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.
|Place of Publication||Enschede|
|Publisher||University of Twente, Department of Applied Mathematics|
|Number of pages||9|
|Publication status||Published - Aug 2007|
|Name||Memorandum / Department of Applied Mathematics|
|Publisher||University of Twente, Department of Computer Science|
- Birth-death process
- Interval of orthogonality
- Decay parameter
- Three-terms recurrence relation
van Doorn, E. A., van Foreest, N. D., & Zeifman, A. I. (2007). Representations for the extreme zeros of orthogonal polynomials. (Memorandum / Department of Applied Mathematics; No. LNCS4549/1850). Enschede: University of Twente, Department of Applied Mathematics.