A Characterization of Polynomials

Kurt Munk Andersen

    Research output: Contribution to journalJournal articleResearchpeer-review

    Abstract

    Given the problem:which functions f(x) are characterized by a relation of the form:f[x1,x2,...,xn]=h(x1+x2+...+xn), where n>1 and h(x) is a given function? Here f[x1,x2,...,xn] denotes the divided difference on n points x1,x2,...,xn of the function f(x).The answer is: f(x) is a polynomial of degree at most n. This can be proved in various ways. In this article it is proved elementary.
    Original languageEnglish
    JournalMathematics Magazine
    Volume69
    Issue number2
    Pages (from-to)137-142
    ISSN0025-570X
    Publication statusPublished - 1996

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