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Title: Zeon algebra and combinatorial identities.
Authors: Francisco Neto, Antônio
Anjos, Petrus Henrique Ribeiro dos
Keywords: Cauchy integral
Grassmann–Berezin integration
Faà di Bruno formula
Spivey identity
Special polynomials
Issue Date: 2014
Citation: FRANCISCO NETO, A.; ANJOS, P. H. R. dos. Zeon algebra and combinatorial identities. SIAM Review, v. 56, p. 353-370, 2014. Disponível em: <>. Acesso em: 20 jul. 2017.
Abstract: We show that the ordinary derivative of a real analytic function of one variable can be realized as a Grassmann–Berezin-type integration over the Zeon algebra, the Z-integral. As a by-product of this representation, we give new proofs of the Fa`a di Bruno formula and Spivey’s identity [M. Z. Spivey, J. Integer Seq., 11 (2008), 08.2.5], and we recover the representation of the Stirling numbers of the second kind and the Bell numbers of Staples and Schott [European J. Combin., 29 (2008), pp. 1133–1138]. The approach described here is suitable to accommodate new Z-integral representations including Stirling numbers of the first kind, central Delannoy, Euler, Fibonacci, and Genocchi numbers, and the special polynomials of Bell, generalized Bell, Hermite, and Laguerre.
ISSN: 1095-7200
Appears in Collections:DEPRO - Artigos publicados em periódicos

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