Representations for the extreme zeros of orthogonal polynomials

We establish some representations for the smallest and largest zeros of orthogonal polynomials in terms of the parameters in the three-terms recurrence relation. As a corollary we obtain representations for the endpoints of the true interval of orthogonality. Implications of these results for the decay parameter of a birth-death process (with killing) are displayed. (C) 2009 Elsevier B.V. All rights reserved.