Sequences of binomial type with persistent roots

    Research output: Contribution to journalArticleAcademicpeer-review

    10 Citations (Scopus)

    Abstract

    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
    Volume199
    Issue number1
    DOIs
    Publication statusPublished - 1996

    Fingerprint Dive into the research topics of 'Sequences of binomial type with persistent roots'. Together they form a unique fingerprint.

    Cite this