A selected survey of umbral calculus

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    Abstract

    We survey the mathematical literature on umbral calculus (otherwise known as the calculus of finite differences) from its roots in the 19th century (and earlier) as a set of "magic rules" for lowering and raising indices, through its rebirth in the 1970’s as Rota’s school set it on a firm logical foundation using operator methods, to the current state of the art with numerous generalizations and applications. The survey itself is complemented by a fairly complete bibliography (over 500 references) which we expect to update regularly.
    Original languageEnglish
    Article numberDS3
    Number of pages34
    JournalThe Electronic Journal of Combinatorics
    Volume1
    Publication statusPublished - 1995

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