General Mathematics, Vol. 8,nr. 1-2, pp. 39-44, 2000

Emil C. Popa - Note on a Delta operator

Abstract: In the end of the paper "Finite operator calculus" by Gian-Carlo
Rota, D. Kahaner, A. Odlyzko [3] are raised a set to find formulas
for pn(Q) where (pn) is a Sheffer sequence relative to
the delta-operator Q In this paper we consider the Abel
polynomials

                               an(x) = x(x+ nb)n-1 ,    n = 1, 2, ...

and we study some umbral properties for delta operator

    (1)           an(Q) = Q(Q + nbI )n-1 ,   b 0  ,   n fixed

defined on the algebra of polynomials, where Q is a delta
operator.

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