (C) 2017 Elsevier B.V. All rights reserved.