Representations for the extreme zeros of orthogonal polynomials

Erik A. van Doorn, N.D. van Foreest, Alexander I. Zeifman

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    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.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Number of pages9
    Publication statusPublished - Aug 2007

    Publication series

    NameMemorandum / Department of Applied Mathematics
    PublisherUniversity of Twente, Department of Computer Science
    No.LNCS4549/1850
    ISSN (Print)1874-4850
    ISSN (Electronic)1874-4850

    Keywords

    • Birth-death process
    • IR-64326
    • MSC-60J80
    • MSC-42C05
    • EWI-10994
    • Interval of orthogonality
    • Decay parameter
    • METIS-241876
    • Three-terms recurrence relation

    Cite this

    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.