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.
- Three-terms recurrence relation
- Interval of orthogonality
- Birth-death process
- Decay parameter
van Doorn, E. A., van Foreest, N. D., & Zeifman, A. I. (2009). Representations for the extreme zeros of orthogonal polynomials. Journal of computational and applied mathematics, 233(3), 847-851. https://doi.org/10.1016/j.cam.2009.02.051