Some new results for chain-sequence polynomials

Erik A. van Doorn

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    Abstract

    We study the class of (generalized) orthogonal polynomial sequences {Pn(x)}n=0∞ satisfying a recurrence relation of the type Pn(x) = (x − cn)Pn−1(x) − λnPn−2(x), n> 1, where λn ≠ 0 and the sequence {λn+1/(cncn+1)}n=1∞ constitutes a chain sequence. We obtain a new characterization of in terms of the moment sequence associated with an orthogonal polynomial sequence, and contribute to the solution of the problem of determining a (signed) orthogonalizing measure for a member of C.
    Original languageEnglish
    Pages (from-to)309-317
    Number of pages9
    JournalJournal of computational and applied mathematics
    Volume57
    Issue number1-2
    DOIs
    Publication statusPublished - 1995

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