Sequences of binomial type with persistent roots

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    11 Citations (Scopus)


    We find all sequences of polynomials (pn)n¿0with persistent roots (i.e.,pn(x)=cn(x-r1)(x-r2)···(x-rn)) that are of binomial type in Viskov's generalization of Rota's umbral calculus to generalized Appell polynomials. We show that such sequences only exist in the classical umbral calculus, the divided difference umbral calculus, and the new "hyperbolic" umbral calculus generated by[formula]. In each of these three umbral calculi, we also find all Sheffer sequences with persistent roots.
    Original languageEnglish
    Pages (from-to)39-58
    Number of pages20
    JournalJournal of Mathematical Analysis and Applications
    Issue number1
    Publication statusPublished - 1996


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