Representations for the extreme zeros of orthogonal polynomials

Abstract: 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. [Copyright &y& Elsevier]