Weighted sums of orthogonal polynomials with positive zeros

Masaaki Kijima, Erik A. van Doorn

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    Abstract

    We study the two sequences of polynomials which arise as denominators of the approximants of even and odd order, respectively, of a Stieltjes fraction, and which may be defined alternatively as a sequence of orthogonal polynomials with positive zeros and the associated sequence of kernel polynomials. Motivated by problems in the setting of birth-death processes, where these sequences play a major role, we focus on the asymptotic behaviour of the sequences and establish convergence of certain weighted sums of the polynomials at hand.
    Original languageEnglish
    Pages (from-to)195-206
    JournalJournal of computational and applied mathematics
    Volume65
    Issue number1-3
    DOIs
    Publication statusPublished - 1995

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